20.096/20.096 YES 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 Confluence Problem: 20.096/20.096 (VAR vNonEmpty x' x'' x y' y y'') 20.096/20.096 (REPLACEMENT-MAP 20.096/20.096 (f 1, 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 ) 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Inlining of Conditions Processor [STERN17]: 20.096/20.096 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 Confluence Problem: 20.096/20.096 (VAR vNonEmpty x' x'' x y' y y'') 20.096/20.096 (REPLACEMENT-MAP 20.096/20.096 (f 1, 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 ) 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Clean CTRS Processor: 20.096/20.096 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 Confluence Problem: 20.096/20.096 (VAR x' x'' x y' y y'') 20.096/20.096 (REPLACEMENT-MAP 20.096/20.096 (f 1, 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 ) 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 20.096/20.096 CRule InfChecker Info: 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 Rule remains 20.096/20.096 Proof: 20.096/20.096 NO 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Infeasibility Problem: 20.096/20.096 [(VAR vNonEmpty x' x'' x y' y y'' vNonEmpty x' x'' x) 20.096/20.096 (STRATEGY CONTEXTSENSITIVE 20.096/20.096 (f 1 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 )] 20.096/20.096 20.096/20.096 Infeasibility Conditions: 20.096/20.096 x' ->* x, x'' ->* x 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Obtaining a proof using Prover9: 20.096/20.096 20.096/20.096 -> Prover9 Output: 20.096/20.096 ============================== Prover9 =============================== 20.096/20.096 Prover9 (64) version 2009-11A, November 2009. 20.096/20.096 Process 20951 was started by ubuntu on ubuntu, 20.096/20.096 Wed Mar 9 09:31:42 2022 20.096/20.096 The command was "./prover9 -f /tmp/prover920942-0.in". 20.096/20.096 ============================== end of head =========================== 20.096/20.096 20.096/20.096 ============================== INPUT ================================= 20.096/20.096 20.096/20.096 % Reading from file /tmp/prover920942-0.in 20.096/20.096 20.096/20.096 assign(max_seconds,20). 20.096/20.096 20.096/20.096 formulas(assumptions). 20.096/20.096 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.096/20.096 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.096/20.096 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 20.096/20.096 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 20.096/20.096 ->*_s0(x1,x3) & ->*_s0(x2,x3) -> ->_s0(f(x1,x2),g(x3)) # label(replacement). 20.096/20.096 ->*_s0(x4,x5) & ->*_s0(x6,x5) -> ->_s0(f(x4,h(x6)),g(x5)) # label(replacement). 20.096/20.096 ->*_s0(x,x) # label(reflexivity). 20.096/20.096 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(goals). 20.096/20.096 (exists x8 exists x9 exists x10 (->*_s0(x8,x10) & ->*_s0(x9,x10))) # label(goal). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of input ========================== 20.096/20.096 20.096/20.096 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.096/20.096 20.096/20.096 % Formulas that are not ordinary clauses: 20.096/20.096 1 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 2 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 3 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 5 ->*_s0(x1,x3) & ->*_s0(x2,x3) -> ->_s0(f(x1,x2),g(x3)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 6 ->*_s0(x4,x5) & ->*_s0(x6,x5) -> ->_s0(f(x4,h(x6)),g(x5)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.096/20.096 8 (exists x8 exists x9 exists x10 (->*_s0(x8,x10) & ->*_s0(x9,x10))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.096/20.096 20.096/20.096 ============================== end of process non-clausal formulas === 20.096/20.096 20.096/20.096 ============================== PROCESS INITIAL CLAUSES =============== 20.096/20.096 20.096/20.096 % Clauses before input processing: 20.096/20.096 20.096/20.096 formulas(usable). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(sos). 20.096/20.096 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y)) # label(replacement). [clausify(5)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,h(z)),g(y)) # label(replacement). [clausify(6)]. 