--- a/src/HOL/BNF_Examples/IsaFoR_Datatypes.thy Thu Jul 24 00:24:00 2014 +0200
+++ b/src/HOL/BNF_Examples/IsaFoR_Datatypes.thy Thu Jul 24 00:24:00 2014 +0200
@@ -1,37 +1,39 @@
(* Title: HOL/BNF_Examples/IsaFoR_Datatypes.thy
- Author: René Thiemann
+ Author: Rene Thiemann, UIBK
Copyright 2014
-Benchmark of datatypes defined in IsaFoR
+Benchmark consisting of datatypes defined in IsaFoR.
*)
+header {* Benchmark Consisting of Datatypes Defined in IsaFoR *}
+
theory IsaFoR_Datatypes
-imports
- Real
+imports Real
begin
datatype_new ('f, 'l) lab =
- Lab "('f, 'l) lab" 'l
-| FunLab "('f, 'l) lab" "('f, 'l) lab list"
-| UnLab 'f
-| Sharp "('f, 'l) lab"
+ Lab "('f, 'l) lab" 'l
+ | FunLab "('f, 'l) lab" "('f, 'l) lab list"
+ | UnLab 'f
+ | Sharp "('f, 'l) lab"
datatype_new 'f projL = Projection "(('f \<times> nat) \<times> nat) list"
datatype_new ('f, 'v) "term" = Var 'v | Fun 'f "('f, 'v) term list"
datatype_new ('f, 'v) ctxt =
- Hole ("\<box>")
-| More 'f "('f, 'v) term list" "('f, 'v) ctxt" "('f, 'v) term list"
-
+ Hole ("\<box>")
+ | More 'f "('f, 'v) term list" "('f, 'v) ctxt" "('f, 'v) term list"
type_synonym ('f, 'v) rule = "('f, 'v) term \<times> ('f, 'v) term"
type_synonym ('f, 'v) trs = "('f, 'v) rule set"
-type_synonym ('f, 'v) rules = "('f,'v) rule list"
+type_synonym ('f, 'v) rules = "('f, 'v) rule list"
type_synonym ('f, 'l, 'v) ruleLL = "(('f, 'l) lab, 'v) rule"
type_synonym ('f, 'l, 'v) trsLL = "(('f, 'l) lab, 'v) rules"
type_synonym ('f, 'l, 'v) termsLL = "(('f, 'l) lab, 'v) term list"
+
datatype_new pos = Empty ("\<epsilon>") | PCons "nat" "pos" (infixr "<#" 70)
+
type_synonym ('f, 'v) prseq = "(pos \<times> ('f, 'v) rule \<times> bool \<times> ('f, 'v) term) list"
type_synonym ('f, 'v) rseq = "(pos \<times> ('f, 'v) rule \<times> ('f, 'v) term) list"
@@ -49,43 +51,45 @@
datatype_new location = H | A | B | R
-type_synonym ('f,'v)forb_pattern = "('f,'v)ctxt \<times> ('f,'v)term \<times> location"
-type_synonym ('f,'v)forb_patterns = "('f,'v)forb_pattern set"
+type_synonym ('f, 'v) forb_pattern = "('f, 'v) ctxt \<times> ('f, 'v) term \<times> location"
+type_synonym ('f, 'v) forb_patterns = "('f, 'v) forb_pattern set"
type_synonym ('f, 'l, 'v) fptrsLL =
- "(('f, 'l)lab, 'v) forb_pattern list \<times> ('f, 'l, 'v) trsLL"
+ "(('f, 'l) lab, 'v) forb_pattern list \<times> ('f, 'l, 'v) trsLL"
type_synonym ('f, 'l, 'v) prob = "('f, 'l, 'v) qreltrsLL + ('f, 'l, 'v) dppLL"
type_synonym ('f, 'a) lpoly_inter = "'f \<times> nat \<Rightarrow> ('a \<times> 'a list)"
type_synonym ('f, 'a) lpoly_interL = "(('f \<times> nat) \<times> ('a \<times> 'a list)) list"
-type_synonym 'v monom = "('v \<times> nat)list"
-type_synonym ('v,'a)poly = "('v monom \<times> 'a)list"
-type_synonym ('f,'a)poly_inter_list = "(('f \<times> nat) \<times> (nat,'a)poly)list"
+type_synonym 'v monom = "('v \<times> nat) list"
+type_synonym ('v, 'a) poly = "('v monom \<times> 'a) list"
+type_synonym ('f, 'a) poly_inter_list = "(('f \<times> nat) \<times> (nat, 'a) poly) list"
type_synonym 'a vec = "'a list"
-type_synonym 'a mat = "'a vec list"
-
+type_synonym 'a mat = "'a vec list"
datatype_new arctic = MinInfty | Num_arc int
datatype_new 'a arctic_delta = MinInfty_delta | Num_arc_delta 'a
datatype_new order_tag = Lex | Mul
-type_synonym 'f status_prec_repr = "(('f \<times> nat) \<times> (nat \<times> order_tag))list"
-datatype_new af_entry = Collapse nat | AFList "nat list"
-type_synonym 'f afs_list = "(('f \<times> nat) \<times> af_entry)list"
-type_synonym 'f prec_weight_repr = "(('f \<times> nat) \<times> (nat \<times> nat \<times> (nat list option)))list \<times> nat"
+type_synonym 'f status_prec_repr = "(('f \<times> nat) \<times> (nat \<times> order_tag)) list"
+
+datatype_new af_entry =
+ Collapse nat
+ | AFList "nat list"
