20.082/20.082 YES
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082 Confluence Problem:
20.082/20.082 (VAR vNonEmpty:S x:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 )
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Inlining of Conditions Processor [STERN17]:
20.082/20.082
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082 Confluence Problem:
20.082/20.082 (VAR vNonEmpty:S x:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 )
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Clean CTRS Processor:
20.082/20.082
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082 Confluence Problem:
20.082/20.082 (VAR x:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 )
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082
20.082/20.082 CRule InfChecker Info:
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 Rule remains
20.082/20.082 Proof:
20.082/20.082 NO
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Infeasibility Problem:
20.082/20.082 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S:S) -> a | a ->* x:S:S
20.082/20.082 f(x:S:S) -> b | b ->* x:S:S
20.082/20.082 )]
20.082/20.082
20.082/20.082 Infeasibility Conditions:
20.082/20.082 a ->* x:S:S
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Obtaining a proof using Prover9:
20.082/20.082
20.082/20.082 -> Prover9 Output:
20.082/20.082 ============================== Prover9 ===============================
20.082/20.082 Prover9 (64) version 2009-11A, November 2009.
20.082/20.082 Process 117282 was started by ubuntu on ubuntu,
20.082/20.082 Fri Jul 16 15:29:13 2021
20.082/20.082 The command was "./prover9 -f /tmp/prover9117273-0.in".
20.082/20.082 ============================== end of head ===========================
20.082/20.082
20.082/20.082 ============================== INPUT =================================
20.082/20.082
20.082/20.082 % Reading from file /tmp/prover9117273-0.in
20.082/20.082
20.082/20.082 assign(max_seconds,20).
20.082/20.082
20.082/20.082 formulas(assumptions).
20.082/20.082 ->*_s0(x,x) # label(reflexivity).
20.082/20.082 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
20.082/20.082 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
20.082/20.082 ->*_s0(a,x2) -> ->_s0(f(x2),a) # label(replacement).
20.082/20.082 ->*_s0(b,x2) -> ->_s0(f(x2),b) # label(replacement).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(goals).
20.082/20.082 (exists x2 ->*_s0(a,x2)) # label(goal).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== end of input ==========================
20.082/20.082
20.082/20.082 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.082/20.082
20.082/20.082 % Formulas that are not ordinary clauses:
20.082/20.082 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
20.082/20.082 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.082/20.082 3 ->*_s0(a,x2) -> ->_s0(f(x2),a) # label(replacement) # label(non_clause). [assumption].
20.082/20.082 4 ->*_s0(b,x2) -> ->_s0(f(x2),b) # label(replacement) # label(non_clause). [assumption].
20.082/20.082 5 (exists x2 ->*_s0(a,x2)) # label(goal) # label(non_clause) # label(goal). [goal].
20.082/20.082
20.082/20.082 ============================== end of process non-clausal formulas ===
20.082/20.082
20.082/20.082 ============================== PROCESS INITIAL CLAUSES ===============
20.082/20.082
20.082/20.082 % Clauses before input processing:
20.082/20.082
20.082/20.082 formulas(usable).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(sos).
20.082/20.082 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
20.082/20.082 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
20.082/20.082 -->*_s0(a,x) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
20.082/20.082 -->*_s0(b,x) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
20.082/20.082 -->*_s0(a,x) # label(goal). [deny(5)].
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(demodulators).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== PREDICATE ELIMINATION =================
20.082/20.082
20.082/20.082 No predicates eliminated.
20.082/20.082
20.082/20.082 ============================== end predicate elimination =============
20.082/20.082
20.082/20.082 Auto_denials:
20.082/20.082 % copying label goal to answer in negative clause
20.082/20.082
20.082/20.082 Term ordering decisions:
20.082/20.082 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
20.082/20.082 Function symbol precedence: function_order([ a, b, f ]).
20.082/20.082 After inverse_order: (no changes).
20.082/20.082 Unfolding symbols: (none).
20.082/20.082
20.082/20.082 Auto_inference settings:
20.082/20.082 % set(neg_binary_resolution). % (HNE depth_diff=-3)
20.082/20.082 % clear(ordered_res). % (HNE depth_diff=-3)
20.082/20.082 % set(ur_resolution). % (HNE depth_diff=-3)
20.082/20.082 % set(ur_resolution) -> set(pos_ur_resolution).
20.082/20.082 % set(ur_resolution) -> set(neg_ur_resolution).
20.082/20.082
20.082/20.082 Auto_process settings: (no changes).
