25.018/25.018 YES 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 Confluence Problem: 25.018/25.018 (VAR vNonEmpty:S x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (c) 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 c -> c 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 ) 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Inlining of Conditions Processor [STERN17]: 25.018/25.018 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 Confluence Problem: 25.018/25.018 (VAR vNonEmpty:S x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (c) 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 c -> c 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 ) 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Clean CTRS Processor: 25.018/25.018 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 Confluence Problem: 25.018/25.018 (VAR x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (c) 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 ) 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 25.018/25.018 CRule InfChecker Info: 25.018/25.018 c -> c 25.018/25.018 Rule deleted 25.018/25.018 Proof: 25.018/25.018 SAME_LHS_AND_RHS 25.018/25.018 25.018/25.018 CRule InfChecker Info: 25.018/25.018 f(a,x:S) -> a 25.018/25.018 Rule remains 25.018/25.018 Proof: 25.018/25.018 NO_CONDS 25.018/25.018 25.018/25.018 CRule InfChecker Info: 25.018/25.018 f(b,x:S) -> b 25.018/25.018 Rule remains 25.018/25.018 Proof: 25.018/25.018 NO_CONDS 25.018/25.018 25.018/25.018 CRule InfChecker Info: 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 Rule remains 25.018/25.018 Proof: 25.018/25.018 NO 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Infeasibility Problem: 25.018/25.018 [(VAR vNonEmpty:S x:S:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (c) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S:S) -> a 25.018/25.018 f(b,x:S:S) -> b 25.018/25.018 g(a,x:S:S) -> c | f(x:S:S,a) ->* a 25.018/25.018 g(x:S:S,a) -> d | f(x:S:S,b) ->* b 25.018/25.018 )] 25.018/25.018 25.018/25.018 Infeasibility Conditions: 25.018/25.018 f(x:S:S,a) ->* a 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Obtaining a proof using Prover9: 25.018/25.018 25.018/25.018 -> Prover9 Output: 25.018/25.018 ============================== Prover9 =============================== 25.018/25.018 Prover9 (64) version 2009-11A, November 2009. 25.018/25.018 Process 117854 was started by ubuntu on ubuntu, 25.018/25.018 Fri Jul 16 15:30:44 2021 25.018/25.018 The command was "./prover9 -f /tmp/prover9117845-0.in". 25.018/25.018 ============================== end of head =========================== 25.018/25.018 25.018/25.018 ============================== INPUT ================================= 25.018/25.018 25.018/25.018 % Reading from file /tmp/prover9117845-0.in 25.018/25.018 25.018/25.018 assign(max_seconds,20). 25.018/25.018 25.018/25.018 formulas(assumptions). 25.018/25.018 ->*_s0(x,x) # label(reflexivity). 25.018/25.018 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.018/25.018 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 25.018/25.018 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 25.018/25.018 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 25.018/25.018 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 25.018/25.018 ->_s0(f(a,x1),a) # label(replacement). 25.018/25.018 ->_s0(f(b,x1),b) # label(replacement). 25.018/25.018 ->*_s0(f(x1,a),a) -> ->_s0(g(a,x1),c) # label(replacement). 25.018/25.018 ->*_s0(f(x1,b),b) -> ->_s0(g(x1,a),d) # label(replacement). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(goals). 25.018/25.018 (exists x1 ->*_s0(f(x1,a),a)) # label(goal). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of input ========================== 25.018/25.018 25.018/25.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.018/25.018 25.018/25.018 % Formulas that are not ordinary clauses: 25.018/25.018 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.018/25.018 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 4 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 5 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 6 ->*_s0(f(x1,a),a) -> ->_s0(g(a,x1),c) # label(replacement) # label(non_clause). [assumption]. 25.018/25.018 7 ->*_s0(f(x1,b),b) -> ->_s0(g(x1,a),d) # label(replacement) # label(non_clause). [assumption]. 