+type_synonym 'f afs_list = "(('f \<times> nat) \<times> af_entry) list"
+type_synonym 'f prec_weight_repr = "(('f \<times> nat) \<times> (nat \<times> nat \<times> (nat list option))) list \<times> nat"
-datatype_new 'f redtriple_impl =
- Int_carrier "('f, int) lpoly_interL"
- | Int_nl_carrier "('f, int) poly_inter_list"
+datatype_new 'f redtriple_impl =
+ Int_carrier "('f, int) lpoly_interL"
+ | Int_nl_carrier "('f, int) poly_inter_list"
| Rat_carrier "('f, rat) lpoly_interL"
| Rat_nl_carrier rat "('f, rat) poly_inter_list"
| Real_carrier "('f, real) lpoly_interL"
| Real_nl_carrier real "('f, real) poly_inter_list"
- | Arctic_carrier "('f, arctic) lpoly_interL"
- | Arctic_rat_carrier "('f, rat arctic_delta) lpoly_interL"
+ | Arctic_carrier "('f, arctic) lpoly_interL"
+ | Arctic_rat_carrier "('f, rat arctic_delta) lpoly_interL"
| Int_mat_carrier nat nat "('f, int mat) lpoly_interL"
| Rat_mat_carrier nat nat "('f, rat mat) lpoly_interL"
| Real_mat_carrier nat nat "('f, real mat) lpoly_interL"
@@ -94,151 +98,155 @@
| RPO "'f status_prec_repr" "'f afs_list"
| KBO "'f prec_weight_repr" "'f afs_list"
-datatype_new list_order_type = MS_Ext | Max_Ext | Min_Ext | Dms_Ext
+datatype_new list_order_type = MS_Ext | Max_Ext | Min_Ext | Dms_Ext
type_synonym 'f scnp_af = "(('f \<times> nat) \<times> (nat \<times> nat) list) list"
datatype_new 'f root_redtriple_impl = SCNP list_order_type "'f scnp_af" "'f redtriple_impl"
type_synonym 'f sig_map_list = "(('f \<times> nat) \<times> 'f list) list"
-type_synonym ('f,'v) uncurry_info = "'f \<times> 'f sig_map_list \<times> ('f,'v)rules \<times> ('f,'v)rules"
+type_synonym ('f, 'v) uncurry_info = "'f \<times> 'f sig_map_list \<times> ('f, 'v) rules \<times> ('f, 'v) rules"
datatype_new arithFun =
- Arg nat
-| Const nat
-| Sum "arithFun list"
-| Max "arithFun list"
-| Min "arithFun list"
-| Prod "arithFun list"
-| IfEqual arithFun arithFun arithFun arithFun
+ Arg nat
+ | Const nat
+ | Sum "arithFun list"
+ | Max "arithFun list"
+ | Min "arithFun list"
+ | Prod "arithFun list"
+ | IfEqual arithFun arithFun arithFun arithFun
datatype_new 'f sl_inter = SL_Inter nat "(('f \<times> nat) \<times> arithFun) list"
-datatype_new ('f,'v)sl_variant = Rootlab "('f \<times> nat) option" | Finitelab "'f sl_inter" | QuasiFinitelab "'f sl_inter" 'v
+datatype_new ('f, 'v) sl_variant =
+ Rootlab "('f \<times> nat) option"
+ | Finitelab "'f sl_inter"
+ | QuasiFinitelab "'f sl_inter" 'v
-type_synonym ('f,'v)crit_pair_joins = "(('f,'v)term \<times> ('f,'v)rseq \<times> ('f,'v)term \<times> ('f,'v)rseq)list"
-datatype_new 'f join_info = Guided "('f,string)crit_pair_joins" | Join_NF | Join_BFS nat
+type_synonym ('f, 'v) crit_pair_joins = "(('f, 'v) term \<times> ('f, 'v) rseq \<times> ('f, 'v) term \<times> ('f, 'v) rseq) list"
+
+datatype_new 'f join_info = Guided "('f, string) crit_pair_joins" | Join_NF | Join_BFS nat
type_synonym unknown_info = string
type_synonym dummy_prf = unit
-
-datatype_new ('f,'v)complex_constant_removal_prf = Complex_Constant_Removal_Proof
- "('f,'v)term"
- "(('f,'v)rule \<times> ('f,'v)rule) list"
+datatype_new ('f, 'v) complex_constant_removal_prf = Complex_Constant_Removal_Proof
+ "('f, 'v) term"
+ "(('f, 'v) rule \<times> ('f, 'v) rule) list"
-datatype_new ('f,'v)cond_constraint
- = CC_cond bool "('f,'v)rule"
- | CC_rewr "('f,'v)term" "('f,'v)term"
- | CC_impl "('f,'v)cond_constraint list" "('f,'v)cond_constraint"
- | CC_all 'v "('f,'v)cond_constraint"
+datatype_new ('f, 'v) cond_constraint =
+ CC_cond bool "('f, 'v) rule"
+ | CC_rewr "('f, 'v) term" "('f, 'v) term"
+ | CC_impl "('f, 'v) cond_constraint list" "('f, 'v) cond_constraint"
+ | CC_all 'v "('f, 'v) cond_constraint"
type_synonym ('f, 'v, 'w) gsubstL = "('v \<times> ('f, 'w) term) list"