20.096/20.096 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) # label(goal). [deny(8)]. 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(demodulators). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== PREDICATE ELIMINATION ================= 20.096/20.096 20.096/20.096 No predicates eliminated. 20.096/20.096 20.096/20.096 ============================== end predicate elimination ============= 20.096/20.096 20.096/20.096 Auto_denials: 20.096/20.096 % copying label goal to answer in negative clause 20.096/20.096 20.096/20.096 Term ordering decisions: 20.096/20.096 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.096/20.096 Function symbol precedence: function_order([ f, g, h ]). 20.096/20.096 After inverse_order: (no changes). 20.096/20.096 Unfolding symbols: (none). 20.096/20.096 20.096/20.096 Auto_inference settings: 20.096/20.096 % set(neg_binary_resolution). % (HNE depth_diff=-7) 20.096/20.096 % clear(ordered_res). % (HNE depth_diff=-7) 20.096/20.096 % set(ur_resolution). % (HNE depth_diff=-7) 20.096/20.096 % set(ur_resolution) -> set(pos_ur_resolution). 20.096/20.096 % set(ur_resolution) -> set(neg_ur_resolution). 20.096/20.096 20.096/20.096 Auto_process settings: 20.096/20.096 % set(unit_deletion). % (Horn set with negative nonunits) 20.096/20.096 20.096/20.096 kept: 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 kept: 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 kept: 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 kept: 13 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y)) # label(replacement). [clausify(5)]. 20.096/20.096 kept: 14 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,h(z)),g(y)) # label(replacement). [clausify(6)]. 20.096/20.096 kept: 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 kept: 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 kept: 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 20.096/20.096 ============================== end of process initial clauses ======== 20.096/20.096 20.096/20.096 ============================== CLAUSES FOR SEARCH ==================== 20.096/20.096 20.096/20.096 % Clauses after input processing: 20.096/20.096 20.096/20.096 formulas(usable). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(sos). 20.096/20.096 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(demodulators). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of clauses for search ============= 20.096/20.096 20.096/20.096 ============================== SEARCH ================================ 20.096/20.096 20.096/20.096 % Starting search at 0.00 seconds. 20.096/20.096 20.096/20.096 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 20.096/20.096 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 20.096/20.096 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 20.096/20.096 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 20.096/20.096 given #5 (I,wt=3): 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 20.096/20.096 given #6 (I,wt=9): 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 20.096/20.096 given #7 (I,wt=6): 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 20.096/20.096 ============================== PROOF ================================= 20.096/20.096 20.096/20.096 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.096/20.096 % Length of proof is 5. 20.096/20.096 % Level of proof is 3. 20.096/20.096 % Maximum clause weight is 6.000. 20.096/20.096 % Given clauses 7. 20.096/20.096 20.096/20.096 8 (exists x8 exists x9 exists x10 (->*_s0(x8,x10) & ->*_s0(x9,x10))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.096/20.096 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 18 -->*_s0(x,y) # answer(goal). [resolve(17,a,15,a)]. 20.096/20.096 19 $F # answer(goal). [resolve(18,a,15,a)]. 20.096/20.096 20.096/20.096 ============================== end of proof ========================== 20.096/20.096 20.096/20.096 ============================== STATISTICS ============================ 20.096/20.096 20.096/20.096 Given=7. Generated=11. Kept=10. proofs=1. 20.096/20.096 Usable=7. Sos=0. Demods=0. Limbo=0, Disabled=11. Hints=0. 20.096/20.096 Kept_by_rule=0, Deleted_by_rule=0. 20.096/20.096 Forward_subsumed=1. Back_subsumed=2. 