25.022/25.022 YES
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022 Confluence Problem:
25.022/25.022 (VAR vNonEmpty:S x:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 )
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Inlining of Conditions Processor [STERN17]:
25.022/25.022
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022 Confluence Problem:
25.022/25.022 (VAR vNonEmpty:S x:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 )
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Clean CTRS Processor:
25.022/25.022
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022 Confluence Problem:
25.022/25.022 (VAR x:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 )
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022
25.022/25.022 CRule InfChecker Info:
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 Rule remains
25.022/25.022 Proof:
25.022/25.022 NO
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Infeasibility Problem:
25.022/25.022 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S:S) -> a | x:S:S ->* a
25.022/25.022 f(x:S:S) -> b | x:S:S ->* b
25.022/25.022 )]
25.022/25.022
25.022/25.022 Infeasibility Conditions:
25.022/25.022 x:S:S ->* a
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Obtaining a proof using Prover9:
25.022/25.022
25.022/25.022 -> Prover9 Output:
25.022/25.022 ============================== Prover9 ===============================
25.022/25.022 Prover9 (64) version 2009-11A, November 2009.
25.022/25.022 Process 59682 was started by ubuntu on ubuntu,
25.022/25.022 Wed Jul 14 11:31:52 2021
25.022/25.022 The command was "./prover9 -f /tmp/prover959673-0.in".
25.022/25.022 ============================== end of head ===========================
25.022/25.022
25.022/25.022 ============================== INPUT =================================
25.022/25.022
25.022/25.022 % Reading from file /tmp/prover959673-0.in
25.022/25.022
25.022/25.022 assign(max_seconds,20).
25.022/25.022
25.022/25.022 formulas(assumptions).
25.022/25.022 ->*_s0(x,x) # label(reflexivity).
25.022/25.022 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
25.022/25.022 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
25.022/25.022 ->*_s0(x2,a) -> ->_s0(f(x2),a) # label(replacement).
25.022/25.022 ->*_s0(x2,b) -> ->_s0(f(x2),b) # label(replacement).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(goals).
25.022/25.022 (exists x2 ->*_s0(x2,a)) # label(goal).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== end of input ==========================
25.022/25.022
25.022/25.022 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
25.022/25.022
25.022/25.022 % Formulas that are not ordinary clauses:
25.022/25.022 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
25.022/25.022 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
25.022/25.022 3 ->*_s0(x2,a) -> ->_s0(f(x2),a) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 4 ->*_s0(x2,b) -> ->_s0(f(x2),b) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 5 (exists x2 ->*_s0(x2,a)) # label(goal) # label(non_clause) # label(goal). [goal].
25.022/25.022
25.022/25.022 ============================== end of process non-clausal formulas ===
25.022/25.022
25.022/25.022 ============================== PROCESS INITIAL CLAUSES ===============
25.022/25.022
25.022/25.022 % Clauses before input processing:
25.022/25.022
25.022/25.022 formulas(usable).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(sos).
25.022/25.022 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
25.022/25.022 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
25.022/25.022 -->*_s0(x,a) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
25.022/25.022 -->*_s0(x,b) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
25.022/25.022 -->*_s0(x,a) # label(goal). [deny(5)].
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(demodulators).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== PREDICATE ELIMINATION =================
25.022/25.022
25.022/25.022 No predicates eliminated.
25.022/25.022
25.022/25.022 ============================== end predicate elimination =============
25.022/25.022
25.022/25.022 Auto_denials:
25.022/25.022 % copying label goal to answer in negative clause
25.022/25.022
25.022/25.022 Term ordering decisions:
25.022/25.022 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
25.022/25.022 Function symbol precedence: function_order([ a, b, f ]).
25.022/25.022 After inverse_order: (no changes).
25.022/25.022 Unfolding symbols: (none).
25.022/25.022
25.022/25.022 Auto_inference settings:
25.022/25.022 % set(neg_binary_resolution). % (HNE depth_diff=-3)
25.022/25.022 % clear(ordered_res). % (HNE depth_diff=-3)
25.022/25.022 % set(ur_resolution). % (HNE depth_diff=-3)
25.022/25.022 % set(ur_resolution) -> set(pos_ur_resolution).
