20.041/20.041 YES
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041 Confluence Problem:
20.041/20.041 (VAR vNonEmpty x)
20.041/20.041 (REPLACEMENT-MAP
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Inlining of Conditions Processor [STERN17]:
20.041/20.041
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041 Confluence Problem:
20.041/20.041 (VAR vNonEmpty x)
20.041/20.041 (REPLACEMENT-MAP
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Clean CTRS Processor:
20.041/20.041
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041 Confluence Problem:
20.041/20.041 (VAR x)
20.041/20.041 (REPLACEMENT-MAP
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041
20.041/20.041 CRule InfChecker Info:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 Rule remains
20.041/20.041 Proof:
20.041/20.041 NO
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Infeasibility Problem:
20.041/20.041 [(VAR vNonEmpty x vNonEmpty x)
20.041/20.041 (STRATEGY CONTEXTSENSITIVE
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )]
20.041/20.041
20.041/20.041 Infeasibility Conditions:
20.041/20.041 a ->* x
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Obtaining a proof using Prover9:
20.041/20.041
20.041/20.041 -> Prover9 Output:
20.041/20.041 ============================== Prover9 ===============================
20.041/20.041 Prover9 (64) version 2009-11A, November 2009.
20.041/20.041 Process 74397 was started by ubuntu on ubuntu,
20.041/20.041 Wed Mar 9 10:08:25 2022
20.041/20.041 The command was "./prover9 -f /tmp/prover974388-0.in".
20.041/20.041 ============================== end of head ===========================
20.041/20.041
20.041/20.041 ============================== INPUT =================================
20.041/20.041
20.041/20.041 % Reading from file /tmp/prover974388-0.in
20.041/20.041
20.041/20.041 assign(max_seconds,20).
20.041/20.041
20.041/20.041 formulas(assumptions).
20.041/20.041 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
20.041/20.041 ->*_s0(x,x) # label(reflexivity).
20.041/20.041 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(goals).
20.041/20.041 (exists x3 ->*_s0(a,x3)) # label(goal).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== end of input ==========================
20.041/20.041
20.041/20.041 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.041/20.041
20.041/20.041 % Formulas that are not ordinary clauses:
20.041/20.041 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.041/20.041 2 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
20.041/20.041 3 (exists x3 ->*_s0(a,x3)) # label(goal) # label(non_clause) # label(goal). [goal].
20.041/20.041
20.041/20.041 ============================== end of process non-clausal formulas ===
20.041/20.041
20.041/20.041 ============================== PROCESS INITIAL CLAUSES ===============
20.041/20.041
20.041/20.041 % Clauses before input processing:
20.041/20.041
20.041/20.041 formulas(usable).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(sos).
20.041/20.041 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)].
20.041/20.041 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(2)].
20.041/20.041 -->*_s0(a,x) # label(goal). [deny(3)].
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(demodulators).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== PREDICATE ELIMINATION =================
20.041/20.041
20.041/20.041 No predicates eliminated.
20.041/20.041
20.041/20.041 ============================== end predicate elimination =============
20.041/20.041
20.041/20.041 Auto_denials:
20.041/20.041 % copying label goal to answer in negative clause
20.041/20.041
20.041/20.041 Term ordering decisions:
20.041/20.041 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
20.041/20.041 Function symbol precedence: function_order([ a, f ]).
20.041/20.041 After inverse_order: (no changes).
20.041/20.041 Unfolding symbols: (none).
20.041/20.041
20.041/20.041 Auto_inference settings:
20.041/20.041 % set(neg_binary_resolution). % (HNE depth_diff=-1)
20.041/20.041 % clear(ordered_res). % (HNE depth_diff=-1)
20.041/20.041 % set(ur_resolution). % (HNE depth_diff=-1)
20.041/20.041 % set(ur_resolution) -> set(pos_ur_resolution).
20.041/20.041 % set(ur_resolution) -> set(neg_ur_resolution).
20.041/20.041
20.041/20.041 Auto_process settings: (no changes).
20.041/20.041
20.041/20.041 kept: 4 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)].
20.041/20.041 kept: 5 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 kept: 6 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(2)].
20.041/20.041 kept: 7 -->*_s0(a,x) # label(goal) # answer(goal). [deny(3)].
20.041/20.041
20.041/20.041 ============================== PROOF =================================
20.041/20.041
20.041/20.041 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
20.041/20.041 % Length of proof is 4.
20.041/20.041 % Level of proof is 2.