25.018/25.018 8 (exists x1 ->*_s0(f(x1,a),a)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.018/25.018 25.018/25.018 ============================== end of process non-clausal formulas === 25.018/25.018 25.018/25.018 ============================== PROCESS INITIAL CLAUSES =============== 25.018/25.018 25.018/25.018 % Clauses before input processing: 25.018/25.018 25.018/25.018 formulas(usable). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(sos). 25.018/25.018 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 -->*_s0(f(x,a),a) | ->_s0(g(a,x),c) # label(replacement). [clausify(6)]. 25.018/25.018 -->*_s0(f(x,b),b) | ->_s0(g(x,a),d) # label(replacement). [clausify(7)]. 25.018/25.018 -->*_s0(f(x,a),a) # label(goal). [deny(8)]. 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(demodulators). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== PREDICATE ELIMINATION ================= 25.018/25.018 25.018/25.018 No predicates eliminated. 25.018/25.018 25.018/25.018 ============================== end predicate elimination ============= 25.018/25.018 25.018/25.018 Auto_denials: 25.018/25.018 % copying label goal to answer in negative clause 25.018/25.018 25.018/25.018 Term ordering decisions: 25.018/25.018 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.018/25.018 Function symbol precedence: function_order([ a, b, c, d, f, g ]). 25.018/25.018 After inverse_order: (no changes). 25.018/25.018 Unfolding symbols: (none). 25.018/25.018 25.018/25.018 Auto_inference settings: 25.018/25.018 % set(neg_binary_resolution). % (HNE depth_diff=-4) 25.018/25.018 % clear(ordered_res). % (HNE depth_diff=-4) 25.018/25.018 % set(ur_resolution). % (HNE depth_diff=-4) 25.018/25.018 % set(ur_resolution) -> set(pos_ur_resolution). 25.018/25.018 % set(ur_resolution) -> set(neg_ur_resolution). 25.018/25.018 25.018/25.018 Auto_process settings: (no changes). 25.018/25.018 25.018/25.018 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 kept: 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 kept: 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 kept: 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 kept: 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 kept: 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 kept: 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 kept: 17 -->*_s0(f(x,a),a) | ->_s0(g(a,x),c) # label(replacement). [clausify(6)]. 25.018/25.018 kept: 18 -->*_s0(f(x,b),b) | ->_s0(g(x,a),d) # label(replacement). [clausify(7)]. 25.018/25.018 kept: 19 -->*_s0(f(x,a),a) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 25.018/25.018 ============================== end of process initial clauses ======== 25.018/25.018 25.018/25.018 ============================== CLAUSES FOR SEARCH ==================== 25.018/25.018 25.018/25.018 % Clauses after input processing: 25.018/25.018 25.018/25.018 formulas(usable). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(sos). 25.018/25.018 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 18 -->*_s0(f(x,b),b) | ->_s0(g(x,a),d) # label(replacement). [clausify(7)]. 25.018/25.018 19 -->*_s0(f(x,a),a) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(demodulators). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of clauses for search ============= 25.018/25.018 25.018/25.018 ============================== SEARCH ================================ 25.018/25.018 25.018/25.018 % Starting search at 0.00 seconds. 25.018/25.018 25.018/25.018 given #1 (I,wt=3): 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 25.018/25.018 given #2 (I,wt=9): 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 25.018/25.018 given #3 (I,wt=10): 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 25.018/25.018 given #4 (I,wt=10): 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 25.018/25.018 given #5 (I,wt=10): 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 25.018/25.018 given #6 (I,wt=10): 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 25.018/25.018 given #7 (I,wt=5): 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 25.018/25.018 ============================== PROOF ================================= 25.018/25.018 25.018/25.018 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.018/25.018 % Length of proof is 8. 25.018/25.018 % Level of proof is 3. 