25.022/25.022 % set(ur_resolution) -> set(neg_ur_resolution).
25.022/25.022
25.022/25.022 Auto_process settings: (no changes).
25.022/25.022
25.022/25.022 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
25.022/25.022 kept: 8 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
25.022/25.022 kept: 9 -->*_s0(x,a) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
25.022/25.022 kept: 10 -->*_s0(x,b) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
25.022/25.022 kept: 11 -->*_s0(x,a) # label(goal) # answer(goal). [deny(5)].
25.022/25.022
25.022/25.022 ============================== PROOF =================================
25.022/25.022
25.022/25.022 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
25.022/25.022 % Length of proof is 4.
25.022/25.022 % Level of proof is 2.
25.022/25.022 % Maximum clause weight is 3.000.
25.022/25.022 % Given clauses 0.
25.022/25.022
25.022/25.022 5 (exists x2 ->*_s0(x2,a)) # label(goal) # label(non_clause) # label(goal). [goal].
25.022/25.022 6 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 11 -->*_s0(x,a) # label(goal) # answer(goal). [deny(5)].
25.022/25.022 12 $F # answer(goal). [resolve(11,a,6,a)].
25.022/25.022
25.022/25.022 ============================== end of proof ==========================
25.022/25.022
25.022/25.022 ============================== STATISTICS ============================
25.022/25.022
25.022/25.022 Given=0. Generated=6. Kept=6. proofs=1.
25.022/25.022 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0.
25.022/25.022 Kept_by_rule=0, Deleted_by_rule=0.
25.022/25.022 Forward_subsumed=0. Back_subsumed=0.
25.022/25.022 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
25.022/25.022 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
25.022/25.022 Demod_attempts=0. Demod_rewrites=0.
25.022/25.022 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
25.022/25.022 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
25.022/25.022 Megabytes=0.04.
25.022/25.022 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
25.022/25.022
25.022/25.022 ============================== end of statistics =====================
25.022/25.022
25.022/25.022 ============================== end of search =========================
25.022/25.022
25.022/25.022 THEOREM PROVED
25.022/25.022
25.022/25.022 Exiting with 1 proof.
25.022/25.022
25.022/25.022 Process 59682 exit (max_proofs) Wed Jul 14 11:31:52 2021
25.022/25.022
25.022/25.022
25.022/25.022 The problem is feasible.
25.022/25.022
25.022/25.022
25.022/25.022 CRule InfChecker Info:
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 Rule remains
25.022/25.022 Proof:
25.022/25.022 NO
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Infeasibility Problem:
25.022/25.022 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S:S) -> a | x:S:S ->* a
25.022/25.022 f(x:S:S) -> b | x:S:S ->* b
25.022/25.022 )]
25.022/25.022
25.022/25.022 Infeasibility Conditions:
25.022/25.022 x:S:S ->* b
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Obtaining a proof using Prover9:
25.022/25.022
25.022/25.022 -> Prover9 Output:
25.022/25.022 ============================== Prover9 ===============================
25.022/25.022 Prover9 (64) version 2009-11A, November 2009.
25.022/25.022 Process 59704 was started by ubuntu on ubuntu,
25.022/25.022 Wed Jul 14 11:31:52 2021
25.022/25.022 The command was "./prover9 -f /tmp/prover959694-0.in".
25.022/25.022 ============================== end of head ===========================
25.022/25.022
25.022/25.022 ============================== INPUT =================================
25.022/25.022
25.022/25.022 % Reading from file /tmp/prover959694-0.in
25.022/25.022
25.022/25.022 assign(max_seconds,20).
25.022/25.022
25.022/25.022 formulas(assumptions).
25.022/25.022 ->*_s0(x,x) # label(reflexivity).
25.022/25.022 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
25.022/25.022 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence).
25.022/25.022 ->*_s0(x2,a) -> ->_s0(f(x2),a) # label(replacement).