20.096/20.096 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.096/20.096 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.096/20.096 Demod_attempts=0. Demod_rewrites=0. 20.096/20.096 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.096/20.096 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=14. 20.096/20.096 Megabytes=0.06. 20.096/20.096 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.096/20.096 20.096/20.096 ============================== end of statistics ===================== 20.096/20.096 20.096/20.096 ============================== end of search ========================= 20.096/20.096 20.096/20.096 THEOREM PROVED 20.096/20.096 20.096/20.096 Exiting with 1 proof. 20.096/20.096 20.096/20.096 Process 20951 exit (max_proofs) Wed Mar 9 09:31:42 2022 20.096/20.096 20.096/20.096 20.096/20.096 The problem is feasible. 20.096/20.096 20.096/20.096 20.096/20.096 CRule InfChecker Info: 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 Rule remains 20.096/20.096 Proof: 20.096/20.096 NO 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Infeasibility Problem: 20.096/20.096 [(VAR vNonEmpty x' x'' x y' y y'' vNonEmpty y' y y'') 20.096/20.096 (STRATEGY CONTEXTSENSITIVE 20.096/20.096 (f 1 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 )] 20.096/20.096 20.096/20.096 Infeasibility Conditions: 20.096/20.096 y' ->* y, y'' ->* y 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Obtaining a proof using Prover9: 20.096/20.096 20.096/20.096 -> Prover9 Output: 20.096/20.096 ============================== Prover9 =============================== 20.096/20.096 Prover9 (64) version 2009-11A, November 2009. 20.096/20.096 Process 20973 was started by ubuntu on ubuntu, 20.096/20.096 Wed Mar 9 09:31:42 2022 20.096/20.096 The command was "./prover9 -f /tmp/prover920964-0.in". 20.096/20.096 ============================== end of head =========================== 20.096/20.096 20.096/20.096 ============================== INPUT ================================= 20.096/20.096 20.096/20.096 % Reading from file /tmp/prover920964-0.in 20.096/20.096 20.096/20.096 assign(max_seconds,20). 20.096/20.096 20.096/20.096 formulas(assumptions). 20.096/20.096 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.096/20.096 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.096/20.096 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 20.096/20.096 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 20.096/20.096 ->*_s0(x1,x3) & ->*_s0(x2,x3) -> ->_s0(f(x1,x2),g(x3)) # label(replacement). 20.096/20.096 ->*_s0(x4,x5) & ->*_s0(x6,x5) -> ->_s0(f(x4,h(x6)),g(x5)) # label(replacement). 20.096/20.096 ->*_s0(x,x) # label(reflexivity). 20.096/20.096 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(goals). 20.096/20.096 (exists x8 exists x9 exists x10 (->*_s0(x8,x9) & ->*_s0(x10,x9))) # label(goal). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of input ========================== 20.096/20.096 20.096/20.096 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.096/20.096 20.096/20.096 % Formulas that are not ordinary clauses: 20.096/20.096 1 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 2 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 3 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 5 ->*_s0(x1,x3) & ->*_s0(x2,x3) -> ->_s0(f(x1,x2),g(x3)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 6 ->*_s0(x4,x5) & ->*_s0(x6,x5) -> ->_s0(f(x4,h(x6)),g(x5)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.096/20.096 8 (exists x8 exists x9 exists x10 (->*_s0(x8,x9) & ->*_s0(x10,x9))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.096/20.096 20.096/20.096 ============================== end of process non-clausal formulas === 20.096/20.096 20.096/20.096 ============================== PROCESS INITIAL CLAUSES =============== 20.096/20.096 20.096/20.096 % Clauses before input processing: 20.096/20.096 20.096/20.096 formulas(usable). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(sos). 20.096/20.096 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y)) # label(replacement). [clausify(5)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,h(z)),g(y)) # label(replacement). [clausify(6)]. 20.096/20.096 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 -->*_s0(x,y) | -->*_s0(z,y) # label(goal). [deny(8)]. 