src/HOL/BNF_Examples/IsaFoR_Datatypes.thy
 changeset 57634 efc00b9b8680 parent 57586 5efff4075b63 child 58139 e4c69c0985f5
```     1.1 --- a/src/HOL/BNF_Examples/IsaFoR_Datatypes.thy	Thu Jul 24 00:24:00 2014 +0200
1.2 +++ b/src/HOL/BNF_Examples/IsaFoR_Datatypes.thy	Thu Jul 24 00:24:00 2014 +0200
1.3 @@ -1,37 +1,39 @@
1.4  (*  Title:      HOL/BNF_Examples/IsaFoR_Datatypes.thy
1.6 +    Author:     Rene Thiemann, UIBK
1.8
1.9 -Benchmark of datatypes defined in IsaFoR
1.10 +Benchmark consisting of datatypes defined in IsaFoR.
1.11  *)
1.12
1.13 +header {* Benchmark Consisting of Datatypes Defined in IsaFoR *}
1.14 +
1.15  theory IsaFoR_Datatypes
1.16 -imports
1.17 -  Real
1.18 +imports Real
1.19  begin
1.20
1.21  datatype_new ('f, 'l) lab =
1.22 -  Lab "('f, 'l) lab" 'l
1.23 -| FunLab "('f, 'l) lab" "('f, 'l) lab list"
1.24 -| UnLab 'f
1.25 -| Sharp "('f, 'l) lab"
1.26 +    Lab "('f, 'l) lab" 'l
1.27 +  | FunLab "('f, 'l) lab" "('f, 'l) lab list"
1.28 +  | UnLab 'f
1.29 +  | Sharp "('f, 'l) lab"
1.30
1.31  datatype_new 'f projL = Projection "(('f \<times> nat) \<times> nat) list"
1.32
1.33  datatype_new ('f, 'v) "term" = Var 'v | Fun 'f "('f, 'v) term list"
1.34  datatype_new ('f, 'v) ctxt =
1.35 -  Hole ("\<box>")
1.36 -| More 'f "('f, 'v) term list" "('f, 'v) ctxt" "('f, 'v) term list"
1.37 -
1.38 +    Hole ("\<box>")
1.39 +  | More 'f "('f, 'v) term list" "('f, 'v) ctxt" "('f, 'v) term list"
1.40
1.41  type_synonym ('f, 'v) rule = "('f, 'v) term \<times> ('f, 'v) term"
1.42  type_synonym ('f, 'v) trs  = "('f, 'v) rule set"
1.43
1.44 -type_synonym ('f, 'v) rules = "('f,'v) rule list"
1.45 +type_synonym ('f, 'v) rules = "('f, 'v) rule list"
1.46  type_synonym ('f, 'l, 'v) ruleLL  = "(('f, 'l) lab, 'v) rule"
1.47  type_synonym ('f, 'l, 'v) trsLL   = "(('f, 'l) lab, 'v) rules"
1.48  type_synonym ('f, 'l, 'v) termsLL = "(('f, 'l) lab, 'v) term list"
1.49 +
1.50  datatype_new pos = Empty ("\<epsilon>") | PCons "nat" "pos" (infixr "<#" 70)
1.51 +
1.52  type_synonym  ('f, 'v) prseq = "(pos \<times> ('f, 'v) rule \<times> bool \<times> ('f, 'v) term) list"
1.53  type_synonym  ('f, 'v) rseq = "(pos \<times> ('f, 'v) rule \<times> ('f, 'v) term) list"
1.54
1.55 @@ -49,43 +51,45 @@
1.56
1.57  datatype_new location = H | A | B | R
1.58
1.59 -type_synonym ('f,'v)forb_pattern = "('f,'v)ctxt \<times> ('f,'v)term \<times> location"
1.60 -type_synonym ('f,'v)forb_patterns = "('f,'v)forb_pattern set"
1.61 +type_synonym ('f, 'v) forb_pattern = "('f, 'v) ctxt \<times> ('f, 'v) term \<times> location"
1.62 +type_synonym ('f, 'v) forb_patterns = "('f, 'v) forb_pattern set"
1.63
1.64  type_synonym ('f, 'l, 'v) fptrsLL =
1.65 -  "(('f, 'l)lab, 'v) forb_pattern list \<times> ('f, 'l, 'v) trsLL"
1.66 +  "(('f, 'l) lab, 'v) forb_pattern list \<times> ('f, 'l, 'v) trsLL"
1.67
1.68  type_synonym ('f, 'l, 'v) prob = "('f, 'l, 'v) qreltrsLL + ('f, 'l, 'v) dppLL"
1.69
1.70  type_synonym ('f, 'a) lpoly_inter = "'f \<times> nat \<Rightarrow> ('a \<times> 'a list)"
1.71  type_synonym ('f, 'a) lpoly_interL = "(('f \<times> nat) \<times> ('a \<times> 'a list)) list"
1.72
1.73 -type_synonym 'v monom = "('v \<times> nat)list"
1.74 -type_synonym ('v,'a)poly = "('v monom \<times> 'a)list"
1.75 -type_synonym ('f,'a)poly_inter_list = "(('f \<times> nat) \<times> (nat,'a)poly)list"
1.76 +type_synonym 'v monom = "('v \<times> nat) list"
1.77 +type_synonym ('v, 'a) poly = "('v monom \<times> 'a) list"
1.78 +type_synonym ('f, 'a) poly_inter_list = "(('f \<times> nat) \<times> (nat, 'a) poly) list"
1.79  type_synonym 'a vec = "'a list"
1.80 -type_synonym 'a mat = "'a vec list"
1.81 -
1.82 +type_synonym 'a mat = "'a vec list"
1.83
1.84  datatype_new arctic = MinInfty | Num_arc int
1.85  datatype_new 'a arctic_delta = MinInfty_delta | Num_arc_delta 'a
1.86  datatype_new order_tag = Lex | Mul
1.87
1.88 -type_synonym 'f status_prec_repr = "(('f \<times> nat) \<times> (nat \<times> order_tag))list"
1.89 -datatype_new af_entry = Collapse nat | AFList "nat list"
1.90 -type_synonym 'f afs_list = "(('f \<times> nat) \<times> af_entry)list"
1.91 -type_synonym 'f prec_weight_repr = "(('f \<times> nat) \<times> (nat \<times> nat \<times> (nat list option)))list \<times> nat"
1.92 +type_synonym 'f status_prec_repr = "(('f \<times> nat) \<times> (nat \<times> order_tag)) list"
1.93 +
1.94 +datatype_new af_entry =
1.95 +    Collapse nat
1.96 +  | AFList "nat list"
1.97
1.98 +type_synonym 'f afs_list = "(('f \<times> nat) \<times> af_entry) list"
1.99 +type_synonym 'f prec_weight_repr = "(('f \<times> nat) \<times> (nat \<times> nat \<times> (nat list option))) list \<times> nat"
1.100
1.101 -datatype_new 'f redtriple_impl =