25.022/25.022 ->*_s0(x2,b) -> ->_s0(f(x2),b) # label(replacement).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(goals).
25.022/25.022 (exists x2 ->*_s0(x2,b)) # label(goal).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== end of input ==========================
25.022/25.022
25.022/25.022 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
25.022/25.022
25.022/25.022 % Formulas that are not ordinary clauses:
25.022/25.022 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
25.022/25.022 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
25.022/25.022 3 ->*_s0(x2,a) -> ->_s0(f(x2),a) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 4 ->*_s0(x2,b) -> ->_s0(f(x2),b) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 5 (exists x2 ->*_s0(x2,b)) # label(goal) # label(non_clause) # label(goal). [goal].
25.022/25.022
25.022/25.022 ============================== end of process non-clausal formulas ===
25.022/25.022
25.022/25.022 ============================== PROCESS INITIAL CLAUSES ===============
25.022/25.022
25.022/25.022 % Clauses before input processing:
25.022/25.022
25.022/25.022 formulas(usable).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(sos).
25.022/25.022 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
25.022/25.022 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
25.022/25.022 -->*_s0(x,a) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
25.022/25.022 -->*_s0(x,b) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
25.022/25.022 -->*_s0(x,b) # label(goal). [deny(5)].
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(demodulators).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== PREDICATE ELIMINATION =================
25.022/25.022
25.022/25.022 No predicates eliminated.
25.022/25.022
25.022/25.022 ============================== end predicate elimination =============
25.022/25.022
25.022/25.022 Auto_denials:
25.022/25.022 % copying label goal to answer in negative clause
25.022/25.022
25.022/25.022 Term ordering decisions:
25.022/25.022 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]).
25.022/25.022 Function symbol precedence: function_order([ a, b, f ]).
25.022/25.022 After inverse_order: (no changes).
25.022/25.022 Unfolding symbols: (none).
25.022/25.022
25.022/25.022 Auto_inference settings:
25.022/25.022 % set(neg_binary_resolution). % (HNE depth_diff=-3)
25.022/25.022 % clear(ordered_res). % (HNE depth_diff=-3)
25.022/25.022 % set(ur_resolution). % (HNE depth_diff=-3)
25.022/25.022 % set(ur_resolution) -> set(pos_ur_resolution).
25.022/25.022 % set(ur_resolution) -> set(neg_ur_resolution).
25.022/25.022
25.022/25.022 Auto_process settings: (no changes).
25.022/25.022
25.022/25.022 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)].
25.022/25.022 kept: 8 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)].
25.022/25.022 kept: 9 -->*_s0(x,a) | ->_s0(f(x),a) # label(replacement). [clausify(3)].
25.022/25.022 kept: 10 -->*_s0(x,b) | ->_s0(f(x),b) # label(replacement). [clausify(4)].
25.022/25.022 kept: 11 -->*_s0(x,b) # label(goal) # answer(goal). [deny(5)].
25.022/25.022
25.022/25.022 ============================== PROOF =================================
25.022/25.022
25.022/25.022 % Proof 1 at 0.00 (+ 0.00) seconds: goal.
25.022/25.022 % Length of proof is 4.
25.022/25.022 % Level of proof is 2.
25.022/25.022 % Maximum clause weight is 3.000.
25.022/25.022 % Given clauses 0.
25.022/25.022
25.022/25.022 5 (exists x2 ->*_s0(x2,b)) # label(goal) # label(non_clause) # label(goal). [goal].
25.022/25.022 6 ->*_s0(x,x) # label(reflexivity). [assumption].
25.022/25.022 11 -->*_s0(x,b) # label(goal) # answer(goal). [deny(5)].
25.022/25.022 12 $F # answer(goal). [resolve(11,a,6,a)].
25.022/25.022
25.022/25.022 ============================== end of proof ==========================
25.022/25.022
25.022/25.022 ============================== STATISTICS ============================
25.022/25.022
25.022/25.022 Given=0. Generated=6. Kept=6. proofs=1.
25.022/25.022 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0.