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(demodulators). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== PREDICATE ELIMINATION ================= 20.096/20.096 20.096/20.096 No predicates eliminated. 20.096/20.096 20.096/20.096 ============================== end predicate elimination ============= 20.096/20.096 20.096/20.096 Auto_denials: 20.096/20.096 % copying label goal to answer in negative clause 20.096/20.096 20.096/20.096 Term ordering decisions: 20.096/20.096 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.096/20.096 Function symbol precedence: function_order([ f, g, h ]). 20.096/20.096 After inverse_order: (no changes). 20.096/20.096 Unfolding symbols: (none). 20.096/20.096 20.096/20.096 Auto_inference settings: 20.096/20.096 % set(neg_binary_resolution). % (HNE depth_diff=-7) 20.096/20.096 % clear(ordered_res). % (HNE depth_diff=-7) 20.096/20.096 % set(ur_resolution). % (HNE depth_diff=-7) 20.096/20.096 % set(ur_resolution) -> set(pos_ur_resolution). 20.096/20.096 % set(ur_resolution) -> set(neg_ur_resolution). 20.096/20.096 20.096/20.096 Auto_process settings: 20.096/20.096 % set(unit_deletion). % (Horn set with negative nonunits) 20.096/20.096 20.096/20.096 kept: 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 kept: 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 kept: 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 kept: 13 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y)) # label(replacement). [clausify(5)]. 20.096/20.096 kept: 14 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,h(z)),g(y)) # label(replacement). [clausify(6)]. 20.096/20.096 kept: 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 kept: 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 kept: 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 20.096/20.096 ============================== end of process initial clauses ======== 20.096/20.096 20.096/20.096 ============================== CLAUSES FOR SEARCH ==================== 20.096/20.096 20.096/20.096 % Clauses after input processing: 20.096/20.096 20.096/20.096 formulas(usable). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(sos). 20.096/20.096 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(demodulators). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of clauses for search ============= 20.096/20.096 20.096/20.096 ============================== SEARCH ================================ 20.096/20.096 20.096/20.096 % Starting search at 0.00 seconds. 20.096/20.096 20.096/20.096 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.096/20.096 20.096/20.096 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.096/20.096 20.096/20.096 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.096/20.096 20.096/20.096 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 20.096/20.096 20.096/20.096 given #5 (I,wt=3): 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 20.096/20.096 given #6 (I,wt=9): 16 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 20.096/20.096 20.096/20.096 given #7 (I,wt=6): 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 20.096/20.096 ============================== PROOF ================================= 20.096/20.096 20.096/20.096 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.096/20.096 % Length of proof is 5. 20.096/20.096 % Level of proof is 3. 20.096/20.096 % Maximum clause weight is 6.000. 20.096/20.096 % Given clauses 7. 20.096/20.096 20.096/20.096 8 (exists x8 exists x9 exists x10 (->*_s0(x8,x9) & ->*_s0(x10,x9))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.096/20.096 15 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.096/20.096 17 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(8)]. 20.096/20.096 18 -->*_s0(x,y) # answer(goal). [resolve(17,a,15,a)]. 20.096/20.096 19 $F # answer(goal). [resolve(18,a,15,a)]. 20.096/20.096 20.096/20.096 ============================== end of proof ========================== 20.096/20.096 20.096/20.096 ============================== STATISTICS ============================ 20.096/20.096 20.096/20.096 Given=7. Generated=11. Kept=10. proofs=1. 20.096/20.096 Usable=7. Sos=0. Demods=0. Limbo=0, Disabled=11. Hints=0. 