25.018/25.018 % Maximum clause weight is 9.000. 25.018/25.018 % Given clauses 7. 25.018/25.018 25.018/25.018 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.018/25.018 8 (exists x1 ->*_s0(f(x1,a),a)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.018/25.018 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 19 -->*_s0(f(x,a),a) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 24 ->*_s0(f(a,x),a). [ur(10,a,15,a,b,9,a)]. 25.018/25.018 25 $F # answer(goal). [resolve(24,a,19,a)]. 25.018/25.018 25.018/25.018 ============================== end of proof ========================== 25.018/25.018 25.018/25.018 ============================== STATISTICS ============================ 25.018/25.018 25.018/25.018 Given=7. Generated=16. Kept=16. proofs=1. 25.018/25.018 Usable=7. Sos=3. Demods=0. Limbo=4, Disabled=12. Hints=0. 25.018/25.018 Kept_by_rule=0, Deleted_by_rule=0. 25.018/25.018 Forward_subsumed=0. Back_subsumed=1. 25.018/25.018 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.018/25.018 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.018/25.018 Demod_attempts=0. Demod_rewrites=0. 25.018/25.018 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.018/25.018 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=13. 25.018/25.018 Megabytes=0.07. 25.018/25.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.018/25.018 25.018/25.018 ============================== end of statistics ===================== 25.018/25.018 25.018/25.018 ============================== end of search ========================= 25.018/25.018 25.018/25.018 THEOREM PROVED 25.018/25.018 25.018/25.018 Exiting with 1 proof. 25.018/25.018 25.018/25.018 Process 117854 exit (max_proofs) Fri Jul 16 15:30:44 2021 25.018/25.018 25.018/25.018 25.018/25.018 The problem is feasible. 25.018/25.018 25.018/25.018 25.018/25.018 CRule InfChecker Info: 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 Rule remains 25.018/25.018 Proof: 25.018/25.018 NO 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Infeasibility Problem: 25.018/25.018 [(VAR vNonEmpty:S x:S:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (c) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S:S) -> a 25.018/25.018 f(b,x:S:S) -> b 25.018/25.018 g(a,x:S:S) -> c | f(x:S:S,a) ->* a 25.018/25.018 g(x:S:S,a) -> d | f(x:S:S,b) ->* b 25.018/25.018 )] 25.018/25.018 25.018/25.018 Infeasibility Conditions: 25.018/25.018 f(x:S:S,b) ->* b 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Obtaining a proof using Prover9: 25.018/25.018 25.018/25.018 -> Prover9 Output: 25.018/25.018 ============================== Prover9 =============================== 25.018/25.018 Prover9 (64) version 2009-11A, November 2009. 25.018/25.018 Process 117876 was started by ubuntu on ubuntu, 25.018/25.018 Fri Jul 16 15:30:44 2021 25.018/25.018 The command was "./prover9 -f /tmp/prover9117866-0.in". 25.018/25.018 ============================== end of head =========================== 25.018/25.018 25.018/25.018 ============================== INPUT ================================= 25.018/25.018 25.018/25.018 % Reading from file /tmp/prover9117866-0.in 25.018/25.018 25.018/25.018 assign(max_seconds,20). 25.018/25.018 25.018/25.018 formulas(assumptions). 25.018/25.018 ->*_s0(x,x) # label(reflexivity). 25.018/25.018 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.018/25.018 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 25.018/25.018 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 25.018/25.018 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 25.018/25.018 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 25.018/25.018 ->_s0(f(a,x1),a) # label(replacement). 25.018/25.018 ->_s0(f(b,x1),b) # label(replacement). 25.018/25.018 ->*_s0(f(x1,a),a) -> ->_s0(g(a,x1),c) # label(replacement). 25.018/25.018 ->*_s0(f(x1,b),b) -> ->_s0(g(x1,a),d) # label(replacement). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(goals). 25.018/25.018 (exists x1 ->*_s0(f(x1,b),b)) # label(goal). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of input ========================== 25.018/25.018 25.018/25.