25.022/25.022 Kept_by_rule=0, Deleted_by_rule=0.
25.022/25.022 Forward_subsumed=0. Back_subsumed=0.
25.022/25.022 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
25.022/25.022 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
25.022/25.022 Demod_attempts=0. Demod_rewrites=0.
25.022/25.022 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
25.022/25.022 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
25.022/25.022 Megabytes=0.04.
25.022/25.022 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
25.022/25.022
25.022/25.022 ============================== end of statistics =====================
25.022/25.022
25.022/25.022 ============================== end of search =========================
25.022/25.022
25.022/25.022 THEOREM PROVED
25.022/25.022
25.022/25.022 Exiting with 1 proof.
25.022/25.022
25.022/25.022 Process 59704 exit (max_proofs) Wed Jul 14 11:31:52 2021
25.022/25.022
25.022/25.022
25.022/25.022 The problem is feasible.
25.022/25.022
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022 Confluence Problem:
25.022/25.022 (VAR x:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 )
25.022/25.022 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.022/25.022
25.022/25.022 Critical Pairs Processor:
25.022/25.022 -> Rules:
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 -> Vars:
25.022/25.022 "x", "x"
25.022/25.022 -> FVars:
25.022/25.022 "x2", "x3"
25.022/25.022 -> PVars:
25.022/25.022 "x": ["x2", "x3"]
25.022/25.022
25.022/25.022 -> Rlps:
25.022/25.022 crule: f(x2:S) -> a | x2:S ->* a, id: 1, possubterms: f(x2:S)-> []
25.022/25.022 crule: f(x3:S) -> b | x3:S ->* b, id: 2, possubterms: f(x3:S)-> []
25.022/25.022
25.022/25.022 -> Unifications:
25.022/25.022 R2 unifies with R1 at p: [], l: f(x3:S), lp: f(x3:S), conds: {x3:S ->* b, x:S ->* a}, sig: {x3:S -> x:S}, l': f(x:S), r: b, r': a
25.022/25.022
25.022/25.022 -> Critical pairs info:
25.022/25.022 | x:S ->* b, x:S ->* a => Not trivial, Overlay, N1
25.022/25.022
25.022/25.022 -> Problem conclusions:
25.022/25.022 Left linear, Right linear, Linear
25.022/25.022 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
25.022/25.022 CTRS Type: 1
25.022/25.022 Deterministic, Strongly deterministic
25.022/25.022 Oriented CTRS, Properly oriented CTRS, Not join CTRS
25.022/25.022 Maybe right-stable CTRS, Overlay CTRS
25.022/25.022 Maybe normal CTRS, Maybe almost normal CTRS
25.022/25.022 Maybe terminating CTRS, Maybe joinable CCPs
25.022/25.022 Maybe level confluent
25.022/25.022 Maybe confluent
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022 Clean Infeasible CCPs Processor:
25.022/25.022 Num of CPIs: 1
25.022/25.022 Timeout: 60
25.022/25.022 Timeout for each infeasibility problem: 60 s
25.022/25.022 | x:S ->* b, x:S ->* a => Not trivial, Overlay, N1
25.022/25.022 (PROBLEM INFEASIBILITY)
25.022/25.022 (VAR x)
25.022/25.022 (RULES
25.022/25.022 f(x) -> a | x ->* a
25.022/25.022 f(x) -> b | x ->* b)
25.022/25.022 (VAR x2)
25.022/25.022 (CONDITION x2 ->* b, x2 ->* a)
25.022/25.022
25.022/25.022 Proof:
25.022/25.022 YES
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Infeasibility Problem:
25.022/25.022 [(VAR vNonEmpty:S x:S x2:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 (fSNonEmpty)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022 )]
25.022/25.022
25.022/25.022 Infeasibility Conditions:
25.022/25.022 x2:S ->* b, x2:S ->* a
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Obtaining a model using Mace4:
25.022/25.022
25.022/25.022 -> Usable Rules:
25.022/25.022 f(x:S) -> a | x:S ->* a
25.022/25.022 f(x:S) -> b | x:S ->* b
25.022/25.022
25.022/25.022 -> Mace4 Output:
25.022/25.022 ============================== Mace4 =================================
25.022/25.022 Mace4 (64) version 2009-11A, November 2009.