type_synonym ('f, 'v) substL = "('f, 'v, 'v) gsubstL"
-datatype_new ('f,'v)cond_constraint_prf =
- Final
-| Delete_Condition "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
-| Different_Constructor "('f,'v)cond_constraint"
-| Same_Constructor "('f,'v)cond_constraint" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
-| Variable_Equation 'v "('f,'v)term" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
-| Funarg_Into_Var "('f,'v)cond_constraint" nat 'v "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
-| Simplify_Condition "('f,'v)cond_constraint" "('f,'v)substL" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
-| 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"
+datatype_new ('f, 'v) cond_constraint_prf =
+ Final
+ | Delete_Condition "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
+ | Different_Constructor "('f, 'v) cond_constraint"
+ | Same_Constructor "('f, 'v) cond_constraint" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
+ | Variable_Equation 'v "('f, 'v) term" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
+ | Funarg_Into_Var "('f, 'v) cond_constraint" nat 'v "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
+ | Simplify_Condition "('f, 'v) cond_constraint" "('f, 'v) substL" "('f, 'v) cond_constraint" "('f, 'v) cond_constraint_prf"
+ | 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"
+datatype_new ('f, 'v) cond_red_pair_prf =
+ Cond_Red_Pair_Prf
+ 'f "(('f, 'v) cond_constraint \<times> ('f, 'v) rules \<times> ('f, 'v) cond_constraint_prf) list" nat nat
-datatype_new ('f,'v)cond_red_pair_prf = Cond_Red_Pair_Prf
- 'f
- "(('f,'v)cond_constraint \<times> ('f,'v)rules \<times> ('f,'v)cond_constraint_prf) list"
- nat
- nat
-
-datatype_new ('q,'f)ta_rule = TA_rule 'f "'q list" 'q ("_ _ \<rightarrow> _")
-datatype_new ('q,'f)tree_automaton = Tree_Automaton "'q list" "('q,'f)ta_rule list" "('q \<times> 'q)list"
-datatype_new 'q ta_relation = Decision_Proc | Id_Relation | Some_Relation "('q \<times> 'q) list"
+datatype_new ('q, 'f) ta_rule = TA_rule 'f "'q list" 'q ("_ _ \<rightarrow> _")
+datatype_new ('q, 'f) tree_automaton = Tree_Automaton "'q list" "('q, 'f) ta_rule list" "('q \<times> 'q) list"
+datatype_new 'q ta_relation =
+ Decision_Proc
+ | Id_Relation
+ | Some_Relation "('q \<times> 'q) list"
datatype_new boundstype = Roof | Match
-datatype_new ('f,'q)bounds_info = Bounds_Info boundstype nat "'q list" "('q, 'f \<times> nat) tree_automaton" "'q ta_relation"
+datatype_new ('f, 'q) bounds_info = Bounds_Info boundstype nat "'q list" "('q, 'f \<times> nat) tree_automaton" "'q ta_relation"
datatype_new ('f, 'v) pat_eqv_prf =
- Pat_Dom_Renaming "('f, 'v) substL"
-| Pat_Irrelevant "('f, 'v) substL" "('f, 'v) substL"
-| Pat_Simplify "('f, 'v) substL" "('f, 'v) substL"
+ Pat_Dom_Renaming "('f, 'v) substL"
+ | Pat_Irrelevant "('f, 'v) substL" "('f, 'v) substL"
+ | Pat_Simplify "('f, 'v) substL" "('f, 'v) substL"
datatype_new pat_rule_pos = Pat_Base | Pat_Pump | Pat_Close
-datatype_new ('f, 'v) pat_rule_prf =
- Pat_OrigRule "('f, 'v) rule" bool
-| Pat_InitPump "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL"
-| Pat_InitPumpCtxt "('f, 'v) pat_rule_prf" "('f, 'v) substL" pos 'v
-| Pat_Equiv "('f, 'v) pat_rule_prf" bool "('f, 'v) pat_eqv_prf"
-| Pat_Narrow "('f, 'v) pat_rule_prf" "('f, 'v) pat_rule_prf" pos
-| Pat_Inst "('f, 'v) pat_rule_prf" "('f, 'v) substL" pat_rule_pos
-| Pat_Rewr "('f, 'v) pat_rule_prf" "('f, 'v) term \<times> ('f, 'v) rseq" pat_rule_pos 'v
-| Pat_Exp_Sigma "('f, 'v) pat_rule_prf" nat
+datatype_new ('f, 'v) pat_rule_prf =
+ Pat_OrigRule "('f, 'v) rule" bool
+ | Pat_InitPump "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL"
+ | Pat_InitPumpCtxt "('f, 'v) pat_rule_prf" "('f, 'v) substL" pos 'v