20.041/20.041 % Maximum clause weight is 3.000.
20.041/20.041 % Given clauses 0.
20.041/20.041
20.041/20.041 3 (exists x3 ->*_s0(a,x3)) # label(goal) # label(non_clause) # label(goal). [goal].
20.041/20.041 5 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 7 -->*_s0(a,x) # label(goal) # answer(goal). [deny(3)].
20.041/20.041 8 $F # answer(goal). [resolve(7,a,5,a)].
20.041/20.041
20.041/20.041 ============================== end of proof ==========================
20.041/20.041
20.041/20.041 ============================== STATISTICS ============================
20.041/20.041
20.041/20.041 Given=0. Generated=4. Kept=4. proofs=1.
20.041/20.041 Usable=0. Sos=0. Demods=0. Limbo=3, Disabled=4. Hints=0.
20.041/20.041 Kept_by_rule=0, Deleted_by_rule=0.
20.041/20.041 Forward_subsumed=0. Back_subsumed=0.
20.041/20.041 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
20.041/20.041 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
20.041/20.041 Demod_attempts=0. Demod_rewrites=0.
20.041/20.041 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
20.041/20.041 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
20.041/20.041 Megabytes=0.03.
20.041/20.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.041/20.041
20.041/20.041 ============================== end of statistics =====================
20.041/20.041
20.041/20.041 ============================== end of search =========================
20.041/20.041
20.041/20.041 THEOREM PROVED
20.041/20.041
20.041/20.041 Exiting with 1 proof.
20.041/20.041
20.041/20.041 Process 74397 exit (max_proofs) Wed Mar 9 10:08:25 2022
20.041/20.041
20.041/20.041
20.041/20.041 The problem is feasible.
20.041/20.041
20.041/20.041
20.041/20.041 CRule InfChecker Info:
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 Rule remains
20.041/20.041 Proof:
20.041/20.041 NO
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Infeasibility Problem:
20.041/20.041 [(VAR vNonEmpty x vNonEmpty x)
20.041/20.041 (STRATEGY CONTEXTSENSITIVE
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )]
20.041/20.041
20.041/20.041 Infeasibility Conditions:
20.041/20.041 b ->* x
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Obtaining a proof using Prover9:
20.041/20.041
20.041/20.041 -> Prover9 Output:
20.041/20.041 ============================== Prover9 ===============================
20.041/20.041 Prover9 (64) version 2009-11A, November 2009.
20.041/20.041 Process 74420 was started by ubuntu on ubuntu,
20.041/20.041 Wed Mar 9 10:08:25 2022
20.041/20.041 The command was "./prover9 -f /tmp/prover974411-0.in".
20.041/20.041 ============================== end of head ===========================
20.041/20.041
20.041/20.041 ============================== INPUT =================================
20.041/20.041
20.041/20.041 % Reading from file /tmp/prover974411-0.in
20.041/20.041
20.041/20.041 assign(max_seconds,20).
20.041/20.041
20.041/20.041 formulas(assumptions).
20.041/20.041 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
20.041/20.041 ->*_s0(x,x) # label(reflexivity).
20.041/20.041 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(goals).
20.041/20.041 (exists x3 ->*_s0(b,x3)) # label(goal).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== end of input ==========================
20.041/20.041
20.041/20.041 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.041/20.041
20.041/20.041 % Formulas that are not ordinary clauses:
20.041/20.041 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.041/20.041 2 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
20.041/20.041 3 (exists x3 ->*_s0(b,x3)) # label(goal) # label(non_clause) # label(goal). [goal].
20.041/20.041
20.041/20.041 ============================== end of process non-clausal formulas ===
20.041/20.041
20.041/20.041 ============================== PROCESS INITIAL CLAUSES ===============
20.041/20.041
20.041/20.041 % Clauses before input processing:
20.041/20.041
20.041/20.041 formulas(usable).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(sos).
20.041/20.041 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)].
20.041/20.041 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(2)].
20.041/20.041 -->*_s0(b,x) # label(goal). [deny(3)].
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(demodulators).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== PREDICATE ELIMINATION =================
20.041/20.041
20.041/20.041 No predicates eliminated.
20.041/20.041
20.041/20.041 ============================== end predicate elimination =============
20.041/20.041
20.041/20.041 Auto_denials:
20.041/20.041 % copying label goal to answer in negative clause
20.041/20.041
20.041/20.041 Term ordering decisions:
20.041/20.041 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
20.041/20.041 Function symbol precedence: function_order([ b, f ]).