25.022/25.022 Process 59751 was started by ubuntu on ubuntu,
25.022/25.022 Wed Jul 14 11:31:52 2021
25.022/25.022 The command was "./mace4 -c -f /tmp/mace459733-2.in".
25.022/25.022 ============================== end of head ===========================
25.022/25.022
25.022/25.022 ============================== INPUT =================================
25.022/25.022
25.022/25.022 % Reading from file /tmp/mace459733-2.in
25.022/25.022
25.022/25.022 assign(max_seconds,20).
25.022/25.022
25.022/25.022 formulas(assumptions).
25.022/25.022 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
25.022/25.022 ->*(x1,a) -> ->(f(x1),a) # label(replacement).
25.022/25.022 ->*(x1,b) -> ->(f(x1),b) # label(replacement).
25.022/25.022 ->*(x,x) # label(reflexivity).
25.022/25.022 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 formulas(goals).
25.022/25.022 (exists x2 (->*(x2,b) & ->*(x2,a))) # label(goal).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== end of input ==========================
25.022/25.022
25.022/25.022 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
25.022/25.022
25.022/25.022 % Formulas that are not ordinary clauses:
25.022/25.022 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption].
25.022/25.022 2 ->*(x1,a) -> ->(f(x1),a) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 3 ->*(x1,b) -> ->(f(x1),b) # label(replacement) # label(non_clause). [assumption].
25.022/25.022 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption].
25.022/25.022 5 (exists x2 (->*(x2,b) & ->*(x2,a))) # label(goal) # label(non_clause) # label(goal). [goal].
25.022/25.022
25.022/25.022 ============================== end of process non-clausal formulas ===
25.022/25.022
25.022/25.022 ============================== CLAUSES FOR SEARCH ====================
25.022/25.022
25.022/25.022 formulas(mace4_clauses).
25.022/25.022 -->(x,y) | ->(f(x),f(y)) # label(congruence).
25.022/25.022 -->*(x,a) | ->(f(x),a) # label(replacement).
25.022/25.022 -->*(x,b) | ->(f(x),b) # label(replacement).
25.022/25.022 ->*(x,x) # label(reflexivity).
25.022/25.022 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
25.022/25.022 -->*(x,b) | -->*(x,a) # label(goal).
25.022/25.022 end_of_list.
25.022/25.022
25.022/25.022 ============================== end of clauses for search =============
25.022/25.022
25.022/25.022 % There are no natural numbers in the input.
25.022/25.022
25.022/25.022 ============================== DOMAIN SIZE 2 =========================
25.022/25.022
25.022/25.022 ============================== MODEL =================================
25.022/25.022
25.022/25.022 interpretation( 2, [number=1, seconds=0], [
25.022/25.022
25.022/25.022 function(a, [ 0 ]),
25.022/25.022
25.022/25.022 function(b, [ 1 ]),
25.022/25.022
25.022/25.022 function(f(_), [ 0, 1 ]),
25.022/25.022
25.022/25.022 relation(->*(_,_), [
25.022/25.022 1, 0,
25.022/25.022 0, 1 ]),
25.022/25.022
25.022/25.022 relation(->(_,_), [
25.022/25.022 1, 0,
25.022/25.022 0, 1 ])
25.022/25.022 ]).
25.022/25.022
25.022/25.022 ============================== end of model ==========================
25.022/25.022
25.022/25.022 ============================== STATISTICS ============================
25.022/25.022
25.022/25.022 For domain size 2.
25.022/25.022
25.022/25.022 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
25.022/25.022 Ground clauses: seen=20, kept=16.
25.022/25.022 Selections=1, assignments=1, propagations=11, current_models=1.
25.022/25.022 Rewrite_terms=24, rewrite_bools=25, indexes=6.
25.022/25.022 Rules_from_neg_clauses=3, cross_offs=3.