20.096/20.096 Kept_by_rule=0, Deleted_by_rule=0. 20.096/20.096 Forward_subsumed=1. Back_subsumed=2. 20.096/20.096 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.096/20.096 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.096/20.096 Demod_attempts=0. Demod_rewrites=0. 20.096/20.096 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.096/20.096 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=14. 20.096/20.096 Megabytes=0.06. 20.096/20.096 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.096/20.096 20.096/20.096 ============================== end of statistics ===================== 20.096/20.096 20.096/20.096 ============================== end of search ========================= 20.096/20.096 20.096/20.096 THEOREM PROVED 20.096/20.096 20.096/20.096 Exiting with 1 proof. 20.096/20.096 20.096/20.096 Process 20973 exit (max_proofs) Wed Mar 9 09:31:42 2022 20.096/20.096 20.096/20.096 20.096/20.096 The problem is feasible. 20.096/20.096 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 Confluence Problem: 20.096/20.096 (VAR x' x'' x y' y y'') 20.096/20.096 (REPLACEMENT-MAP 20.096/20.096 (f 1, 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 ) 20.096/20.096 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.096/20.096 20.096/20.096 Critical Pairs Processor: 20.096/20.096 -> Rules: 20.096/20.096 f(x',x'') -> g(x) | x' ->* x, x'' ->* x 20.096/20.096 f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y 20.096/20.096 -> Vars: 20.096/20.096 "x'", "x''", "x", "y'", "y", "y''" 20.096/20.096 20.096/20.096 -> Rlps: 20.096/20.096 crule: f(x',x'') -> g(x) | x' ->* x, x'' ->* x, id: 1, possubterms: f(x',x'')-> [] 20.096/20.096 crule: f(y',h(y'')) -> g(y) | y' ->* y, y'' ->* y, id: 2, possubterms: f(y',h(y''))-> [], h(y'')-> [2] 20.096/20.096 20.096/20.096 -> Unifications: 20.096/20.096 R2 unifies with R1 at p: [], l: f(y',h(y'')), lp: f(y',h(y'')), conds: {y' ->* y, y'' ->* y, x' ->* x, x'' ->* x}, sig: {y' -> x',x'' -> h(y'')}, l': f(x',x''), r: g(y), r': g(x) 20.096/20.096 20.096/20.096 -> Critical pairs info: 20.096/20.096 | x' ->* y, y'' ->* y, x' ->* x, h(y'') ->* x => Not trivial, Overlay, NW2, N1 20.096/20.096 20.096/20.096 -> Problem conclusions: 20.096/20.096 Left linear, Right linear, Linear 20.096/20.096 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.096/20.096 CTRS Type: 3 20.096/20.096 Deterministic, Strongly deterministic 20.096/20.096 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.096/20.096 Maybe right-stable CTRS, Overlay CTRS 20.096/20.096 Maybe normal CTRS, Maybe almost normal CTRS 20.096/20.096 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.096/20.096 Maybe level confluent 20.096/20.096 Maybe confluent 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 Clean Infeasible CCPs Processor: 20.096/20.096 Num of CPIs: 1 20.096/20.096 Timeout: 60 20.096/20.096 Timeout for each infeasibility problem: 60 s 20.096/20.096 | x' ->* y, y'' ->* y, x' ->* x, h(y'') ->* x => Not trivial, Overlay, NW2, N1 20.096/20.096 (CONDITIONTYPE ORIENTED) 20.096/20.096 (VAR x1 x11 x y1 y y11 x1 x) 20.096/20.096 (RULES 20.096/20.096 f(x1,x11) -> g(x) | x1 ->* x, x11 ->* x 20.096/20.096 f(y1,h(y11)) -> g(y) | y1 ->* y, y11 ->* y) 20.096/20.096 (VAR x13 x14 x15 x16) 20.096/20.096 (CONDITION x15 ->* x13, x14 ->* x13, x15 ->* x16, h(x14) ->* x16) 20.096/20.096 20.096/20.096 Proof: 20.096/20.096 YES 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Infeasibility Problem: 20.096/20.096 [(VAR vNonEmpty x1 x11 x y1 y y11 vNonEmpty x13 x14 x15 x16) 20.096/20.096 (STRATEGY CONTEXTSENSITIVE 20.096/20.096 (f 1 2) 20.096/20.096 (fSNonEmpty) 20.096/20.096 (g 1) 20.096/20.096 (h 1) 20.096/20.096 ) 20.096/20.096 (RULES 20.096/20.096 f(x1,x11) -> g(x) | x1 ->* x, x11 ->* x 20.096/20.096 f(y1,h(y11)) -> g(y) | y1 ->* y, y11 ->* y 20.096/20.096 )] 20.096/20.096 20.096/20.096 Infeasibility Conditions: 20.096/20.096 x15 ->* x13, x14 ->* x13, x15 ->* x16, h(x14) ->* x16 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 Obtaining a model using Mace4: 20.096/20.096 20.096/20.096 -> Usable Rules: 20.096/20.096 f(x1,x11) -> g(x) | x1 ->* x, x11 ->* x 20.096/20.096 f(y1,h(y11)) -> g(y) | y1 ->* y, y11 ->* y 20.096/20.096 20.096/20.096 -> Mace4 Output: 20.096/20.096 ============================== Mace4 ================================= 20.096/20.096 Mace4 (64) version 2009-11A, November 2009. 