1.102 -    Int_carrier "('f, int) lpoly_interL"
1.103 -  | Int_nl_carrier "('f, int) poly_inter_list"
1.104 +datatype_new 'f redtriple_impl =
1.105 +    Int_carrier "('f, int) lpoly_interL"
1.106 +  | Int_nl_carrier "('f, int) poly_inter_list"
1.107    | Rat_carrier "('f, rat) lpoly_interL"
1.108    | Rat_nl_carrier rat "('f, rat) poly_inter_list"
1.109    | Real_carrier "('f, real) lpoly_interL"
1.110    | Real_nl_carrier real "('f, real) poly_inter_list"
1.111 -  | Arctic_carrier "('f, arctic) lpoly_interL"
1.112 -  | Arctic_rat_carrier "('f, rat arctic_delta) lpoly_interL"
1.113 +  | Arctic_carrier "('f, arctic) lpoly_interL"
1.114 +  | Arctic_rat_carrier "('f, rat arctic_delta) lpoly_interL"
1.115    | Int_mat_carrier nat nat "('f, int mat) lpoly_interL"
1.116    | Rat_mat_carrier nat nat "('f, rat mat) lpoly_interL"
1.117    | Real_mat_carrier nat nat "('f, real mat) lpoly_interL"
1.118 @@ -94,151 +98,155 @@
1.119    | RPO "'f status_prec_repr" "'f afs_list"
1.120    | KBO "'f prec_weight_repr" "'f afs_list"
1.121
1.122 -datatype_new list_order_type = MS_Ext | Max_Ext | Min_Ext  | Dms_Ext
1.123 +datatype_new list_order_type = MS_Ext | Max_Ext | Min_Ext  | Dms_Ext
1.124  type_synonym 'f scnp_af = "(('f \<times> nat) \<times> (nat \<times> nat) list) list"
1.125
1.126  datatype_new 'f root_redtriple_impl = SCNP list_order_type "'f scnp_af" "'f redtriple_impl"
1.127
1.128  type_synonym 'f sig_map_list = "(('f \<times> nat) \<times> 'f list) list"
1.129 -type_synonym ('f,'v) uncurry_info = "'f \<times> 'f sig_map_list \<times> ('f,'v)rules \<times> ('f,'v)rules"
1.130 +type_synonym ('f, 'v) uncurry_info = "'f \<times> 'f sig_map_list \<times> ('f, 'v) rules \<times> ('f, 'v) rules"
1.131
1.132  datatype_new arithFun =
1.133 -  Arg nat
1.134 -| Const nat
1.135 -| Sum "arithFun list"
1.136 -| Max "arithFun list"
1.137 -| Min "arithFun list"
1.138 -| Prod "arithFun list"
1.139 -| IfEqual arithFun arithFun arithFun arithFun
1.140 +    Arg nat
1.141 +  | Const nat
1.142 +  | Sum "arithFun list"
1.143 +  | Max "arithFun list"
1.144 +  | Min "arithFun list"
1.145 +  | Prod "arithFun list"
1.146 +  | IfEqual arithFun arithFun arithFun arithFun
1.147
1.148  datatype_new 'f sl_inter = SL_Inter nat "(('f \<times> nat) \<times> arithFun) list"
1.149 -datatype_new ('f,'v)sl_variant = Rootlab "('f \<times> nat) option" | Finitelab "'f sl_inter" | QuasiFinitelab "'f sl_inter" 'v
1.150 +datatype_new ('f, 'v) sl_variant =
1.151 +    Rootlab "('f \<times> nat) option"
1.152 +  | Finitelab "'f sl_inter"
1.153 +  | QuasiFinitelab "'f sl_inter" 'v
1.154
1.155 -type_synonym ('f,'v)crit_pair_joins = "(('f,'v)term \<times> ('f,'v)rseq \<times> ('f,'v)term \<times> ('f,'v)rseq)list"
1.156 -datatype_new 'f join_info = Guided "('f,string)crit_pair_joins" | Join_NF | Join_BFS nat
1.157 +type_synonym ('f, 'v) crit_pair_joins = "(('f, 'v) term \<times> ('f, 'v) rseq \<times> ('f, 'v) term \<times> ('f, 'v) rseq) list"
1.158 +
1.159 +datatype_new 'f join_info = Guided "('f, string) crit_pair_joins" | Join_NF | Join_BFS nat
1.160
1.161  type_synonym unknown_info = string
1.162
1.163  type_synonym dummy_prf = unit
1.164
1.165 -
1.166 -datatype_new ('f,'v)complex_constant_removal_prf = Complex_Constant_Removal_Proof
1.167 -  "('f,'v)term"
1.168 -  "(('f,'v)rule \<times> ('f,'v)rule) list"
1.169 +datatype_new ('f, 'v) complex_constant_removal_prf = Complex_Constant_Removal_Proof
1.170 +  "('f, 'v) term"
1.171 +  "(('f, 'v) rule \<times> ('f, 'v) rule) list"
1.172
1.173 -datatype_new ('f,'v)cond_constraint
1.174 -  = CC_cond bool "('f,'v)rule"
1.175 -  | CC_rewr "('f,'v)term" "('f,'v)term"
1.176 -  | CC_impl "('f,'v)cond_constraint list" "('f,'v)cond_constraint"
1.177 -  | CC_all 'v "('f,'v)cond_constraint"
1.178 +datatype_new ('f, 'v) cond_constraint =
1.179 +    CC_cond bool "('f, 'v) rule"
1.180 +  | CC_rewr "('f, 'v) term" "('f, 'v) term"
1.181 +  | CC_impl "('f, 'v) cond_constraint list" "('f, 'v) cond_constraint"
1.182 +  | CC_all 'v "('f, 'v) cond_constraint"
1.183
1.184  type_synonym ('f, 'v, 'w) gsubstL = "('v \<times> ('f, 'w) term) list"
1.185  type_synonym ('f, 'v) substL = "('f, 'v, 'v) gsubstL"
1.186
1.187 -datatype_new ('f,'v)cond_constraint_prf =
1.188 -  Final
1.189 -| Delete_Condition "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
1.190 -| Different_Constructor "('f,'v)cond_constraint"
1.191 -| Same_Constructor "('f,'v)cond_constraint" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
1.192 -| Variable_Equation 'v "('f,'v)term" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
1.193 -| Funarg_Into_Var "('f,'v)cond_constraint" nat 'v "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