20.082/20.082
20.082/20.082 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
20.082/20.082 kept: 8 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
20.082/20.082 kept: 9 -->*_s0(a,x) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
20.082/20.082 kept: 10 -->*_s0(b,x) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
20.082/20.082 kept: 11 -->*_s0(a,x) # label(goal) # answer(goal). [deny(5)].
20.082/20.082
20.082/20.082 ============================== PROOF =================================
20.082/20.082
20.082/20.082 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
20.082/20.082 % Length of proof is 4.
20.082/20.082 % Level of proof is 2.
20.082/20.082 % Maximum clause weight is 3.000.
20.082/20.082 % Given clauses 0.
20.082/20.082
20.082/20.082 5 (exists x2 ->*_s0(a,x2)) # label(goal) # label(non_clause) # label(goal). [goal].
20.082/20.082 6 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 11 -->*_s0(a,x) # label(goal) # answer(goal). [deny(5)].
20.082/20.082 12 $F # answer(goal). [resolve(11,a,6,a)].
20.082/20.082
20.082/20.082 ============================== end of proof ==========================
20.082/20.082
20.082/20.082 ============================== STATISTICS ============================
20.082/20.082
20.082/20.082 Given=0. Generated=6. Kept=6. proofs=1.
20.082/20.082 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0.
20.082/20.082 Kept_by_rule=0, Deleted_by_rule=0.
20.082/20.082 Forward_subsumed=0. Back_subsumed=0.
20.082/20.082 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
20.082/20.082 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
20.082/20.082 Demod_attempts=0. Demod_rewrites=0.
20.082/20.082 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
20.082/20.082 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
20.082/20.082 Megabytes=0.04.
20.082/20.082 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.082/20.082
20.082/20.082 ============================== end of statistics =====================
20.082/20.082
20.082/20.082 ============================== end of search =========================
20.082/20.082
20.082/20.082 THEOREM PROVED
20.082/20.082
20.082/20.082 Exiting with 1 proof.
20.082/20.082
20.082/20.082 Process 117282 exit (max_proofs) Fri Jul 16 15:29:13 2021
20.082/20.082
20.082/20.082
20.082/20.082 The problem is feasible.
20.082/20.082
20.082/20.082
20.082/20.082 CRule InfChecker Info:
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 Rule remains
20.082/20.082 Proof:
20.082/20.082 NO
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Infeasibility Problem:
20.082/20.082 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S:S) -> a | a ->* x:S:S
20.082/20.082 f(x:S:S) -> b | b ->* x:S:S
20.082/20.082 )]
20.082/20.082
20.082/20.082 Infeasibility Conditions:
20.082/20.082 b ->* x:S:S
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Obtaining a proof using Prover9:
20.082/20.082
20.082/20.082 -> Prover9 Output:
20.082/20.082 ============================== Prover9 ===============================
20.082/20.082 Prover9 (64) version 2009-11A, November 2009.
20.082/20.082 Process 117305 was started by ubuntu on ubuntu,
20.082/20.082 Fri Jul 16 15:29:13 2021
20.082/20.082 The command was "./prover9 -f /tmp/prover9117294-0.in".
20.082/20.082 ============================== end of head ===========================
20.082/20.082
20.082/20.082 ============================== INPUT =================================
20.082/20.082
20.082/20.082 % Reading from file /tmp/prover9117294-0.in
20.082/20.082
20.082/20.082 assign(max_seconds,20).
20.082/20.082
20.082/20.082 formulas(assumptions).
20.082/20.082 ->*_s0(x,x) # label(reflexivity).
20.082/20.082 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
20.082/20.082 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
20.082/20.082 ->*_s0(a,x2) -> ->_s0(f(x2),a) # label(replacement).
20.082/20.082 ->*_s0(b,x2) -> ->_s0(f(x2),b) # label(replacement).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(goals).
20.082/20.082 (exists x2 ->*_s0(b,x2)) # label(goal).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== end of input ==========================
20.082/20.082
20.082/20.082 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.082/20.082
20.082/20.082 % Formulas that are not ordinary clauses:
20.082/20.082 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
20.082/20.082 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.082/20.082 3 ->*_s0(a,x2) -> ->_s0(f(x2),a) # label(replacement) # label(non_clause). [assumption].
20.082/20.082 4 ->*_s0(b,x2) -> ->_s0(f(x2),b) # label(replacement) # label(non_clause). [assumption].
20.082/20.082 5 (exists x2 ->*_s0(b,x2)) # label(goal) # label(non_clause) # label(goal). [goal].
20.082/20.082
20.082/20.082 ============================== end of process non-clausal formulas ===
20.082/20.082
20.082/20.082 ============================== PROCESS INITIAL CLAUSES ===============
20.082/20.082
20.082/20.082 % Clauses before input processing:
20.082/20.082
20.082/20.082 formulas(usable).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(sos).