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.018/25.018 25.018/25.018 % Formulas that are not ordinary clauses: 25.018/25.018 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.018/25.018 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 4 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 5 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 6 ->*_s0(f(x1,a),a) -> ->_s0(g(a,x1),c) # label(replacement) # label(non_clause). [assumption]. 25.018/25.018 7 ->*_s0(f(x1,b),b) -> ->_s0(g(x1,a),d) # label(replacement) # label(non_clause). [assumption]. 25.018/25.018 8 (exists x1 ->*_s0(f(x1,b),b)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.018/25.018 25.018/25.018 ============================== end of process non-clausal formulas === 25.018/25.018 25.018/25.018 ============================== PROCESS INITIAL CLAUSES =============== 25.018/25.018 25.018/25.018 % Clauses before input processing: 25.018/25.018 25.018/25.018 formulas(usable). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(sos). 25.018/25.018 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 -->*_s0(f(x,a),a) | ->_s0(g(a,x),c) # label(replacement). [clausify(6)]. 25.018/25.018 -->*_s0(f(x,b),b) | ->_s0(g(x,a),d) # label(replacement). [clausify(7)]. 25.018/25.018 -->*_s0(f(x,b),b) # label(goal). [deny(8)]. 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(demodulators). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== PREDICATE ELIMINATION ================= 25.018/25.018 25.018/25.018 No predicates eliminated. 25.018/25.018 25.018/25.018 ============================== end predicate elimination ============= 25.018/25.018 25.018/25.018 Auto_denials: 25.018/25.018 % copying label goal to answer in negative clause 25.018/25.018 25.018/25.018 Term ordering decisions: 25.018/25.018 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.018/25.018 Function symbol precedence: function_order([ a, b, c, d, f, g ]). 25.018/25.018 After inverse_order: (no changes). 25.018/25.018 Unfolding symbols: (none). 25.018/25.018 25.018/25.018 Auto_inference settings: 25.018/25.018 % set(neg_binary_resolution). % (HNE depth_diff=-4) 25.018/25.018 % clear(ordered_res). % (HNE depth_diff=-4) 25.018/25.018 % set(ur_resolution). % (HNE depth_diff=-4) 25.018/25.018 % set(ur_resolution) -> set(pos_ur_resolution). 25.018/25.018 % set(ur_resolution) -> set(neg_ur_resolution). 25.018/25.018 25.018/25.018 Auto_process settings: (no changes). 25.018/25.018 25.018/25.018 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 kept: 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 kept: 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 kept: 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 kept: 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 kept: 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 kept: 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 kept: 17 -->*_s0(f(x,a),a) | ->_s0(g(a,x),c) # label(replacement). [clausify(6)]. 25.018/25.018 kept: 18 -->*_s0(f(x,b),b) | ->_s0(g(x,a),d) # label(replacement). [clausify(7)]. 25.018/25.018 kept: 19 -->*_s0(f(x,b),b) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 25.018/25.018 ============================== end of process initial clauses ======== 25.018/25.018 25.018/25.018 ============================== CLAUSES FOR SEARCH ==================== 25.018/25.018 25.018/25.018 % Clauses after input processing: 25.018/25.018 25.018/25.018 formulas(usable). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(sos). 25.018/25.018 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 17 -->*_s0(f(x,a),a) | ->_s0(g(a,x),c) # label(replacement). [clausify(6)]. 25.018/25.018 19 -->*_s0(f(x,b),b) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(demodulators). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of clauses for search ============= 25.018/25.018 25.018/25.018 ============================== SEARCH ================================ 25.018/25.018 25.018/25.018 % Starting search at 0.00 seconds. 25.018/25.018 25.018/25.018 given #1 (I,wt=3): 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 25.018/25.018 given #2 (I,wt=9): 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 25.018/25.018 given #3 (I,wt=10): 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 25.018/25.018 25.018/25.018 given #4 (I,wt=10): 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 25.018/25.018 25.018/25.018 given #5 (I,wt=10): 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 25.018/25.018 25.018/25.018 given #6 (I,wt=10): 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 25.018/25.018 25.018/25.018 given #7 (I,wt=5): 15 ->_s0(f(a,x),a) # label(replacement). [assumption]. 