1.194 -| Simplify_Condition "('f,'v)cond_constraint" "('f,'v)substL" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
1.195 -| Induction "('f,'v)cond_constraint" "('f,'v)cond_constraint list" "(('f,'v)rule \<times> (('f,'v)term \<times> 'v list) list \<times> ('f,'v)cond_constraint \<times> ('f,'v)cond_constraint_prf) list"
1.196 +datatype_new ('f, 'v) cond_constraint_prf =
1.197 +    Final
1.198 +  | Delete_Condition "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
1.199 +  | Different_Constructor "('f, 'v) cond_constraint"
1.200 +  | Same_Constructor "('f, 'v) cond_constraint" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
1.201 +  | Variable_Equation 'v "('f, 'v) term" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
1.202 +  | Funarg_Into_Var "('f, 'v) cond_constraint" nat 'v "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
1.203 +  | Simplify_Condition "('f, 'v) cond_constraint" "('f, 'v) substL" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
1.204 +  | Induction "('f, 'v) cond_constraint" "('f, 'v) cond_constraint list" "(('f, 'v) rule \<times> (('f, 'v) term \<times> 'v list) list \<times> ('f, 'v) cond_constraint \<times> ('f, 'v) cond_constraint_prf) list"
1.205
1.206 +datatype_new ('f, 'v) cond_red_pair_prf =
1.207 +  Cond_Red_Pair_Prf
1.208 +    'f "(('f, 'v) cond_constraint \<times> ('f, 'v) rules \<times> ('f, 'v) cond_constraint_prf) list" nat nat
1.209
1.210 -datatype_new ('f,'v)cond_red_pair_prf = Cond_Red_Pair_Prf
1.211 -  'f
1.212 -  "(('f,'v)cond_constraint \<times> ('f,'v)rules \<times> ('f,'v)cond_constraint_prf) list"
1.213 -  nat
1.214 -  nat
1.215 -
1.216 -datatype_new ('q,'f)ta_rule = TA_rule 'f "'q list" 'q ("_ _ \<rightarrow> _")
1.217 -datatype_new ('q,'f)tree_automaton = Tree_Automaton "'q list" "('q,'f)ta_rule list" "('q \<times> 'q)list"
1.218 -datatype_new 'q ta_relation = Decision_Proc | Id_Relation | Some_Relation "('q \<times> 'q) list"
1.219 +datatype_new ('q, 'f) ta_rule = TA_rule 'f "'q list" 'q ("_ _ \<rightarrow> _")
1.220 +datatype_new ('q, 'f) tree_automaton = Tree_Automaton "'q list" "('q, 'f) ta_rule list" "('q \<times> 'q) list"
1.221 +datatype_new 'q ta_relation =
1.222 +    Decision_Proc
1.223 +  | Id_Relation
1.224 +  | Some_Relation "('q \<times> 'q) list"
1.225
1.226  datatype_new boundstype = Roof | Match
1.227 -datatype_new ('f,'q)bounds_info = Bounds_Info boundstype nat "'q list" "('q, 'f \<times> nat) tree_automaton" "'q ta_relation"
1.228 +datatype_new ('f, 'q) bounds_info = Bounds_Info boundstype nat "'q list" "('q, 'f \<times> nat) tree_automaton" "'q ta_relation"
1.229
1.230  datatype_new ('f, 'v) pat_eqv_prf =
1.231 -  Pat_Dom_Renaming "('f, 'v) substL"
1.232 -| Pat_Irrelevant "('f, 'v) substL" "('f, 'v) substL"
1.233 -| Pat_Simplify "('f, 'v) substL" "('f, 'v) substL"
1.234 +    Pat_Dom_Renaming "('f, 'v) substL"
1.235 +  | Pat_Irrelevant "('f, 'v) substL" "('f, 'v) substL"
1.236 +  | Pat_Simplify "('f, 'v) substL" "('f, 'v) substL"
1.237
1.238  datatype_new pat_rule_pos = Pat_Base | Pat_Pump | Pat_Close
1.239
1.240 -datatype_new ('f, 'v) pat_rule_prf =
1.241 -  Pat_OrigRule "('f, 'v) rule" bool
1.242 -| Pat_InitPump "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL"
1.243 -| Pat_InitPumpCtxt "('f, 'v) pat_rule_prf" "('f, 'v) substL" pos 'v
1.244 -| Pat_Equiv "('f, 'v) pat_rule_prf" bool "('f, 'v) pat_eqv_prf"
1.245 -| Pat_Narrow "('f, 'v) pat_rule_prf" "('f, 'v) pat_rule_prf" pos
1.246 -| Pat_Inst "('f, 'v) pat_rule_prf" "('f, 'v) substL" pat_rule_pos
1.247 -| Pat_Rewr "('f, 'v) pat_rule_prf" "('f, 'v) term \<times> ('f, 'v) rseq" pat_rule_pos 'v
1.248 -| Pat_Exp_Sigma "('f, 'v) pat_rule_prf" nat
1.249 +datatype_new ('f, 'v) pat_rule_prf =
1.250 +    Pat_OrigRule "('f, 'v) rule" bool
1.251 +  | Pat_InitPump "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL"
1.252 +  | Pat_InitPumpCtxt "('f, 'v) pat_rule_prf" "('f, 'v) substL" pos 'v
1.253 +  | Pat_Equiv "('f, 'v) pat_rule_prf" bool "('f, 'v) pat_eqv_prf"
1.254 +  | Pat_Narrow "('f, 'v) pat_rule_prf" "('f, 'v) pat_rule_prf" pos
1.255 +  | Pat_Inst "('f, 'v) pat_rule_prf" "('f, 'v) substL" pat_rule_pos
1.256 +  | Pat_Rewr "('f, 'v) pat_rule_prf" "('f, 'v) term \<times> ('f, 'v) rseq" pat_rule_pos 'v
1.257 +  | Pat_Exp_Sigma "('f, 'v) pat_rule_prf" nat
1.258
1.259  datatype_new ('f, 'v) non_loop_prf =
1.260 -  Non_Loop_Prf "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL" nat nat pos
1.261 -
1.262 +    Non_Loop_Prf "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL" nat nat pos
1.263
1.264 -datatype_new ('f, 'l, 'v) problem =
1.265 -  SN_TRS "('f,'l,'v)qreltrsLL"
