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