+ | Pat_Equiv "('f, 'v) pat_rule_prf" bool "('f, 'v) pat_eqv_prf"
+ | Pat_Narrow "('f, 'v) pat_rule_prf" "('f, 'v) pat_rule_prf" pos
+ | Pat_Inst "('f, 'v) pat_rule_prf" "('f, 'v) substL" pat_rule_pos
+ | Pat_Rewr "('f, 'v) pat_rule_prf" "('f, 'v) term \<times> ('f, 'v) rseq" pat_rule_pos 'v
+ | Pat_Exp_Sigma "('f, 'v) pat_rule_prf" nat
datatype_new ('f, 'v) non_loop_prf =
- Non_Loop_Prf "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL" nat nat pos
-
+ Non_Loop_Prf "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL" nat nat pos
-datatype_new ('f, 'l, 'v) problem =
- SN_TRS "('f,'l,'v)qreltrsLL"
-| SN_FP_TRS "('f,'l,'v)fptrsLL"
-| Finite_DPP "('f,'l,'v) dppLL"
-| Unknown_Problem unknown_info
-| Not_SN_TRS "('f,'l,'v)qtrsLL"
-| Not_RelSN_TRS "('f,'l,'v)qreltrsLL"
-| Infinite_DPP "('f,'l,'v) dppLL"
-| Not_SN_FP_TRS "('f,'l,'v)fptrsLL"
+datatype_new ('f, 'l, 'v) problem =
+ SN_TRS "('f, 'l, 'v) qreltrsLL"
+ | SN_FP_TRS "('f, 'l, 'v) fptrsLL"
+ | Finite_DPP "('f, 'l, 'v) dppLL"
+ | Unknown_Problem unknown_info
+ | Not_SN_TRS "('f, 'l, 'v) qtrsLL"
+ | Not_RelSN_TRS "('f, 'l, 'v) qreltrsLL"
+ | Infinite_DPP "('f, 'l, 'v) dppLL"
+ | Not_SN_FP_TRS "('f, 'l, 'v) fptrsLL"
+
declare [[bnf_timing]]
-datatype_new ('f, 'l, 'v, 'a, 'b, 'c, 'd, 'e) generic_assm_proof =
- SN_assm_proof "('f,'l,'v)qreltrsLL" 'a
-| Finite_assm_proof "('f,'l,'v)dppLL" 'b
-| SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'c
-| Not_SN_assm_proof "('f,'l,'v)qtrsLL" 'a
-| Infinite_assm_proof "('f,'l,'v)dppLL" 'b
-| Not_RelSN_assm_proof "('f,'l,'v)qreltrsLL" 'c
-| Not_SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'd
-| Unknown_assm_proof unknown_info 'e
-type_synonym ('f,'l,'v,'a,'b,'c,'d)assm_proof = "('f,'l,'v,'a,'b,'c,dummy_prf,'d)generic_assm_proof"
+datatype_new ('f, 'l, 'v, 'a, 'b, 'c, 'd, 'e) generic_assm_proof =
+ SN_assm_proof "('f, 'l, 'v) qreltrsLL" 'a
+ | Finite_assm_proof "('f, 'l, 'v) dppLL" 'b
+ | SN_FP_assm_proof "('f, 'l, 'v) fptrsLL" 'c
+ | Not_SN_assm_proof "('f, 'l, 'v) qtrsLL" 'a
+ | Infinite_assm_proof "('f, 'l, 'v) dppLL" 'b
+ | Not_RelSN_assm_proof "('f, 'l, 'v) qreltrsLL" 'c
+ | Not_SN_FP_assm_proof "('f, 'l, 'v) fptrsLL" 'd
+ | Unknown_assm_proof unknown_info 'e
-datatype_new ('f, 'l, 'v) assm =
- SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
-| SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
-| Finite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
-| Unknown_assm "('f,'l,'v)problem list" unknown_info
-| Not_SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qtrsLL"
-| Not_RelSN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
-| Not_SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
-| Infinite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
+type_synonym ('f, 'l, 'v, 'a, 'b, 'c, 'd) assm_proof = "('f, 'l, 'v, 'a, 'b, 'c, dummy_prf, 'd) generic_assm_proof"
-fun satisfied :: "('f,'l,'v)problem \<Rightarrow> bool" where
+datatype_new ('f, 'l, 'v) assm =
+ SN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qreltrsLL"
+ | SN_FP_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) fptrsLL"
+ | Finite_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) dppLL"
+ | Unknown_assm "('f, 'l, 'v) problem list" unknown_info
+ | Not_SN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qtrsLL"
+ | Not_RelSN_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) qreltrsLL"
+ | Not_SN_FP_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) fptrsLL"
+ | Infinite_assm "('f, 'l, 'v) problem list" "('f, 'l, 'v) dppLL"
+
+fun satisfied :: "('f, 'l, 'v) problem \<Rightarrow> bool" where
"satisfied (SN_TRS t) = (t = t)"
| "satisfied (SN_FP_TRS t) = (t \<noteq> t)"
| "satisfied (Finite_DPP d) = (d \<noteq> d)"
| "satisfied (Unknown_Problem s) = (s = ''foo'')"