20.096/20.096 Process 21007 was started by ubuntu on ubuntu, 20.096/20.096 Wed Mar 9 09:31:42 2022 20.096/20.096 The command was "./mace4 -c -f /tmp/mace420990-2.in". 20.096/20.096 ============================== end of head =========================== 20.096/20.096 20.096/20.096 ============================== INPUT ================================= 20.096/20.096 20.096/20.096 % Reading from file /tmp/mace420990-2.in 20.096/20.096 20.096/20.096 assign(max_seconds,20). 20.096/20.096 20.096/20.096 formulas(assumptions). 20.096/20.096 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.096/20.096 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.096/20.096 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence). 20.096/20.096 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 20.096/20.096 ->*(x1,x3) & ->*(x2,x3) -> ->(f(x1,x2),g(x3)) # label(replacement). 20.096/20.096 ->*(x4,x5) & ->*(x6,x5) -> ->(f(x4,h(x6)),g(x5)) # label(replacement). 20.096/20.096 ->*(x,x) # label(reflexivity). 20.096/20.096 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 formulas(goals). 20.096/20.096 (exists x8 exists x9 exists x10 exists x11 (->*(x10,x8) & ->*(x9,x8) & ->*(x10,x11) & ->*(h(x9),x11))) # label(goal). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of input ========================== 20.096/20.096 20.096/20.096 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.096/20.096 20.096/20.096 % Formulas that are not ordinary clauses: 20.096/20.096 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 3 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 4 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.096/20.096 5 ->*(x1,x3) & ->*(x2,x3) -> ->(f(x1,x2),g(x3)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 6 ->*(x4,x5) & ->*(x6,x5) -> ->(f(x4,h(x6)),g(x5)) # label(replacement) # label(non_clause). [assumption]. 20.096/20.096 7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.096/20.096 8 (exists x8 exists x9 exists x10 exists x11 (->*(x10,x8) & ->*(x9,x8) & ->*(x10,x11) & ->*(h(x9),x11))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.096/20.096 20.096/20.096 ============================== end of process non-clausal formulas === 20.096/20.096 20.096/20.096 ============================== CLAUSES FOR SEARCH ==================== 20.096/20.096 20.096/20.096 formulas(mace4_clauses). 20.096/20.096 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.096/20.096 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.096/20.096 -->(x,y) | ->(g(x),g(y)) # label(congruence). 20.096/20.096 -->(x,y) | ->(h(x),h(y)) # label(congruence). 20.096/20.096 -->*(x,y) | -->*(z,y) | ->(f(x,z),g(y)) # label(replacement). 20.096/20.096 -->*(x,y) | -->*(z,y) | ->(f(x,h(z)),g(y)) # label(replacement). 20.096/20.096 ->*(x,x) # label(reflexivity). 20.096/20.096 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.096/20.096 -->*(x,y) | -->*(z,y) | -->*(x,u) | -->*(h(z),u) # label(goal). 20.096/20.096 end_of_list. 20.096/20.096 20.096/20.096 ============================== end of clauses for search ============= 20.096/20.096 20.096/20.096 % There are no natural numbers in the input. 20.096/20.096 20.096/20.096 ============================== DOMAIN SIZE 2 ========================= 20.096/20.096 20.096/20.096 ============================== MODEL ================================= 20.096/20.096 20.096/20.096 interpretation( 2, [number=1, seconds=0], [ 20.096/20.096 20.096/20.096 function(g(_), [ 0, 0 ]), 20.096/20.096 20.096/20.096 function(h(_), [ 1, 0 ]), 20.096/20.096 20.096/20.096 function(f(_,_), [ 20.096/20.096 0, 0, 20.096/20.096 0, 0 ]), 20.096/20.096 20.096/20.096 relation(->*(_,_), [ 20.096/20.096 1, 0, 20.096/20.096 0, 1 ]), 20.096/20.096 20.096/20.096 relation(->(_,_), [ 20.096/20.096 1, 0, 20.096/20.096 0, 1 ]) 20.096/20.096 ]). 20.096/20.096 20.096/20.096 ============================== end of model ========================== 20.096/20.096 20.096/20.096 ============================== STATISTICS ============================ 20.096/20.096 20.096/20.096 For domain size 2. 