20.041/20.041 After inverse_order: (no changes).
20.041/20.041 Unfolding symbols: (none).
20.041/20.041
20.041/20.041 Auto_inference settings:
20.041/20.041 % set(neg_binary_resolution). % (HNE depth_diff=-1)
20.041/20.041 % clear(ordered_res). % (HNE depth_diff=-1)
20.041/20.041 % set(ur_resolution). % (HNE depth_diff=-1)
20.041/20.041 % set(ur_resolution) -> set(pos_ur_resolution).
20.041/20.041 % set(ur_resolution) -> set(neg_ur_resolution).
20.041/20.041
20.041/20.041 Auto_process settings: (no changes).
20.041/20.041
20.041/20.041 kept: 4 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)].
20.041/20.041 kept: 5 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 kept: 6 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(2)].
20.041/20.041 kept: 7 -->*_s0(b,x) # label(goal) # answer(goal). [deny(3)].
20.041/20.041
20.041/20.041 ============================== PROOF =================================
20.041/20.041
20.041/20.041 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
20.041/20.041 % Length of proof is 4.
20.041/20.041 % Level of proof is 2.
20.041/20.041 % Maximum clause weight is 3.000.
20.041/20.041 % Given clauses 0.
20.041/20.041
20.041/20.041 3 (exists x3 ->*_s0(b,x3)) # label(goal) # label(non_clause) # label(goal). [goal].
20.041/20.041 5 ->*_s0(x,x) # label(reflexivity). [assumption].
20.041/20.041 7 -->*_s0(b,x) # label(goal) # answer(goal). [deny(3)].
20.041/20.041 8 $F # answer(goal). [resolve(7,a,5,a)].
20.041/20.041
20.041/20.041 ============================== end of proof ==========================
20.041/20.041
20.041/20.041 ============================== STATISTICS ============================
20.041/20.041
20.041/20.041 Given=0. Generated=4. Kept=4. proofs=1.
20.041/20.041 Usable=0. Sos=0. Demods=0. Limbo=3, Disabled=4. Hints=0.
20.041/20.041 Kept_by_rule=0, Deleted_by_rule=0.
20.041/20.041 Forward_subsumed=0. Back_subsumed=0.
20.041/20.041 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
20.041/20.041 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
20.041/20.041 Demod_attempts=0. Demod_rewrites=0.
20.041/20.041 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
20.041/20.041 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
20.041/20.041 Megabytes=0.03.
20.041/20.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.041/20.041
20.041/20.041 ============================== end of statistics =====================
20.041/20.041
20.041/20.041 ============================== end of search =========================
20.041/20.041
20.041/20.041 THEOREM PROVED
20.041/20.041
20.041/20.041 Exiting with 1 proof.
20.041/20.041
20.041/20.041 Process 74420 exit (max_proofs) Wed Mar 9 10:08:25 2022
20.041/20.041
20.041/20.041
20.041/20.041 The problem is feasible.
20.041/20.041
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041 Confluence Problem:
20.041/20.041 (VAR x)
20.041/20.041 (REPLACEMENT-MAP
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )
20.041/20.041 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.041/20.041
20.041/20.041 Critical Pairs Processor:
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 -> Vars:
20.041/20.041 "x"
20.041/20.041
20.041/20.041 -> Rlps:
20.041/20.041 crule: f(x) -> a | a ->* x, id: 1, possubterms: f(x)-> []
20.041/20.041 crule: f(x) -> b | b ->* x, id: 2, possubterms: f(x)-> []
20.041/20.041
20.041/20.041 -> Unifications:
20.041/20.041 R2 unifies with R1 at p: [], l: f(x), lp: f(x), conds: {b ->* x, a ->* x'}, sig: {x -> x'}, l': f(x'), r: b, r': a
20.041/20.041
20.041/20.041 -> Critical pairs info:
20.041/20.041 | b ->* x', a ->* x' => Not trivial, Overlay, NW2, N1
20.041/20.041
20.041/20.041 -> Problem conclusions:
20.041/20.041 Left linear, Right linear, Linear
20.041/20.041 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
20.041/20.041 CTRS Type: 1
20.041/20.041 Deterministic, Strongly deterministic
20.041/20.041 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS
20.041/20.041 Maybe right-stable CTRS, Overlay CTRS
20.041/20.041 Maybe normal CTRS, Maybe almost normal CTRS
20.041/20.041 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs
20.041/20.041 Maybe level confluent
20.041/20.041 Maybe confluent