1.266 -| SN_FP_TRS "('f,'l,'v)fptrsLL"
1.267 -| Finite_DPP "('f,'l,'v) dppLL"
1.268 -| Unknown_Problem unknown_info
1.269 -| Not_SN_TRS "('f,'l,'v)qtrsLL"
1.270 -| Not_RelSN_TRS "('f,'l,'v)qreltrsLL"
1.271 -| Infinite_DPP "('f,'l,'v) dppLL"
1.272 -| Not_SN_FP_TRS "('f,'l,'v)fptrsLL"
1.273 +datatype_new ('f, 'l, 'v) problem =
1.274 +    SN_TRS "('f, 'l, 'v) qreltrsLL"
1.275 +  | SN_FP_TRS "('f, 'l, 'v) fptrsLL"
1.276 +  | Finite_DPP "('f, 'l, 'v) dppLL"
1.277 +  | Unknown_Problem unknown_info
1.278 +  | Not_SN_TRS "('f, 'l, 'v) qtrsLL"
1.279 +  | Not_RelSN_TRS "('f, 'l, 'v) qreltrsLL"
1.280 +  | Infinite_DPP "('f, 'l, 'v) dppLL"
1.281 +  | Not_SN_FP_TRS "('f, 'l, 'v) fptrsLL"
1.282 +
1.283  declare [[bnf_timing]]
1.284 -datatype_new ('f, 'l, 'v, 'a, 'b, 'c, 'd, 'e) generic_assm_proof =
1.285 -  SN_assm_proof "('f,'l,'v)qreltrsLL" 'a
1.286 -| Finite_assm_proof "('f,'l,'v)dppLL" 'b
1.287 -| SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'c
1.288 -| Not_SN_assm_proof "('f,'l,'v)qtrsLL" 'a
1.289 -| Infinite_assm_proof "('f,'l,'v)dppLL" 'b
1.290 -| Not_RelSN_assm_proof "('f,'l,'v)qreltrsLL" 'c
1.291 -| Not_SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'd
1.292 -| Unknown_assm_proof unknown_info 'e
1.293
1.294 -type_synonym ('f,'l,'v,'a,'b,'c,'d)assm_proof = "('f,'l,'v,'a,'b,'c,dummy_prf,'d)generic_assm_proof"
1.295 +datatype_new ('f, 'l, 'v, 'a, 'b, 'c, 'd, 'e) generic_assm_proof =
1.296 +    SN_assm_proof "('f, 'l, 'v) qreltrsLL" 'a
1.297 +  | Finite_assm_proof "('f, 'l, 'v) dppLL" 'b
1.298 +  | SN_FP_assm_proof "('f, 'l, 'v) fptrsLL" 'c
1.299 +  | Not_SN_assm_proof "('f, 'l, 'v) qtrsLL" 'a
1.300 +  | Infinite_assm_proof "('f, 'l, 'v) dppLL" 'b
1.301 +  | Not_RelSN_assm_proof "('f, 'l, 'v) qreltrsLL" 'c
1.302 +  | Not_SN_FP_assm_proof "('f, 'l, 'v) fptrsLL" 'd
1.303 +  | Unknown_assm_proof unknown_info 'e
1.304
1.305 -datatype_new ('f, 'l, 'v) assm =
1.306 -  SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
1.307 -| SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
1.308 -| Finite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
1.309 -| Unknown_assm "('f,'l,'v)problem list" unknown_info
1.310 -| Not_SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qtrsLL"
1.311 -| Not_RelSN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
1.312 -| Not_SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
1.313 -| Infinite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
1.314 +type_synonym ('f, 'l, 'v, 'a, 'b, 'c, 'd) assm_proof = "('f, 'l, 'v, 'a, 'b, 'c, dummy_prf, 'd) generic_assm_proof"
1.315
1.316 -fun satisfied :: "('f,'l,'v)problem \<Rightarrow> bool" where
1.317 +datatype_new ('f, 'l, 'v) assm =
1.318 +    SN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qreltrsLL"
1.319 +  | SN_FP_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) fptrsLL"
1.320 +  | Finite_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) dppLL"
1.321 +  | Unknown_assm "('f, 'l, 'v) problem list" unknown_info
1.322 +  | Not_SN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qtrsLL"
1.323 +  | Not_RelSN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qreltrsLL"
1.324 +  | Not_SN_FP_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) fptrsLL"
1.325 +  | Infinite_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) dppLL"
1.326 +
1.327 +fun satisfied :: "('f, 'l, 'v) problem \<Rightarrow> bool" where
1.328    "satisfied (SN_TRS t) = (t = t)"
1.329  | "satisfied (SN_FP_TRS t) = (t \<noteq> t)"
1.330  | "satisfied (Finite_DPP d) = (d \<noteq> d)"
1.331  | "satisfied (Unknown_Problem s) = (s = ''foo'')"
1.332 -| "satisfied (Not_SN_TRS (nfs,q,r)) = (length q = length r)"
1.333 -| "satisfied (Not_RelSN_TRS (nfs,q,r,rw)) = (r = rw)"
1.334 +| "satisfied (Not_SN_TRS (nfs, q, r)) = (length q = length r)"
1.335 +| "satisfied (Not_RelSN_TRS (nfs, q, r, rw)) = (r = rw)"
1.336  | "satisfied (Infinite_DPP d) = (d = d)"
1.337  | "satisfied (Not_SN_FP_TRS t) = (t = t)"
1.338
1.339 -fun collect_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
1.340 -  \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
1.341 -  \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
1.342 -  \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
1.343 -  \<Rightarrow> ('f,'l,'v,'tp,'dpp,'fptp,'unk) assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
1.344 +fun collect_assms :: "('tp \<Rightarrow> ('f, 'l, 'v) assm list)
1.345 +  \<Rightarrow> ('dpp \<Rightarrow> ('f, 'l, 'v) assm list)
1.346 +  \<Rightarrow> ('fptp \<Rightarrow> ('f, 'l, 'v) assm list)
1.347 +  \<Rightarrow> ('unk \<Rightarrow> ('f, 'l, 'v) assm list)