20.082/20.082 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
20.082/20.082 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
20.082/20.082 -->*_s0(a,x) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
20.082/20.082 -->*_s0(b,x) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
20.082/20.082 -->*_s0(b,x) # label(goal). [deny(5)].
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(demodulators).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== PREDICATE ELIMINATION =================
20.082/20.082
20.082/20.082 No predicates eliminated.
20.082/20.082
20.082/20.082 ============================== end predicate elimination =============
20.082/20.082
20.082/20.082 Auto_denials:
20.082/20.082 % copying label goal to answer in negative clause
20.082/20.082
20.082/20.082 Term ordering decisions:
20.082/20.082 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
20.082/20.082 Function symbol precedence: function_order([ a, b, f ]).
20.082/20.082 After inverse_order: (no changes).
20.082/20.082 Unfolding symbols: (none).
20.082/20.082
20.082/20.082 Auto_inference settings:
20.082/20.082 % set(neg_binary_resolution). % (HNE depth_diff=-3)
20.082/20.082 % clear(ordered_res). % (HNE depth_diff=-3)
20.082/20.082 % set(ur_resolution). % (HNE depth_diff=-3)
20.082/20.082 % set(ur_resolution) -> set(pos_ur_resolution).
20.082/20.082 % set(ur_resolution) -> set(neg_ur_resolution).
20.082/20.082
20.082/20.082 Auto_process settings: (no changes).
20.082/20.082
20.082/20.082 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
20.082/20.082 kept: 8 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
20.082/20.082 kept: 9 -->*_s0(a,x) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
20.082/20.082 kept: 10 -->*_s0(b,x) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
20.082/20.082 kept: 11 -->*_s0(b,x) # label(goal) # answer(goal). [deny(5)].
20.082/20.082
20.082/20.082 ============================== PROOF =================================
20.082/20.082
20.082/20.082 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
20.082/20.082 % Length of proof is 4.
20.082/20.082 % Level of proof is 2.
20.082/20.082 % Maximum clause weight is 3.000.
20.082/20.082 % Given clauses 0.
20.082/20.082
20.082/20.082 5 (exists x2 ->*_s0(b,x2)) # label(goal) # label(non_clause) # label(goal). [goal].
20.082/20.082 6 ->*_s0(x,x) # label(reflexivity). [assumption].
20.082/20.082 11 -->*_s0(b,x) # label(goal) # answer(goal). [deny(5)].
20.082/20.082 12 $F # answer(goal). [resolve(11,a,6,a)].
20.082/20.082
20.082/20.082 ============================== end of proof ==========================
20.082/20.082
20.082/20.082 ============================== STATISTICS ============================
20.082/20.082
20.082/20.082 Given=0. Generated=6. Kept=6. proofs=1.
20.082/20.082 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0.
20.082/20.082 Kept_by_rule=0, Deleted_by_rule=0.
20.082/20.082 Forward_subsumed=0. Back_subsumed=0.
20.082/20.082 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
20.082/20.082 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
20.082/20.082 Demod_attempts=0. Demod_rewrites=0.
20.082/20.082 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
20.082/20.082 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
20.082/20.082 Megabytes=0.04.
20.082/20.082 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.082/20.082
20.082/20.082 ============================== end of statistics =====================
20.082/20.082
20.082/20.082 ============================== end of search =========================
20.082/20.082
20.082/20.082 THEOREM PROVED
20.082/20.082
20.082/20.082 Exiting with 1 proof.
20.082/20.082
20.082/20.082 Process 117305 exit (max_proofs) Fri Jul 16 15:29:13 2021
20.082/20.082
20.082/20.082
20.082/20.082 The problem is feasible.