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041 Clean Infeasible CCPs Processor:
20.041/20.041 Num of CPIs: 1
20.041/20.041 Timeout: 60
20.041/20.041 Timeout for each infeasibility problem: 60 s
20.041/20.041 | b ->* x', a ->* x' => Not trivial, Overlay, NW2, N1
20.041/20.041 (CONDITIONTYPE ORIENTED)
20.041/20.041 (VAR x x1)
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x)
20.041/20.041 (VAR x4)
20.041/20.041 (CONDITION b ->* x4, a ->* x4)
20.041/20.041
20.041/20.041 Proof:
20.041/20.041 YES
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Infeasibility Problem:
20.041/20.041 [(VAR vNonEmpty x x1 vNonEmpty x4)
20.041/20.041 (STRATEGY CONTEXTSENSITIVE
20.041/20.041 (f 1)
20.041/20.041 (a)
20.041/20.041 (b)
20.041/20.041 (fSNonEmpty)
20.041/20.041 )
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )]
20.041/20.041
20.041/20.041 Infeasibility Conditions:
20.041/20.041 b ->* x4, a ->* x4
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 Obtaining a model using Mace4:
20.041/20.041
20.041/20.041 -> Usable Rules:
20.041/20.041 Empty
20.041/20.041
20.041/20.041 -> Mace4 Output:
20.041/20.041 ============================== Mace4 =================================
20.041/20.041 Mace4 (64) version 2009-11A, November 2009.
20.041/20.041 Process 74454 was started by ubuntu on ubuntu,
20.041/20.041 Wed Mar 9 10:08:25 2022
20.041/20.041 The command was "./mace4 -c -f /tmp/mace474439-2.in".
20.041/20.041 ============================== end of head ===========================
20.041/20.041
20.041/20.041 ============================== INPUT =================================
20.041/20.041
20.041/20.041 % Reading from file /tmp/mace474439-2.in
20.041/20.041
20.041/20.041 assign(max_seconds,20).
20.041/20.041
20.041/20.041 formulas(assumptions).
20.041/20.041 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.041/20.041 ->*(x,x) # label(reflexivity).
20.041/20.041 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 formulas(goals).
20.041/20.041 (exists x4 (->*(b,x4) & ->*(a,x4))) # label(goal).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== end of input ==========================
20.041/20.041
20.041/20.041 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.041/20.041
20.041/20.041 % Formulas that are not ordinary clauses:
20.041/20.041 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
20.041/20.041 2 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption].
20.041/20.041 3 (exists x4 (->*(b,x4) & ->*(a,x4))) # label(goal) # label(non_clause) # label(goal). [goal].
20.041/20.041
20.041/20.041 ============================== end of process non-clausal formulas ===
20.041/20.041
20.041/20.041 ============================== CLAUSES FOR SEARCH ====================
20.041/20.041
20.041/20.041 formulas(mace4_clauses).
20.041/20.041 -->(x,y) | ->(f(x),f(y)) # label(congruence).
20.041/20.041 ->*(x,x) # label(reflexivity).
20.041/20.041 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.041/20.041 -->*(b,x) | -->*(a,x) # label(goal).
20.041/20.041 end_of_list.
20.041/20.041
20.041/20.041 ============================== end of clauses for search =============
20.041/20.041
20.041/20.041 % There are no natural numbers in the input.
20.041/20.041
20.041/20.041 ============================== DOMAIN SIZE 2 =========================
20.041/20.041
20.041/20.041 ============================== MODEL =================================
20.041/20.041
20.041/20.041 interpretation( 2, [number=1, seconds=0], [
20.041/20.041
20.041/20.041 function(a, [ 0 ]),
20.041/20.041
20.041/20.041 function(b, [ 1 ]),
20.041/20.041
20.041/20.041 function(f(_), [ 0, 0 ]),
20.041/20.041
20.041/20.041 relation(->*(_,_), [
20.041/20.041 1, 0,
20.041/20.041 0, 1 ]),
20.041/20.041
20.041/20.041 relation(->(_,_), [
20.041/20.041 0, 0,
20.041/20.041 0, 0 ])
20.041/20.041 ]).
20.041/20.041
20.041/20.041 ============================== end of model ==========================
20.041/20.041
20.041/20.041 ============================== STATISTICS ============================
20.041/20.041
20.041/20.041 For domain size 2.
20.041/20.041
20.041/20.041 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.041/20.041 Ground clauses: seen=16, kept=12.