1.348 +  \<Rightarrow> ('f, 'l, 'v, 'tp, 'dpp, 'fptp, 'unk) assm_proof \<Rightarrow> ('f, 'l, 'v) assm list" where
1.349    "collect_assms tp dpp fptp unk (SN_assm_proof t prf) = tp prf"
1.350  | "collect_assms tp dpp fptp unk (SN_FP_assm_proof t prf) = fptp prf"
1.351  | "collect_assms tp dpp fptp unk (Finite_assm_proof d prf) = dpp prf"
1.352  | "collect_assms tp dpp fptp unk (Unknown_assm_proof p prf) = unk prf"
1.353  | "collect_assms _ _ _ _ _ = []"
1.354
1.355 -fun collect_neg_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
1.356 -  \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
1.357 -  \<Rightarrow> ('rtp \<Rightarrow> ('f,'l,'v) assm list)
1.358 -  \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
1.359 -  \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
1.360 -  \<Rightarrow> ('f,'l,'v,'tp,'dpp,'rtp,'fptp,'unk) generic_assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
1.361 +fun collect_neg_assms :: "('tp \<Rightarrow> ('f, 'l, 'v) assm list)
1.362 +  \<Rightarrow> ('dpp \<Rightarrow> ('f, 'l, 'v) assm list)
1.363 +  \<Rightarrow> ('rtp \<Rightarrow> ('f, 'l, 'v) assm list)
1.364 +  \<Rightarrow> ('fptp \<Rightarrow> ('f, 'l, 'v) assm list)
1.365 +  \<Rightarrow> ('unk \<Rightarrow> ('f, 'l, 'v) assm list)
1.366 +  \<Rightarrow> ('f, 'l, 'v, 'tp, 'dpp, 'rtp, 'fptp, 'unk) generic_assm_proof \<Rightarrow> ('f, 'l, 'v) assm list" where
1.367    "collect_neg_assms tp dpp rtp fptp unk (Not_SN_assm_proof t prf) = tp prf"
1.368  | "collect_neg_assms tp dpp rtp fptp unk (Infinite_assm_proof d prf) = dpp prf"
1.369  | "collect_neg_assms tp dpp rtp fptp unk (Not_RelSN_assm_proof t prf) = rtp prf"
1.370 @@ -246,135 +254,127 @@
1.371  | "collect_neg_assms tp dpp rtp fptp unk (Unknown_assm_proof p prf) = unk prf"
1.372  | "collect_neg_assms tp dpp rtp fptp unk _ = []"
1.373
1.374 -
1.375 -
1.376  datatype_new ('f, 'l, 'v) dp_nontermination_proof =
1.377 -  DP_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
1.378 -| DP_Nonloop "(('f,'l)lab, 'v)non_loop_prf"
1.379 -| DP_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) dp_nontermination_proof"
1.380 -| DP_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
1.381 -| DP_Q_Reduction "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
1.382 -| DP_Termination_Switch "('f,'l)lab join_info" "('f,'l,'v) dp_nontermination_proof"
1.383 -| DP_Instantiation "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
1.384 -| DP_Rewriting "('f,'l,'v)trsLL option" "('f,'l,'v)ruleLL" "('f,'l,'v)ruleLL" "('f,'l,'v)ruleLL" "(('f,'l)lab,'v)rule" pos "('f,'l,'v) dp_nontermination_proof"
1.385 -| DP_Narrowing "('f,'l,'v)ruleLL" pos "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
1.386 -| DP_Assume_Infinite  "('f, 'l, 'v) dppLL"
1.387 -    "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
1.388 -     ('f, 'l, 'v) dp_nontermination_proof,
1.389 -     ('f, 'l, 'v) reltrs_nontermination_proof,
1.390 -     ('f, 'l, 'v) fp_nontermination_proof,
1.391 -     ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.392 - and
1.393 -('f,'l,'v) "trs_nontermination_proof" =
1.394 -  TRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
1.395 -| TRS_Not_Well_Formed
1.396 -| TRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) trs_nontermination_proof"
1.397 -| TRS_String_Reversal "('f,'l,'v) trs_nontermination_proof"
1.398 -| TRS_DP_Trans "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
1.399 -| TRS_Nonloop "(('f,'l)lab,'v) non_loop_prf"
1.400 -| TRS_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) trs_nontermination_proof"
1.401 -| TRS_Assume_Not_SN  "('f, 'l, 'v)qtrsLL"
1.402 -    "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
1.403 -     ('f, 'l, 'v) dp_nontermination_proof,
1.404 -     ('f, 'l, 'v) reltrs_nontermination_proof,
1.405 -     ('f, 'l, 'v) fp_nontermination_proof,
1.406 -     ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.407 - and
1.408 -('f,'l,'v)"reltrs_nontermination_proof" =
1.409 -  Rel_Loop "(('f,'l)lab,'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
1.410 -| Rel_Not_Well_Formed
1.411 -| Rel_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) reltrs_nontermination_proof"
1.412 -| Rel_R_Not_SN "('f,'l,'v) trs_nontermination_proof"
1.413 -| Rel_TRS_Assume_Not_SN  "('f, 'l, 'v)qreltrsLL"
1.414 -    "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
1.415 -     ('f, 'l, 'v) dp_nontermination_proof,
1.416 -     ('f, 'l, 'v) reltrs_nontermination_proof,
1.417 -     ('f, 'l, 'v) fp_nontermination_proof,
1.418 -     ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.419 - and
1.420 - ('f, 'l, 'v) "fp_nontermination_proof" =
1.421 -  FPTRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