25.018/25.018 25.018/25.018 given #8 (I,wt=5): 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 25.018/25.018 ============================== PROOF ================================= 25.018/25.018 25.018/25.018 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.018/25.018 % Length of proof is 8. 25.018/25.018 % Level of proof is 3. 25.018/25.018 % Maximum clause weight is 9.000. 25.018/25.018 % Given clauses 8. 25.018/25.018 25.018/25.018 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.018/25.018 8 (exists x1 ->*_s0(f(x1,b),b)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.018/25.018 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.018/25.018 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.018/25.018 16 ->_s0(f(b,x),b) # label(replacement). [assumption]. 25.018/25.018 19 -->*_s0(f(x,b),b) # label(goal) # answer(goal). [deny(8)]. 25.018/25.018 29 ->*_s0(f(b,x),b). [ur(10,a,16,a,b,9,a)]. 25.018/25.018 30 $F # answer(goal). [resolve(29,a,19,a)]. 25.018/25.018 25.018/25.018 ============================== end of proof ========================== 25.018/25.018 25.018/25.018 ============================== STATISTICS ============================ 25.018/25.018 25.018/25.018 Given=8. Generated=21. Kept=21. proofs=1. 25.018/25.018 Usable=8. Sos=7. Demods=0. Limbo=4, Disabled=12. Hints=0. 25.018/25.018 Kept_by_rule=0, Deleted_by_rule=0. 25.018/25.018 Forward_subsumed=0. Back_subsumed=1. 25.018/25.018 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.018/25.018 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.018/25.018 Demod_attempts=0. Demod_rewrites=0. 25.018/25.018 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.018/25.018 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=13. 25.018/25.018 Megabytes=0.08. 25.018/25.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.018/25.018 25.018/25.018 ============================== end of statistics ===================== 25.018/25.018 25.018/25.018 ============================== end of search ========================= 25.018/25.018 25.018/25.018 THEOREM PROVED 25.018/25.018 25.018/25.018 Exiting with 1 proof. 25.018/25.018 25.018/25.018 Process 117876 exit (max_proofs) Fri Jul 16 15:30:44 2021 25.018/25.018 25.018/25.018 25.018/25.018 The problem is feasible. 25.018/25.018 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 Confluence Problem: 25.018/25.018 (VAR x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (c) 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 ) 25.018/25.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.018/25.018 25.018/25.018 Critical Pairs Processor: 25.018/25.018 -> Rules: 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 -> Vars: 25.018/25.018 "x", "x", "x", "x" 25.018/25.018 -> FVars: 25.018/25.018 "x2", "x3", "x4", "x5" 25.018/25.018 -> PVars: 25.018/25.018 "x": ["x2", "x3", "x4", "x5"] 25.018/25.018 25.018/25.018 -> Rlps: 25.018/25.018 crule: f(a,x2:S) -> a, id: 1, possubterms: f(a,x2:S)-> [], a-> [1] 25.018/25.018 crule: f(b,x3:S) -> b, id: 2, possubterms: f(b,x3:S)-> [], b-> [1] 25.018/25.018 crule: g(a,x4:S) -> c | f(x4:S,a) ->* a, id: 3, possubterms: g(a,x4:S)-> [], a-> [1] 25.018/25.018 crule: g(x5:S,a) -> d | f(x5:S,b) ->* b, id: 4, possubterms: g(x5:S,a)-> [], a-> [2] 25.018/25.018 25.018/25.018 -> Unifications: 25.018/25.018 R4 unifies with R3 at p: [], l: g(x5:S,a), lp: g(x5:S,a), conds: {f(x5:S,b) ->* b, f(x:S,a) ->* a}, sig: {x:S -> a,x5:S -> a}, l': g(a,x:S), r: d, r': c 25.018/25.018 25.018/25.018 -> Critical pairs info: 25.018/25.018 | f(a,b) ->* b, f(a,a) ->* a => Not trivial, Overlay, N1 25.018/25.018 25.018/25.018 -> Problem conclusions: 25.018/25.018 Left linear, Right linear, Linear 25.018/25.018 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.018/25.018 CTRS Type: 1 25.018/25.018 Deterministic, Strongly deterministic 25.018/25.018 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.018/25.018 Maybe right-stable CTRS, Overlay CTRS 25.018/25.018 Maybe normal CTRS, Maybe almost normal CTRS 25.018/25.018 Maybe terminating CTRS, Maybe joinable CCPs 25.018/25.018 Maybe level confluent 25.018/25.018 Maybe confluent 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 