20.082/20.082
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082 Confluence Problem:
20.082/20.082 (VAR x:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 )
20.082/20.082 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.082/20.082
20.082/20.082 Critical Pairs Processor:
20.082/20.082 -> Rules:
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 -> Vars:
20.082/20.082 "x", "x"
20.082/20.082 -> FVars:
20.082/20.082 "x2", "x3"
20.082/20.082 -> PVars:
20.082/20.082 "x": ["x2", "x3"]
20.082/20.082
20.082/20.082 -> Rlps:
20.082/20.082 crule: f(x2:S) -> a | a ->* x2:S, id: 1, possubterms: f(x2:S)-> []
20.082/20.082 crule: f(x3:S) -> b | b ->* x3:S, id: 2, possubterms: f(x3:S)-> []
20.082/20.082
20.082/20.082 -> Unifications:
20.082/20.082 R2 unifies with R1 at p: [], l: f(x3:S), lp: f(x3:S), conds: {b ->* x3:S, a ->* x:S}, sig: {x3:S -> x:S}, l': f(x:S), r: b, r': a
20.082/20.082
20.082/20.082 -> Critical pairs info:
20.082/20.082 | b ->* x:S, a ->* x:S => Not trivial, Overlay, N1
20.082/20.082
20.082/20.082 -> Problem conclusions:
20.082/20.082 Left linear, Right linear, Linear
20.082/20.082 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
20.082/20.082 CTRS Type: 1
20.082/20.082 Deterministic, Strongly deterministic
20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS
20.082/20.082 Maybe right-stable CTRS, Overlay CTRS
20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS
20.082/20.082 Maybe terminating CTRS, Maybe joinable CCPs
20.082/20.082 Maybe level confluent
20.082/20.082 Maybe confluent
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082 Clean Infeasible CCPs Processor:
20.082/20.082 Num of CPIs: 1
20.082/20.082 Timeout: 30
20.082/20.082 Timeout for each infeasibility problem: 30 s
20.082/20.082 | b ->* x:S, a ->* x:S => Not trivial, Overlay, N1
20.082/20.082 (PROBLEM INFEASIBILITY)
20.082/20.082 (VAR x)
20.082/20.082 (RULES
20.082/20.082 f(x) -> a | a ->* x
20.082/20.082 f(x) -> b | b ->* x)
20.082/20.082 (VAR x2)
20.082/20.082 (CONDITION b ->* x2, a ->* x2)
20.082/20.082
20.082/20.082 Proof:
20.082/20.082 YES
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Infeasibility Problem:
20.082/20.082 [(VAR vNonEmpty:S x:S x2:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 (fSNonEmpty)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a | a ->* x:S
20.082/20.082 f(x:S) -> b | b ->* x:S
20.082/20.082 )]
20.082/20.082
20.082/20.082 Infeasibility Conditions:
20.082/20.082 b ->* x2:S, a ->* x2:S
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Obtaining a model using Mace4:
20.082/20.082
20.082/20.082 -> Usable Rules:
20.082/20.082 Empty
20.082/20.082
20.082/20.082 -> Mace4 Output:
20.082/20.082 ============================== Mace4 =================================
20.082/20.082 Mace4 (64) version 2009-11A, November 2009.
20.082/20.082 Process 117359 was started by ubuntu on ubuntu,
20.082/20.082 Fri Jul 16 15:29:13 2021
20.082/20.082 The command was "./mace4 -c -f /tmp/mace4117323-2.in".
20.082/20.082 ============================== end of head ===========================
20.082/20.082
20.082/20.082 ============================== INPUT =================================
20.082/20.082
20.082/20.082 % Reading from file /tmp/mace4117323-2.in
20.082/20.082
20.082/20.082 assign(max_seconds,10).
20.082/20.082
20.082/20.082 formulas(assumptions).
20.082/20.082 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.082/20.082 ->*(x,x) # label(reflexivity).
20.082/20.082 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 formulas(goals).
20.082/20.082 (exists x2 (->*(b,x2) & ->*(a,x2))) # label(goal).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== end of input ==========================
20.082/20.082
20.082/20.082 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.082/20.082
20.082/20.082 % Formulas that are not ordinary clauses:
20.082/20.082 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.082/20.082 2 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption].
20.082/20.082 3 (exists x2 (->*(b,x2) & ->*(a,x2))) # label(goal) # label(non_clause) # label(goal). [goal].
20.082/20.082
20.082/20.082 ============================== end of process non-clausal formulas ===
20.082/20.082
20.082/20.082 ============================== CLAUSES FOR SEARCH ====================
20.082/20.082
20.082/20.082 formulas(mace4_clauses).
20.082/20.082 -->(x,y) | ->(f(x),f(y)) # label(congruence).
20.082/20.082 ->*(x,x) # label(reflexivity).
20.082/20.082 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.082/20.082 -->*(b,x) | -->*(a,x) # label(goal).
20.082/20.082 end_of_list.
20.082/20.082
20.082/20.082 ============================== end of clauses for search =============
20.082/20.082
20.082/20.082 % There are no natural numbers in the input.
20.082/20.082
20.082/20.082 ============================== DOMAIN SIZE 2 =========================
20.082/20.082
20.082/20.082 ============================== MODEL =================================
20.082/20.082
20.082/20.082 interpretation( 2, [number=1, seconds=0], [
20.082/20.082
20.082/20.082 function(a, [ 0 ]),
20.082/20.082
20.082/20.082 function(b, [ 1 ]),
20.082/20.082
20.082/20.082 function(f(_), [ 0, 0 ]),
20.082/20.082
20.082/20.082 relation(->*(_,_), [
20.082/20.082 1, 0,
20.082/20.082 0, 1 ]),
20.082/20.082
20.082/20.082 relation(->(_,_), [
20.082/20.082 0, 0,
20.082/20.082 0, 0 ])
20.082/20.082 ]).