-| "satisfied (Not_SN_TRS (nfs,q,r)) = (length q = length r)"
-| "satisfied (Not_RelSN_TRS (nfs,q,r,rw)) = (r = rw)"
+| "satisfied (Not_SN_TRS (nfs, q, r)) = (length q = length r)"
+| "satisfied (Not_RelSN_TRS (nfs, q, r, rw)) = (r = rw)"
| "satisfied (Infinite_DPP d) = (d = d)"
| "satisfied (Not_SN_FP_TRS t) = (t = t)"
-fun collect_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('f,'l,'v,'tp,'dpp,'fptp,'unk) assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
+fun collect_assms :: "('tp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('dpp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('fptp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('unk \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('f, 'l, 'v, 'tp, 'dpp, 'fptp, 'unk) assm_proof \<Rightarrow> ('f, 'l, 'v) assm list" where
"collect_assms tp dpp fptp unk (SN_assm_proof t prf) = tp prf"
| "collect_assms tp dpp fptp unk (SN_FP_assm_proof t prf) = fptp prf"
| "collect_assms tp dpp fptp unk (Finite_assm_proof d prf) = dpp prf"
| "collect_assms tp dpp fptp unk (Unknown_assm_proof p prf) = unk prf"
| "collect_assms _ _ _ _ _ = []"
-fun collect_neg_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('rtp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
- \<Rightarrow> ('f,'l,'v,'tp,'dpp,'rtp,'fptp,'unk) generic_assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
+fun collect_neg_assms :: "('tp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('dpp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('rtp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('fptp \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('unk \<Rightarrow> ('f, 'l, 'v) assm list)
+ \<Rightarrow> ('f, 'l, 'v, 'tp, 'dpp, 'rtp, 'fptp, 'unk) generic_assm_proof \<Rightarrow> ('f, 'l, 'v) assm list" where
"collect_neg_assms tp dpp rtp fptp unk (Not_SN_assm_proof t prf) = tp prf"
| "collect_neg_assms tp dpp rtp fptp unk (Infinite_assm_proof d prf) = dpp prf"
| "collect_neg_assms tp dpp rtp fptp unk (Not_RelSN_assm_proof t prf) = rtp prf"
@@ -246,135 +254,127 @@
| "collect_neg_assms tp dpp rtp fptp unk (Unknown_assm_proof p prf) = unk prf"
| "collect_neg_assms tp dpp rtp fptp unk _ = []"
-
-
datatype_new ('f, 'l, 'v) dp_nontermination_proof =
- DP_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
-| DP_Nonloop "(('f,'l)lab, 'v)non_loop_prf"
-| DP_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) dp_nontermination_proof"
-| DP_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
-| DP_Q_Reduction "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
-| DP_Termination_Switch "('f,'l)lab join_info" "('f,'l,'v) dp_nontermination_proof"
-| DP_Instantiation "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
-| 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"
-| DP_Narrowing "('f,'l,'v)ruleLL" pos "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
-| DP_Assume_Infinite "('f, 'l, 'v) dppLL"
- "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
- ('f, 'l, 'v) dp_nontermination_proof,
- ('f, 'l, 'v) reltrs_nontermination_proof,
- ('f, 'l, 'v) fp_nontermination_proof,
- ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
- and
-('f,'l,'v) "trs_nontermination_proof" =
- TRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
-| TRS_Not_Well_Formed
-| TRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) trs_nontermination_proof"
-| TRS_String_Reversal "('f,'l,'v) trs_nontermination_proof"
-| TRS_DP_Trans "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
-| TRS_Nonloop "(('f,'l)lab,'v) non_loop_prf"
-| TRS_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) trs_nontermination_proof"
-| TRS_Assume_Not_SN "('f, 'l, 'v)qtrsLL"
- "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