Clean Infeasible CCPs Processor: 25.018/25.018 Num of CPIs: 1 25.018/25.018 Timeout: 30 25.018/25.018 Timeout for each infeasibility problem: 30 s 25.018/25.018 | f(a,b) ->* b, f(a,a) ->* a => Not trivial, Overlay, N1 25.018/25.018 (PROBLEM INFEASIBILITY) 25.018/25.018 (VAR x) 25.018/25.018 (RULES 25.018/25.018 f(a,x) -> a 25.018/25.018 f(b,x) -> b 25.018/25.018 g(a,x) -> c | f(x,a) ->* a 25.018/25.018 g(x,a) -> d | f(x,b) ->* b) 25.018/25.018 (CONDITION f(a,b) ->* b, f(a,a) ->* a) 25.018/25.018 25.018/25.018 Proof: 25.018/25.018 YES 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Infeasibility Problem: 25.018/25.018 [(VAR vNonEmpty:S x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (c) 25.018/25.018 (d) 25.018/25.018 (fSNonEmpty) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c | f(x:S,a) ->* a 25.018/25.018 g(x:S,a) -> d | f(x:S,b) ->* b 25.018/25.018 )] 25.018/25.018 25.018/25.018 Infeasibility Conditions: 25.018/25.018 f(a,b) ->* b, f(a,a) ->* a 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Obtaining a model using Mace4: 25.018/25.018 25.018/25.018 -> Usable Rules: 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 25.018/25.018 -> Mace4 Output: 25.018/25.018 ============================== Mace4 ================================= 25.018/25.018 Mace4 (64) version 2009-11A, November 2009. 25.018/25.018 Process 117922 was started by ubuntu on ubuntu, 25.018/25.018 Fri Jul 16 15:30:44 2021 25.018/25.018 The command was "./mace4 -c -f /tmp/mace4117893-2.in". 25.018/25.018 ============================== end of head =========================== 25.018/25.018 25.018/25.018 ============================== INPUT ================================= 25.018/25.018 25.018/25.018 % Reading from file /tmp/mace4117893-2.in 25.018/25.018 25.018/25.018 assign(max_seconds,10). 25.018/25.018 25.018/25.018 formulas(assumptions). 25.018/25.018 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 25.018/25.018 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 25.018/25.018 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 25.018/25.018 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 25.018/25.018 ->(f(a,x1),a) # label(replacement). 25.018/25.018 ->(f(b,x1),b) # label(replacement). 25.018/25.018 ->*(x,x) # label(reflexivity). 25.018/25.018 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 formulas(goals). 25.018/25.018 ->*(f(a,b),b) & ->*(f(a,a),a) # label(goal). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of input ========================== 25.018/25.018 25.018/25.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.018/25.018 25.018/25.018 % Formulas that are not ordinary clauses: 25.018/25.018 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.018/25.018 5 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.018/25.018 6 ->*(f(a,b),b) & ->*(f(a,a),a) # label(goal) # label(non_clause) # label(goal). [goal]. 25.018/25.018 25.018/25.018 ============================== end of process non-clausal formulas === 25.018/25.018 25.018/25.018 ============================== CLAUSES FOR SEARCH ==================== 25.018/25.018 25.018/25.018 formulas(mace4_clauses). 25.018/25.018 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 25.018/25.018 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 25.018/25.018 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 25.018/25.018 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 25.018/25.018 ->(f(a,x),a) # label(replacement). 25.018/25.018 ->(f(b,x),b) # label(replacement). 25.018/25.018 ->*(x,x) # label(reflexivity). 25.018/25.018 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.018/25.018 -->*(f(a,b),b) | -->*(f(a,a),a) # label(goal). 25.018/25.018 end_of_list. 25.018/25.018 25.018/25.018 ============================== end of clauses for search ============= 25.018/25.018 25.018/25.018 % There are no natural numbers in the input. 25.018/25.018 25.018/25.018 ============================== DOMAIN SIZE 2 ========================= 25.018/25.018 25.018/25.018 ============================== MODEL ================================= 25.018/25.018 25.018/25.018 interpretation( 2, [number=1, seconds=0], [ 25.018/25.018 25.018/25.018 function(a, [ 0 ]), 25.018/25.018 25.018/25.018 function(b, [ 1 ]), 25.018/25.018 25.018/25.018 function(f(_,_), [ 25.018/25.018 0, 0, 25.018/25.018 1, 1 ]), 25.018/25.018 25.018/25.018 function(g(_,_), [ 25.018/25.018 0, 0, 25.018/25.018 0, 0 ]), 25.018/25.018 25.018/25.018 relation(->*(_,_), [ 25.018/25.018 1, 0, 25.018/25.018 0, 1 ]), 25.018/25.018 25.018/25.018 relation(->(_,_), [ 25.018/25.018 1, 0, 25.018/25.018 0, 1 ]) 25.018/25.018 ]). 