20.041/20.041 Selections=4, assignments=4, propagations=8, current_models=1.
20.041/20.041 Rewrite_terms=12, rewrite_bools=20, indexes=3.
20.041/20.041 Rules_from_neg_clauses=1, cross_offs=1.
20.041/20.041
20.041/20.041 ============================== end of statistics =====================
20.041/20.041
20.041/20.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.041/20.041
20.041/20.041 Exiting with 1 model.
20.041/20.041
20.041/20.041 Process 74454 exit (max_models) Wed Mar 9 10:08:25 2022
20.041/20.041 The process finished Wed Mar 9 10:08:25 2022
20.041/20.041
20.041/20.041
20.041/20.041 Mace4 cooked interpretation:
20.041/20.041
20.041/20.041
20.041/20.041
20.041/20.041 The problem is infeasible.
20.041/20.041
20.041/20.041
20.041/20.041
20.041/20.041
20.041/20.041 -> Problem conclusions:
20.041/20.041 Left linear, Right linear, Linear
20.041/20.041 Weakly orthogonal, Almost orthogonal, Orthogonal
20.041/20.041 CTRS Type: 1
20.041/20.041 Deterministic, Strongly deterministic
20.041/20.041 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS
20.041/20.041 Maybe right-stable CTRS, Overlay CTRS
20.041/20.041 Maybe normal CTRS, Maybe almost normal CTRS
20.041/20.041 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs
20.041/20.041 Maybe level confluent
20.041/20.041 Maybe confluent
20.041/20.041
20.041/20.041 Resulting CCPs:
20.041/20.041 No CCPs left
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041 Operation Termination Processor:
20.041/20.041 Operational terminating?
20.041/20.041 YES
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 (VAR vu95NonEmpty x xu39)
20.041/20.041 (RULES
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 )
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041 Valid CTRS Processor:
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 -> The system is a deterministic 3-CTRS.
20.041/20.041
20.041/20.041 Problem 1:
20.041/20.041
20.041/20.041 2D Dependency Pair Processor:
20.041/20.041
20.041/20.041 Conditional Termination Problem 1:
20.041/20.041 -> Pairs:
20.041/20.041 Empty
20.041/20.041 -> QPairs:
20.041/20.041 Empty
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041
20.041/20.041 Conditional Termination Problem 2:
20.041/20.041 -> Pairs:
20.041/20.041 Empty
20.041/20.041 -> QPairs:
20.041/20.041 Empty
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041
20.041/20.041
20.041/20.041 The problem is decomposed in 2 subproblems.
20.041/20.041
20.041/20.041 Problem 1.1:
20.041/20.041
20.041/20.041 SCC Processor:
20.041/20.041 -> Pairs:
20.041/20.041 Empty
20.041/20.041 -> QPairs:
20.041/20.041 Empty
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 ->Strongly Connected Components:
20.041/20.041 There is no strongly connected component
20.041/20.041
20.041/20.041 The problem is finite.
20.041/20.041
20.041/20.041 Problem 1.2:
20.041/20.041
20.041/20.041 SCC Processor:
20.041/20.041 -> Pairs:
20.041/20.041 Empty
20.041/20.041 -> QPairs:
20.041/20.041 Empty
20.041/20.041 -> Rules:
20.041/20.041 f(x) -> a | a ->* x
20.041/20.041 f(x) -> b | b ->* x
20.041/20.041 ->Strongly Connected Components:
20.041/20.041 There is no strongly connected component
20.041/20.041
20.041/20.041 The problem is finite.
20.041/20.041
20.041/20.041
20.041/20.041 -> Problem conclusions:
20.041/20.041 Left linear, Right linear, Linear
20.041/20.041 Weakly orthogonal, Almost orthogonal, Orthogonal
20.041/20.041 CTRS Type: 1
20.041/20.041 Deterministic, Strongly deterministic
20.041/20.041 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS
20.041/20.041 Maybe right-stable CTRS, Overlay CTRS
20.041/20.041 Maybe normal CTRS, Maybe almost normal CTRS
20.041/20.041 Terminating CTRS, Operational terminating CTRS, Joinable CCPs
20.041/20.041 Maybe level confluent
20.041/20.041 Confluent
20.041/20.041
20.041/20.041 The problem is joinable.
20.041/20.041 41.79user 0.55system 0:20.41elapsed 207%CPU (0avgtext+0avgdata 130736maxresident)k
20.041/20.041 8inputs+0outputs (0major+83160minor)pagefaults 0swaps