20.096/20.096 20.096/20.096 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.096/20.096 Ground clauses: seen=66, kept=49. 20.096/20.096 Selections=2, assignments=2, propagations=14, current_models=1. 20.096/20.096 Rewrite_terms=90, rewrite_bools=73, indexes=14. 20.096/20.096 Rules_from_neg_clauses=6, cross_offs=6. 20.096/20.096 20.096/20.096 ============================== end of statistics ===================== 20.096/20.096 20.096/20.096 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.096/20.096 20.096/20.096 Exiting with 1 model. 20.096/20.096 20.096/20.096 Process 21007 exit (max_models) Wed Mar 9 09:31:42 2022 20.096/20.096 The process finished Wed Mar 9 09:31:42 2022 20.096/20.096 20.096/20.096 20.096/20.096 Mace4 cooked interpretation: 20.096/20.096 20.096/20.096 20.096/20.096 20.096/20.096 The problem is infeasible. 20.096/20.096 20.096/20.096 20.096/20.096 20.096/20.096 20.096/20.096 -> Problem conclusions: 20.096/20.096 Left linear, Right linear, Linear 20.096/20.096 Weakly orthogonal, Almost orthogonal, Orthogonal 20.096/20.096 CTRS Type: 3 20.096/20.096 Deterministic, Strongly deterministic 20.096/20.096 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.096/20.096 Maybe right-stable CTRS, Overlay CTRS 20.096/20.096 Maybe normal CTRS, Maybe almost normal CTRS 20.096/20.096 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.096/20.096 Maybe level confluent 20.096/20.096 Maybe confluent 20.096/20.096 20.096/20.096 Resulting CCPs: 20.096/20.096 No CCPs left 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 Operation Termination Processor: 20.096/20.096 Operational terminating? 20.096/20.096 YES 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 (VAR vu95NonEmpty xu39 xu39u39 x yu39 y yu39u39) 20.096/20.096 (RULES 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 ) 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 Valid CTRS Processor: 20.096/20.096 -> Rules: 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 -> The system is a deterministic 3-CTRS. 20.096/20.096 20.096/20.096 Problem 1: 20.096/20.096 20.096/20.096 2D Dependency Pair Processor: 20.096/20.096 20.096/20.096 Conditional Termination Problem 1: 20.096/20.096 -> Pairs: 20.096/20.096 Empty 20.096/20.096 -> QPairs: 20.096/20.096 Empty 20.096/20.096 -> Rules: 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 20.096/20.096 Conditional Termination Problem 2: 20.096/20.096 -> Pairs: 20.096/20.096 Empty 20.096/20.096 -> QPairs: 20.096/20.096 Empty 20.096/20.096 -> Rules: 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 20.096/20.096 20.096/20.096 The problem is decomposed in 2 subproblems. 20.096/20.096 20.096/20.096 Problem 1.1: 20.096/20.096 20.096/20.096 SCC Processor: 20.096/20.096 -> Pairs: 20.096/20.096 Empty 20.096/20.096 -> QPairs: 20.096/20.096 Empty 20.096/20.096 -> Rules: 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 ->Strongly Connected Components: 20.096/20.096 There is no strongly connected component 20.096/20.096 20.096/20.096 The problem is finite. 20.096/20.096 20.096/20.096 Problem 1.2: 20.096/20.096 20.096/20.096 SCC Processor: 20.096/20.096 -> Pairs: 20.096/20.096 Empty 20.096/20.096 -> QPairs: 20.096/20.096 Empty 20.096/20.096 -> Rules: 20.096/20.096 f(xu39,xu39u39) -> g(x) | xu39 ->* x, xu39u39 ->* x 20.096/20.096 f(yu39,h(yu39u39)) -> g(y) | yu39 ->* y, yu39u39 ->* y 20.096/20.096 ->Strongly Connected Components: 20.096/20.096 There is no strongly connected component 20.096/20.096 20.096/20.096 The problem is finite. 20.096/20.096 20.096/20.096 20.096/20.096 -> Problem conclusions: 20.096/20.096 Left linear, Right linear, Linear 20.096/20.096 Weakly orthogonal, Almost orthogonal, Orthogonal 20.096/20.096 CTRS Type: 3 20.096/20.096 Deterministic, Strongly deterministic 20.096/20.096 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.096/20.096 Maybe right-stable CTRS, Overlay CTRS 20.096/20.096 Maybe normal CTRS, Maybe almost normal CTRS 20.096/20.096 Terminating CTRS, Operational terminating CTRS, Joinable CCPs 20.096/20.096 Maybe level confluent 20.096/20.096 Confluent 20.096/20.096 20.096/20.096 The problem is joinable. 20.096/20.096 46.50user 1.56system 0:20.96elapsed 229%CPU (0avgtext+0avgdata 262016maxresident)k 20.096/20.096 8inputs+0outputs (0major+112167minor)pagefaults 0swaps