25.022/25.022
25.022/25.022 ============================== end of statistics =====================
25.022/25.022
25.022/25.022 User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
25.022/25.022
25.022/25.022 Exiting with 1 model.
25.022/25.022
25.022/25.022 Process 59751 exit (max_models) Wed Jul 14 11:31:52 2021
25.022/25.022 The process finished Wed Jul 14 11:31:52 2021
25.022/25.022
25.022/25.022
25.022/25.022 Mace4 cooked interpretation:
25.022/25.022
25.022/25.022
25.022/25.022
25.022/25.022 The problem is infeasible.
25.022/25.022
25.022/25.022
25.022/25.022
25.022/25.022
25.022/25.022 -> Problem conclusions:
25.022/25.022 Left linear, Right linear, Linear
25.022/25.022 Weakly orthogonal, Almost orthogonal, Orthogonal
25.022/25.022 CTRS Type: 1
25.022/25.022 Deterministic, Strongly deterministic
25.022/25.022 Oriented CTRS, Properly oriented CTRS, Not join CTRS
25.022/25.022 Maybe right-stable CTRS, Overlay CTRS
25.022/25.022 Maybe normal CTRS, Maybe almost normal CTRS
25.022/25.022 Maybe terminating CTRS, Joinable CCPs
25.022/25.022 Maybe level confluent
25.022/25.022 Maybe confluent
25.022/25.022
25.022/25.022 Resulting CCPs:
25.022/25.022 No CCPs left
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022 Underlying TRS Termination Processor:
25.022/25.022
25.022/25.022 Resulting Underlying TRS:
25.022/25.022 (VAR x:S)
25.022/25.022 (STRATEGY CONTEXTSENSITIVE
25.022/25.022 (f 1)
25.022/25.022 (a)
25.022/25.022 (b)
25.022/25.022 )
25.022/25.022 (RULES
25.022/25.022 f(x:S) -> a
25.022/25.022 f(x:S) -> b
25.022/25.022 )
25.022/25.022 Underlying TRS terminating?
25.022/25.022 YES
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 (VAR vu95NonEmpty:S xu58S:S)
25.022/25.022 (RULES
25.022/25.022 f(xu58S:S) -> a
25.022/25.022 f(xu58S:S) -> b
25.022/25.022 )
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 Dependency Pairs Processor:
25.022/25.022 -> Pairs:
25.022/25.022 Empty
25.022/25.022 -> Rules:
25.022/25.022 f(xu58S:S) -> a
25.022/25.022 f(xu58S:S) -> b
25.022/25.022
25.022/25.022 Problem 1:
25.022/25.022
25.022/25.022 SCC Processor:
25.022/25.022 -> Pairs:
25.022/25.022 Empty
25.022/25.022 -> Rules:
25.022/25.022 f(xu58S:S) -> a
25.022/25.022 f(xu58S:S) -> b
25.022/25.022 ->Strongly Connected Components:
25.022/25.022 There is no strongly connected component
25.022/25.022
25.022/25.022 The problem is finite.
25.022/25.022
25.022/25.022
25.022/25.022 -> Problem conclusions:
25.022/25.022 Left linear, Right linear, Linear
25.022/25.022 Weakly orthogonal, Almost orthogonal, Orthogonal
25.022/25.022 CTRS Type: 1
25.022/25.022 Deterministic, Strongly deterministic
25.022/25.022 Oriented CTRS, Properly oriented CTRS, Not join CTRS
25.022/25.022 Maybe right-stable CTRS, Overlay CTRS
25.022/25.022 Maybe normal CTRS, Maybe almost normal CTRS
25.022/25.022 Terminating CTRS, Joinable CCPs
25.022/25.022 Maybe level confluent
25.022/25.022 Confluent
25.022/25.022
25.022/25.022 The problem is joinable.
25.022/25.022 53.15user 1.15system 0:25.22elapsed 215%CPU (0avgtext+0avgdata 106452maxresident)k
25.022/25.022 8inputs+0outputs (0major+99822minor)pagefaults 0swaps