- ('f, 'l, 'v) dp_nontermination_proof,
- ('f, 'l, 'v) reltrs_nontermination_proof,
- ('f, 'l, 'v) fp_nontermination_proof,
- ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
- and
-('f,'l,'v)"reltrs_nontermination_proof" =
- Rel_Loop "(('f,'l)lab,'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
-| Rel_Not_Well_Formed
-| Rel_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) reltrs_nontermination_proof"
-| Rel_R_Not_SN "('f,'l,'v) trs_nontermination_proof"
-| Rel_TRS_Assume_Not_SN "('f, 'l, 'v)qreltrsLL"
- "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
- ('f, 'l, 'v) dp_nontermination_proof,
- ('f, 'l, 'v) reltrs_nontermination_proof,
- ('f, 'l, 'v) fp_nontermination_proof,
- ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
- and
- ('f, 'l, 'v) "fp_nontermination_proof" =
- FPTRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
-| FPTRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) fp_nontermination_proof"
-| FPTRS_Assume_Not_SN "('f, 'l, 'v)fptrsLL"
- "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
- ('f, 'l, 'v) dp_nontermination_proof,
- ('f, 'l, 'v) reltrs_nontermination_proof,
- ('f, 'l, 'v) fp_nontermination_proof,
- ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
- and
- ('f, 'l, 'v) neg_unknown_proof =
- Assume_NT_Unknown unknown_info
- "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
- ('f, 'l, 'v) dp_nontermination_proof,
- ('f, 'l, 'v) reltrs_nontermination_proof,
- ('f, 'l, 'v) fp_nontermination_proof,
- ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
-
+ DP_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) prseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
+ | DP_Nonloop "(('f, 'l) lab, 'v) non_loop_prf"
+ | DP_Rule_Removal "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_nontermination_proof"
+ | DP_Q_Increase "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_nontermination_proof"
+ | DP_Q_Reduction "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_nontermination_proof"
+ | DP_Termination_Switch "('f, 'l) lab join_info" "('f, 'l, 'v) dp_nontermination_proof"
+ | DP_Instantiation "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
+ | 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"
+ | DP_Narrowing "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
+ | DP_Assume_Infinite "('f, 'l, 'v) dppLL"
+ "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+and ('f, 'l, 'v) "trs_nontermination_proof" =
+ TRS_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) rseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
+ | TRS_Not_Well_Formed
+ | TRS_Rule_Removal "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_nontermination_proof"
+ | TRS_String_Reversal "('f, 'l, 'v) trs_nontermination_proof"
+ | TRS_DP_Trans "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_nontermination_proof"
+ | TRS_Nonloop "(('f, 'l) lab, 'v) non_loop_prf"
+ | TRS_Q_Increase "('f, 'l, 'v) termsLL" "('f, 'l, 'v) trs_nontermination_proof"
+ | TRS_Assume_Not_SN "('f, 'l, 'v) qtrsLL"
+ "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+and ('f, 'l, 'v)"reltrs_nontermination_proof" =
+ Rel_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) prseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
+ | Rel_Not_Well_Formed
+ | Rel_Rule_Removal "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) reltrs_nontermination_proof"
+ | Rel_R_Not_SN "('f, 'l, 'v) trs_nontermination_proof"
+ | Rel_TRS_Assume_Not_SN "('f, 'l, 'v) qreltrsLL"
+ "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+and ('f, 'l, 'v) "fp_nontermination_proof" =
+ FPTRS_Loop "(('f, 'l) lab, 'v) term" "(('f, 'l) lab, 'v) rseq" "(('f, 'l) lab, 'v) substL" "(('f, 'l) lab, 'v) ctxt"
+ | FPTRS_Rule_Removal "('f, 'l, 'v) trsLL" "('f, 'l, 'v) fp_nontermination_proof"