1.422 -| FPTRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) fp_nontermination_proof"
1.423 -| FPTRS_Assume_Not_SN  "('f, 'l, 'v)fptrsLL"
1.424 -    "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
1.425 -     ('f, 'l, 'v) dp_nontermination_proof,
1.426 -     ('f, 'l, 'v) reltrs_nontermination_proof,
1.427 -     ('f, 'l, 'v) fp_nontermination_proof,
1.428 -     ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.429 - and
1.430 - ('f, 'l, 'v) neg_unknown_proof =
1.431 -  Assume_NT_Unknown unknown_info
1.432 -    "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
1.433 -     ('f, 'l, 'v) dp_nontermination_proof,
1.434 -     ('f, 'l, 'v) reltrs_nontermination_proof,
1.435 -     ('f, 'l, 'v) fp_nontermination_proof,
1.436 -     ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.437 -
1.438 +    DP_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) prseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
1.439 +  | DP_Nonloop "(('f, 'l) lab, 'v) non_loop_prf"
1.440 +  | DP_Rule_Removal "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_nontermination_proof"
1.441 +  | DP_Q_Increase "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_nontermination_proof"
1.442 +  | DP_Q_Reduction "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_nontermination_proof"
1.443 +  | DP_Termination_Switch "('f, 'l) lab join_info" "('f, 'l, 'v) dp_nontermination_proof"
1.444 +  | DP_Instantiation "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
1.445 +  | DP_Rewriting "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" "(('f, 'l) lab, 'v) rule" pos "('f, 'l, 'v) dp_nontermination_proof"
1.446 +  | DP_Narrowing "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
1.447 +  | DP_Assume_Infinite  "('f, 'l, 'v) dppLL"
1.448 +      "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
1.449 +       ('f, 'l, 'v) dp_nontermination_proof,
1.450 +       ('f, 'l, 'v) reltrs_nontermination_proof,
1.451 +       ('f, 'l, 'v) fp_nontermination_proof,
1.452 +       ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.453 +and ('f, 'l, 'v) "trs_nontermination_proof" =
1.454 +    TRS_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) rseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
1.455 +  | TRS_Not_Well_Formed
1.456 +  | TRS_Rule_Removal "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_nontermination_proof"
1.457 +  | TRS_String_Reversal "('f, 'l, 'v) trs_nontermination_proof"
1.458 +  | TRS_DP_Trans "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
1.459 +  | TRS_Nonloop "(('f, 'l) lab, 'v) non_loop_prf"
1.460 +  | TRS_Q_Increase "('f, 'l, 'v) termsLL" "('f, 'l, 'v) trs_nontermination_proof"
1.461 +  | TRS_Assume_Not_SN  "('f, 'l, 'v) qtrsLL"
1.462 +      "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
1.463 +       ('f, 'l, 'v) dp_nontermination_proof,
1.464 +       ('f, 'l, 'v) reltrs_nontermination_proof,
1.465 +       ('f, 'l, 'v) fp_nontermination_proof,
1.466 +       ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.467 +and ('f, 'l, 'v)"reltrs_nontermination_proof" =
1.468 +    Rel_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) prseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
1.469 +  | Rel_Not_Well_Formed
1.470 +  | Rel_Rule_Removal "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) reltrs_nontermination_proof"
1.471 +  | Rel_R_Not_SN "('f, 'l, 'v) trs_nontermination_proof"
1.472 +  | Rel_TRS_Assume_Not_SN  "('f, 'l, 'v) qreltrsLL"
1.473 +      "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
1.474 +       ('f, 'l, 'v) dp_nontermination_proof,
1.475 +       ('f, 'l, 'v) reltrs_nontermination_proof,
1.476 +       ('f, 'l, 'v) fp_nontermination_proof,
1.477 +       ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.478 +and ('f, 'l, 'v) "fp_nontermination_proof" =
1.479 +    FPTRS_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) rseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
1.480 +  | FPTRS_Rule_Removal "('f, 'l, 'v) trsLL" "('f, 'l, 'v) fp_nontermination_proof"
1.481 +  | FPTRS_Assume_Not_SN  "('f, 'l, 'v) fptrsLL"
1.482 +      "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
1.483 +       ('f, 'l, 'v) dp_nontermination_proof,
1.484 +       ('f, 'l, 'v) reltrs_nontermination_proof,
1.485 +       ('f, 'l, 'v) fp_nontermination_proof,
1.486 +       ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.487 +and ('f, 'l, 'v) neg_unknown_proof =
1.488 +    Assume_NT_Unknown unknown_info
1.489 +      "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
1.490 +       ('f, 'l, 'v) dp_nontermination_proof,
1.491 +       ('f, 'l, 'v) reltrs_nontermination_proof,