25.018/25.018 25.018/25.018 ============================== end of model ========================== 25.018/25.018 25.018/25.018 ============================== STATISTICS ============================ 25.018/25.018 25.018/25.018 For domain size 2. 25.018/25.018 25.018/25.018 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.018/25.018 Ground clauses: seen=47, kept=43. 25.018/25.018 Selections=9, assignments=11, propagations=13, current_models=1. 25.018/25.018 Rewrite_terms=106, rewrite_bools=75, indexes=20. 25.018/25.018 Rules_from_neg_clauses=3, cross_offs=3. 25.018/25.018 25.018/25.018 ============================== end of statistics ===================== 25.018/25.018 25.018/25.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.018/25.018 25.018/25.018 Exiting with 1 model. 25.018/25.018 25.018/25.018 Process 117922 exit (max_models) Fri Jul 16 15:30:44 2021 25.018/25.018 The process finished Fri Jul 16 15:30:44 2021 25.018/25.018 25.018/25.018 25.018/25.018 Mace4 cooked interpretation: 25.018/25.018 25.018/25.018 25.018/25.018 25.018/25.018 The problem is infeasible. 25.018/25.018 25.018/25.018 25.018/25.018 25.018/25.018 25.018/25.018 -> Problem conclusions: 25.018/25.018 Left linear, Right linear, Linear 25.018/25.018 Weakly orthogonal, Almost orthogonal, Orthogonal 25.018/25.018 CTRS Type: 1 25.018/25.018 Deterministic, Strongly deterministic 25.018/25.018 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.018/25.018 Maybe right-stable CTRS, Overlay CTRS 25.018/25.018 Maybe normal CTRS, Maybe almost normal CTRS 25.018/25.018 Maybe terminating CTRS, Joinable CCPs 25.018/25.018 Maybe level confluent 25.018/25.018 Maybe confluent 25.018/25.018 25.018/25.018 Resulting CCPs: 25.018/25.018 No CCPs left 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 Underlying TRS Termination Processor: 25.018/25.018 25.018/25.018 Resulting Underlying TRS: 25.018/25.018 (VAR x:S) 25.018/25.018 (STRATEGY CONTEXTSENSITIVE 25.018/25.018 (c) 25.018/25.018 (f 1 2) 25.018/25.018 (g 1 2) 25.018/25.018 (a) 25.018/25.018 (b) 25.018/25.018 (d) 25.018/25.018 ) 25.018/25.018 (RULES 25.018/25.018 f(a,x:S) -> a 25.018/25.018 f(b,x:S) -> b 25.018/25.018 g(a,x:S) -> c 25.018/25.018 g(x:S,a) -> d 25.018/25.018 ) 25.018/25.018 Underlying TRS terminating? 25.018/25.018 YES 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 (VAR vu95NonEmpty:S xu58S:S) 25.018/25.018 (RULES 25.018/25.018 f(a,xu58S:S) -> a 25.018/25.018 f(b,xu58S:S) -> b 25.018/25.018 g(a,xu58S:S) -> c 25.018/25.018 g(xu58S:S,a) -> d 25.018/25.018 ) 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 Dependency Pairs Processor: 25.018/25.018 -> Pairs: 25.018/25.018 Empty 25.018/25.018 -> Rules: 25.018/25.018 f(a,xu58S:S) -> a 25.018/25.018 f(b,xu58S:S) -> b 25.018/25.018 g(a,xu58S:S) -> c 25.018/25.018 g(xu58S:S,a) -> d 25.018/25.018 25.018/25.018 Problem 1: 25.018/25.018 25.018/25.018 SCC Processor: 25.018/25.018 -> Pairs: 25.018/25.018 Empty 25.018/25.018 -> Rules: 25.018/25.018 f(a,xu58S:S) -> a 25.018/25.018 f(b,xu58S:S) -> b 25.018/25.018 g(a,xu58S:S) -> c 25.018/25.018 g(xu58S:S,a) -> d 25.018/25.018 ->Strongly Connected Components: 25.018/25.018 There is no strongly connected component 25.018/25.018 25.018/25.018 The problem is finite. 25.018/25.018 25.018/25.018 25.018/25.018 -> Problem conclusions: 25.018/25.018 Left linear, Right linear, Linear 25.018/25.018 Weakly orthogonal, Almost orthogonal, Orthogonal 25.018/25.018 CTRS Type: 1 25.018/25.018 Deterministic, Strongly deterministic 25.018/25.018 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.018/25.018 Maybe right-stable CTRS, Overlay CTRS 25.018/25.018 Maybe normal CTRS, Maybe almost normal CTRS 25.018/25.018 Terminating CTRS, Joinable CCPs 25.018/25.018 Maybe level confluent 25.018/25.018 Confluent 25.018/25.018 25.018/25.018 The problem is joinable. 25.018/25.018 36.78user 0.96system 0:25.18elapsed 149%CPU (0avgtext+0avgdata 39592maxresident)k 25.018/25.018 8inputs+0outputs (0major+58256minor)pagefaults 0swaps