+ | FPTRS_Assume_Not_SN "('f, 'l, 'v) fptrsLL"
+ "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+and ('f, 'l, 'v) neg_unknown_proof =
+ Assume_NT_Unknown unknown_info
+ "('f, 'l, 'v, ('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
datatype_new ('f, 'l, 'v) dp_termination_proof =
- P_is_Empty
-| Subterm_Criterion_Proc "('f, 'l) lab projL" "('f, 'l, 'v) rseqL"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Redpair_Proc "('f,'l)lab root_redtriple_impl + ('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Redpair_UR_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Usable_Rules_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Dep_Graph_Proc "(('f, 'l, 'v) dp_termination_proof option \<times> ('f, 'l, 'v) trsLL) list"
-| Mono_Redpair_Proc "('f, 'l) lab redtriple_impl"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Mono_Redpair_UR_Proc "('f, 'l) lab redtriple_impl"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Size_Change_Subterm_Proc "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
-| Size_Change_Redpair_Proc "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL option"
- "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
-| Uncurry_Proc "nat option" "(('f, 'l) lab, 'v) uncurry_info"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Fcc_Proc "('f, 'l) lab" "(('f, 'l) lab, 'v) ctxt list"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Split_Proc
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
- "('f, 'l, 'v) dp_termination_proof" "('f, 'l, 'v) dp_termination_proof"
-| Semlab_Proc
- "(('f, 'l) lab, 'v) sl_variant" "('f, 'l, 'v) trsLL"
- "(('f, 'l) lab, 'v) term list" "('f, 'l, 'v) trsLL"
- "('f, 'l, 'v) dp_termination_proof"
-| Switch_Innermost_Proc "('f, 'l) lab join_info" "('f, 'l, 'v) dp_termination_proof"
-| Rewriting_Proc
- "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL"
- "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) dp_termination_proof"
-| Instantiation_Proc "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Forward_Instantiation_Proc
- "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_termination_proof"
-| Narrowing_Proc "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Assume_Finite
- "('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"
-| Unlab_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
-| Q_Reduction_Proc "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_termination_proof"
-| Complex_Constant_Removal_Proc "(('f,'l)lab,'v)complex_constant_removal_prf" "('f, 'l, 'v) dp_termination_proof"
-| General_Redpair_Proc
- "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
- "(('f, 'l) lab, 'v) cond_red_pair_prf" "('f, 'l, 'v) dp_termination_proof list"
-| To_Trs_Proc "('f, 'l, 'v) trs_termination_proof"
+ P_is_Empty
+ | Subterm_Criterion_Proc "('f, 'l) lab projL" "('f, 'l, 'v) rseqL"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Redpair_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Redpair_UR_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Usable_Rules_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Dep_Graph_Proc "(('f, 'l, 'v) dp_termination_proof option \<times> ('f, 'l, 'v) trsLL) list"
+ | Mono_Redpair_Proc "('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Mono_Redpair_UR_Proc "('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Size_Change_Subterm_Proc "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
+ | Size_Change_Redpair_Proc "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL option"
+ "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
+ | Uncurry_Proc "nat option" "(('f, 'l) lab, 'v) uncurry_info"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Fcc_Proc "('f, 'l) lab" "(('f, 'l) lab, 'v) ctxt list"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Split_Proc