1.492 +       ('f, 'l, 'v) fp_nontermination_proof,
1.493 +       ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
1.494
1.495  datatype_new ('f, 'l, 'v) dp_termination_proof =
1.496 -  P_is_Empty
1.497 -| Subterm_Criterion_Proc "('f, 'l) lab projL" "('f, 'l, 'v) rseqL"
1.498 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.499 -| Redpair_Proc "('f,'l)lab root_redtriple_impl + ('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL"  "('f, 'l, 'v) dp_termination_proof"
1.500 -| Redpair_UR_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl"
1.501 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.502 -| Usable_Rules_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.503 -| Dep_Graph_Proc "(('f, 'l, 'v) dp_termination_proof option \<times> ('f, 'l, 'v) trsLL) list"
1.504 -| Mono_Redpair_Proc "('f, 'l) lab redtriple_impl"
1.505 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.506 -| Mono_Redpair_UR_Proc "('f, 'l) lab redtriple_impl"
1.507 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.508 -| Size_Change_Subterm_Proc "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
1.509 -| Size_Change_Redpair_Proc "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL option"
1.510 -    "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
1.511 -| Uncurry_Proc "nat option" "(('f, 'l) lab, 'v) uncurry_info"
1.512 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.513 -| Fcc_Proc "('f, 'l) lab" "(('f, 'l) lab, 'v) ctxt list"
1.514 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.515 -| Split_Proc
1.516 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
1.517 -    "('f, 'l, 'v) dp_termination_proof" "('f, 'l, 'v) dp_termination_proof"
1.518 -| Semlab_Proc
1.519 -    "(('f, 'l) lab, 'v) sl_variant" "('f, 'l, 'v) trsLL"
1.520 -    "(('f, 'l) lab, 'v) term list" "('f, 'l, 'v) trsLL"
1.521 -    "('f, 'l, 'v) dp_termination_proof"
1.522 -| Switch_Innermost_Proc "('f, 'l) lab join_info" "('f, 'l, 'v) dp_termination_proof"
1.523 -| Rewriting_Proc
1.524 -    "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL"
1.525 -    "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) dp_termination_proof"
1.526 -| Instantiation_Proc "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.527 -| Forward_Instantiation_Proc
1.528 -    "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_termination_proof"
1.529 -| Narrowing_Proc "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.530 -| Assume_Finite
1.531 -    "('f, 'l, 'v) dppLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
1.532 -| Unlab_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.533 -| Q_Reduction_Proc "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_termination_proof"
1.534 -| Complex_Constant_Removal_Proc "(('f,'l)lab,'v)complex_constant_removal_prf" "('f, 'l, 'v) dp_termination_proof"
1.535 -| General_Redpair_Proc
1.536 -    "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
1.537 -    "(('f, 'l) lab, 'v) cond_red_pair_prf" "('f, 'l, 'v) dp_termination_proof list"
1.538 -| To_Trs_Proc "('f, 'l, 'v) trs_termination_proof"
1.539 +    P_is_Empty
1.540 +  | Subterm_Criterion_Proc "('f, 'l) lab projL" "('f, 'l, 'v) rseqL"
1.541 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.542 +  | Redpair_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL"  "('f, 'l, 'v) dp_termination_proof"
1.543 +  | Redpair_UR_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl"
1.544 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.545 +  | Usable_Rules_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.546 +  | Dep_Graph_Proc "(('f, 'l, 'v) dp_termination_proof option \<times> ('f, 'l, 'v) trsLL) list"
1.547 +  | Mono_Redpair_Proc "('f, 'l) lab redtriple_impl"
1.548 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.549 +  | Mono_Redpair_UR_Proc "('f, 'l) lab redtriple_impl"
1.550 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.551 +  | Size_Change_Subterm_Proc "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
1.552 +  | Size_Change_Redpair_Proc "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL option"
1.553 +      "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
1.554 +  | Uncurry_Proc "nat option" "(('f, 'l) lab, 'v) uncurry_info"
1.555 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.556 +  | Fcc_Proc "('f, 'l) lab" "(('f, 'l) lab, 'v) ctxt list"
1.557 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.558 +  | Split_Proc
1.559 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
1.560 +      "('f, 'l, 'v) dp_termination_proof" "('f, 'l, 'v) dp_termination_proof"
1.561 +  | Semlab_Proc