20.082/20.082
20.082/20.082 ============================== end of model ==========================
20.082/20.082
20.082/20.082 ============================== STATISTICS ============================
20.082/20.082
20.082/20.082 For domain size 2.
20.082/20.082
20.082/20.082 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.082/20.082 Ground clauses: seen=16, kept=12.
20.082/20.082 Selections=4, assignments=4, propagations=8, current_models=1.
20.082/20.082 Rewrite_terms=12, rewrite_bools=20, indexes=3.
20.082/20.082 Rules_from_neg_clauses=1, cross_offs=1.
20.082/20.082
20.082/20.082 ============================== end of statistics =====================
20.082/20.082
20.082/20.082 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.082/20.082
20.082/20.082 Exiting with 1 model.
20.082/20.082
20.082/20.082 Process 117359 exit (max_models) Fri Jul 16 15:29:13 2021
20.082/20.082 The process finished Fri Jul 16 15:29:13 2021
20.082/20.082
20.082/20.082
20.082/20.082 Mace4 cooked interpretation:
20.082/20.082
20.082/20.082
20.082/20.082
20.082/20.082 The problem is infeasible.
20.082/20.082
20.082/20.082
20.082/20.082
20.082/20.082
20.082/20.082 -> Problem conclusions:
20.082/20.082 Left linear, Right linear, Linear
20.082/20.082 Weakly orthogonal, Almost orthogonal, Orthogonal
20.082/20.082 CTRS Type: 1
20.082/20.082 Deterministic, Strongly deterministic
20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS
20.082/20.082 Maybe right-stable CTRS, Overlay CTRS
20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS
20.082/20.082 Maybe terminating CTRS, Joinable CCPs
20.082/20.082 Maybe level confluent
20.082/20.082 Maybe confluent
20.082/20.082
20.082/20.082 Resulting CCPs:
20.082/20.082 No CCPs left
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082 Underlying TRS Termination Processor:
20.082/20.082
20.082/20.082 Resulting Underlying TRS:
20.082/20.082 (VAR x:S)
20.082/20.082 (STRATEGY CONTEXTSENSITIVE
20.082/20.082 (f 1)
20.082/20.082 (a)
20.082/20.082 (b)
20.082/20.082 )
20.082/20.082 (RULES
20.082/20.082 f(x:S) -> a
20.082/20.082 f(x:S) -> b
20.082/20.082 )
20.082/20.082 Underlying TRS terminating?
20.082/20.082 YES
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 (VAR vu95NonEmpty:S xu58S:S)
20.082/20.082 (RULES
20.082/20.082 f(xu58S:S) -> a
20.082/20.082 f(xu58S:S) -> b
20.082/20.082 )
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 Dependency Pairs Processor:
20.082/20.082 -> Pairs:
20.082/20.082 Empty
20.082/20.082 -> Rules:
20.082/20.082 f(xu58S:S) -> a
20.082/20.082 f(xu58S:S) -> b
20.082/20.082
20.082/20.082 Problem 1:
20.082/20.082
20.082/20.082 SCC Processor:
20.082/20.082 -> Pairs:
20.082/20.082 Empty
20.082/20.082 -> Rules:
20.082/20.082 f(xu58S:S) -> a
20.082/20.082 f(xu58S:S) -> b
20.082/20.082 ->Strongly Connected Components:
20.082/20.082 There is no strongly connected component
20.082/20.082
20.082/20.082 The problem is finite.
20.082/20.082
20.082/20.082
20.082/20.082 -> Problem conclusions:
20.082/20.082 Left linear, Right linear, Linear
20.082/20.082 Weakly orthogonal, Almost orthogonal, Orthogonal
20.082/20.082 CTRS Type: 1
20.082/20.082 Deterministic, Strongly deterministic
20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS
20.082/20.082 Maybe right-stable CTRS, Overlay CTRS
20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS
20.082/20.082 Terminating CTRS, Joinable CCPs
20.082/20.082 Maybe level confluent
20.082/20.082 Confluent
20.082/20.082
20.082/20.082 The problem is joinable.
20.082/20.082 41.63user 1.10system 0:20.82elapsed 205%CPU (0avgtext+0avgdata 135808maxresident)k
20.082/20.082 8inputs+0outputs (0major+144552minor)pagefaults 0swaps