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
+ "('f, 'l, 'v) dp_termination_proof" "('f, 'l, 'v) dp_termination_proof"
+ | Semlab_Proc
+ "(('f, 'l) lab, 'v) sl_variant" "('f, 'l, 'v) trsLL"
+ "(('f, 'l) lab, 'v) term list" "('f, 'l, 'v) trsLL"
+ "('f, 'l, 'v) dp_termination_proof"
+ | Switch_Innermost_Proc "('f, 'l) lab join_info" "('f, 'l, 'v) dp_termination_proof"
+ | Rewriting_Proc
+ "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL"
+ "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) dp_termination_proof"
+ | Instantiation_Proc "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Forward_Instantiation_Proc
+ "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_termination_proof"
+ | Narrowing_Proc "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Assume_Finite
+ "('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"
+ | Unlab_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Q_Reduction_Proc "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_termination_proof"
+ | Complex_Constant_Removal_Proc "(('f, 'l) lab, 'v) complex_constant_removal_prf" "('f, 'l, 'v) dp_termination_proof"
+ | General_Redpair_Proc
+ "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
+ "(('f, 'l) lab, 'v) cond_red_pair_prf" "('f, 'l, 'v) dp_termination_proof list"
+ | To_Trs_Proc "('f, 'l, 'v) trs_termination_proof"
and ('f, 'l, 'v) trs_termination_proof =
- DP_Trans bool bool "(('f, 'l) lab, 'v) rules" "('f, 'l, 'v) dp_termination_proof"
-| Rule_Removal "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v)trs_termination_proof"
-| String_Reversal "('f, 'l, 'v) trs_termination_proof"
-| Bounds "(('f, 'l) lab, 'v) bounds_info"
-| Uncurry "(('f, 'l) lab, 'v) uncurry_info" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
-| Semlab
- "(('f, 'l) lab, 'v) sl_variant" "(('f, 'l) lab, 'v) term list"
- "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
-| R_is_Empty
-| Fcc "(('f, 'l) lab, 'v) ctxt list" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
-| Split "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof" "('f, 'l, 'v) trs_termination_proof"
-| Switch_Innermost "('f, 'l) lab join_info" "('f, 'l, 'v) trs_termination_proof"
-| Drop_Equality "('f, 'l, 'v) trs_termination_proof"
-| Remove_Nonapplicable_Rules "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
-| 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"
+ DP_Trans bool bool "(('f, 'l) lab, 'v) rules" "('f, 'l, 'v) dp_termination_proof"
+ | Rule_Removal "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+ | String_Reversal "('f, 'l, 'v) trs_termination_proof"
+ | Bounds "(('f, 'l) lab, 'v) bounds_info"
+ | Uncurry "(('f, 'l) lab, 'v) uncurry_info" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+ | Semlab
+ "(('f, 'l) lab, 'v) sl_variant" "(('f, 'l) lab, 'v) term list"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+ | R_is_Empty
+ | Fcc "(('f, 'l) lab, 'v) ctxt list" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+ | Split "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof" "('f, 'l, 'v) trs_termination_proof"
+ | Switch_Innermost "('f, 'l) lab join_info" "('f, 'l, 'v) trs_termination_proof"
+ | Drop_Equality "('f, 'l, 'v) trs_termination_proof"
+ | Remove_Nonapplicable_Rules "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+ | 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"
and ('f, 'l, 'v) unknown_proof =
- 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"
+ 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"
and ('f, 'l, 'v) fptrs_termination_proof =
- 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"
-
+ 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"
end