1.562 +      "(('f, 'l) lab, 'v) sl_variant" "('f, 'l, 'v) trsLL"
1.563 +      "(('f, 'l) lab, 'v) term list" "('f, 'l, 'v) trsLL"
1.564 +      "('f, 'l, 'v) dp_termination_proof"
1.565 +  | Switch_Innermost_Proc "('f, 'l) lab join_info" "('f, 'l, 'v) dp_termination_proof"
1.566 +  | Rewriting_Proc
1.567 +      "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL"
1.568 +      "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) dp_termination_proof"
1.569 +  | Instantiation_Proc "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.570 +  | Forward_Instantiation_Proc
1.571 +      "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_termination_proof"
1.572 +  | Narrowing_Proc "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.573 +  | Assume_Finite
1.574 +      "('f, 'l, 'v) dppLL" "('f, 'l, 'v, ('f, 'l, 'v) trs_termination_proof, ('f, 'l, 'v) dp_termination_proof, ('f, 'l, 'v) fptrs_termination_proof, ('f, 'l, 'v) unknown_proof) assm_proof list"
1.575 +  | Unlab_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
1.576 +  | Q_Reduction_Proc "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_termination_proof"
1.577 +  | Complex_Constant_Removal_Proc "(('f, 'l) lab, 'v) complex_constant_removal_prf" "('f, 'l, 'v) dp_termination_proof"
1.578 +  | General_Redpair_Proc
1.579 +      "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
1.580 +      "(('f, 'l) lab, 'v) cond_red_pair_prf" "('f, 'l, 'v) dp_termination_proof list"
1.581 +  | To_Trs_Proc "('f, 'l, 'v) trs_termination_proof"
1.582  and ('f, 'l, 'v) trs_termination_proof =
1.583 -  DP_Trans bool bool "(('f, 'l) lab, 'v) rules" "('f, 'l, 'v) dp_termination_proof"
1.584 -| Rule_Removal "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v)trs_termination_proof"
1.585 -| String_Reversal "('f, 'l, 'v) trs_termination_proof"
1.586 -| Bounds "(('f, 'l) lab, 'v) bounds_info"
1.587 -| Uncurry "(('f, 'l) lab, 'v) uncurry_info" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.588 -| Semlab
1.589 -    "(('f, 'l) lab, 'v) sl_variant" "(('f, 'l) lab, 'v) term list"
1.590 -    "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.591 -| R_is_Empty
1.592 -| Fcc "(('f, 'l) lab, 'v) ctxt list" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.593 -| Split "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof" "('f, 'l, 'v) trs_termination_proof"
1.594 -| Switch_Innermost "('f, 'l) lab join_info" "('f, 'l, 'v) trs_termination_proof"
1.595 -| Drop_Equality "('f, 'l, 'v) trs_termination_proof"
1.596 -| Remove_Nonapplicable_Rules "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.597 -| Assume_SN "('f, 'l, 'v) qreltrsLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
1.598 +    DP_Trans bool bool "(('f, 'l) lab, 'v) rules" "('f, 'l, 'v) dp_termination_proof"
1.599 +  | Rule_Removal "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.600 +  | String_Reversal "('f, 'l, 'v) trs_termination_proof"
1.601 +  | Bounds "(('f, 'l) lab, 'v) bounds_info"
1.602 +  | Uncurry "(('f, 'l) lab, 'v) uncurry_info" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.603 +  | Semlab
1.604 +      "(('f, 'l) lab, 'v) sl_variant" "(('f, 'l) lab, 'v) term list"
1.605 +      "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.606 +  | R_is_Empty
1.607 +  | Fcc "(('f, 'l) lab, 'v) ctxt list" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.608 +  | Split "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof" "('f, 'l, 'v) trs_termination_proof"
1.609 +  | Switch_Innermost "('f, 'l) lab join_info" "('f, 'l, 'v) trs_termination_proof"
1.610 +  | Drop_Equality "('f, 'l, 'v) trs_termination_proof"
1.611 +  | Remove_Nonapplicable_Rules "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
1.612 +  | Assume_SN "('f, 'l, 'v) qreltrsLL" "('f, 'l, 'v, ('f, 'l, 'v) trs_termination_proof, ('f, 'l, 'v) dp_termination_proof, ('f, 'l, 'v) fptrs_termination_proof, ('f, 'l, 'v) unknown_proof) assm_proof list"
1.613  and ('f, 'l, 'v) unknown_proof =
1.614 -  Assume_Unknown unknown_info "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
1.615 +    Assume_Unknown unknown_info "('f, 'l, 'v, ('f, 'l, 'v) trs_termination_proof, ('f, 'l, 'v) dp_termination_proof, ('f, 'l, 'v) fptrs_termination_proof, ('f, 'l, 'v) unknown_proof) assm_proof list"
1.616  and ('f, 'l, 'v) fptrs_termination_proof =
1.617 -  Assume_FP_SN "('f,'l,'v)fptrsLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
1.618 -
1.619 +    Assume_FP_SN "('f, 'l, 'v) fptrsLL" "('f, 'l, 'v, ('f, 'l, 'v) trs_termination_proof, ('f, 'l, 'v) dp_termination_proof, ('f, 'l, 'v) fptrs_termination_proof, ('f, 'l, 'v) unknown_proof) assm_proof list"
1.620
1.621  end
```