0.01/0.01 YES 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 Confluence Problem: 0.01/0.01 (VAR vNonEmpty:S x:S x':S x'':S y:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 ) 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Inlining of Conditions Processor [STERN17]: 0.01/0.01 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 Confluence Problem: 0.01/0.01 (VAR vNonEmpty:S x:S x':S x'':S y:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 ) 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Clean CTRS Processor: 0.01/0.01 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 Confluence Problem: 0.01/0.01 (VAR x:S x':S x'':S y:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 ) 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 0.01/0.01 CRule InfChecker Info: 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 Rule remains 0.01/0.01 Proof: 0.01/0.01 NO 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Infeasibility Problem: 0.01/0.01 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S x':S:S x'':S:S y:S:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S:S,x':S:S) -> g(y:S:S,y:S:S) | x:S:S ->* y:S:S, x':S:S ->* y:S:S 0.01/0.01 h(x:S:S,x':S:S,x'':S:S) -> c | x:S:S ->* y:S:S, x':S:S ->* y:S:S, x'':S:S ->* y:S:S 0.01/0.01 )] 0.01/0.01 0.01/0.01 Infeasibility Conditions: 0.01/0.01 x:S:S ->* y:S:S, x':S:S ->* y:S:S 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Obtaining a proof using Prover9: 0.01/0.01 0.01/0.01 -> Prover9 Output: 0.01/0.01 ============================== Prover9 =============================== 0.01/0.01 Prover9 (64) version 2009-11A, November 2009. 0.01/0.01 Process 44597 was started by ubuntu on ubuntu, 0.01/0.01 Wed Jul 14 10:32:35 2021 0.01/0.01 The command was "./prover9 -f /tmp/prover944588-0.in". 0.01/0.01 ============================== end of head =========================== 0.01/0.01 0.01/0.01 ============================== INPUT ================================= 0.01/0.01 0.01/0.01 % Reading from file /tmp/prover944588-0.in 0.01/0.01 0.01/0.01 assign(max_seconds,20). 0.01/0.01 0.01/0.01 formulas(assumptions). 0.01/0.01 ->*_s0(x,x) # label(reflexivity). 0.01/0.01 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.01/0.01 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 0.01/0.01 ->_s0(x1,y) -> ->_s0(h(x1,x2,x3),h(y,x2,x3)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(h(x1,x2,x3),h(x1,y,x3)) # label(congruence). 0.01/0.01 ->_s0(x3,y) -> ->_s0(h(x1,x2,x3),h(x1,x2,y)) # label(congruence). 0.01/0.01 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 0.01/0.01 ->*_s0(x2,x5) & ->*_s0(x3,x5) -> ->_s0(f(x2,x3),g(x5,x5)) # label(replacement). 0.01/0.01 ->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5) -> ->_s0(h(x2,x3,x4),c) # label(replacement). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(goals). 0.01/0.01 (exists x2 exists x3 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5))) # label(goal). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== end of input ========================== 0.01/0.01 0.01/0.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.01/0.01 0.01/0.01 % Formulas that are not ordinary clauses: 0.01/0.01 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.01/0.01 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 4 ->_s0(x1,y) -> ->_s0(h(x1,x2,x3),h(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 5 ->_s0(x2,y) -> ->_s0(h(x1,x2,x3),h(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 6 ->_s0(x3,y) -> ->_s0(h(x1,x2,x3),h(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 7 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 8 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 9 ->*_s0(x2,x5) & ->*_s0(x3,x5) -> ->_s0(f(x2,x3),g(x5,x5)) # label(replacement) # label(non_clause). [assumption]. 0.01/0.01 10 ->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5) -> ->_s0(h(x2,x3,x4),c) # label(replacement) # label(non_clause). [assumption]. 0.01/0.01 11 (exists x2 exists x3 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.01/0.01 0.01/0.01 ============================== end of process non-clausal formulas === 0.01/0.01 0.01/0.01 ============================== PROCESS INITIAL CLAUSES =============== 0.01/0.01 0.01/0.01 % Clauses before input processing: 0.01/0.01 0.01/0.01 formulas(usable). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(sos). 0.01/0.01 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) | ->_s0(h(x,z,u),c) # label(replacement). [clausify(10)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) # label(goal). [deny(11)]. 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(demodulators). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== PREDICATE ELIMINATION ================= 0.01/0.01 0.01/0.01 No predicates eliminated. 0.01/0.01 0.01/0.01 ============================== end predicate elimination ============= 0.01/0.01 0.01/0.01 Auto_denials: 0.01/0.01 % copying label goal to answer in negative clause 0.01/0.01 0.01/0.01 Term ordering decisions: 0.01/0.01 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.01/0.01 Function symbol precedence: function_order([ c, f, g, h ]). 0.01/0.01 After inverse_order: (no changes). 0.01/0.01 Unfolding symbols: (none). 0.01/0.01 0.01/0.01 Auto_inference settings: 0.01/0.01 % set(neg_binary_resolution). % (HNE depth_diff=-9) 0.01/0.01 % clear(ordered_res). % (HNE depth_diff=-9) 0.01/0.01 % set(ur_resolution). % (HNE depth_diff=-9) 0.01/0.01 % set(ur_resolution) -> set(pos_ur_resolution). 0.01/0.01 % set(ur_resolution) -> set(neg_ur_resolution). 0.01/0.01 0.01/0.01 Auto_process settings: 0.01/0.01 % set(unit_deletion). % (Horn set with negative nonunits) 0.01/0.01 0.01/0.01 kept: 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 kept: 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 kept: 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 kept: 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 kept: 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 kept: 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 kept: 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 kept: 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 kept: 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 kept: 21 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 kept: 22 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) | ->_s0(h(x,z,u),c) # label(replacement). [clausify(10)]. 0.01/0.01 kept: 23 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 0.01/0.01 ============================== end of process initial clauses ======== 0.01/0.01 0.01/0.01 ============================== CLAUSES FOR SEARCH ==================== 0.01/0.01 0.01/0.01 % Clauses after input processing: 0.01/0.01 0.01/0.01 formulas(usable). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(sos). 0.01/0.01 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 23 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(demodulators). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== end of clauses for search ============= 0.01/0.01 0.01/0.01 ============================== SEARCH ================================ 0.01/0.01 0.01/0.01 % Starting search at 0.00 seconds. 0.01/0.01 0.01/0.01 given #1 (I,wt=3): 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 0.01/0.01 given #2 (I,wt=9): 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 0.01/0.01 given #3 (I,wt=10): 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 0.01/0.01 given #4 (I,wt=10): 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 0.01/0.01 given #5 (I,wt=12): 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 0.01/0.01 given #6 (I,wt=12): 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 0.01/0.01 given #7 (I,wt=12): 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 0.01/0.01 given #8 (I,wt=10): 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 0.01/0.01 given #9 (I,wt=10): 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 0.01/0.01 given #10 (I,wt=6): 23 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 0.01/0.01 ============================== PROOF ================================= 0.01/0.01 0.01/0.01 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.01/0.01 % Length of proof is 5. 0.01/0.01 % Level of proof is 3. 0.01/0.01 % Maximum clause weight is 6.000. 0.01/0.01 % Given clauses 10. 0.01/0.01 0.01/0.01 11 (exists x2 exists x3 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.01/0.01 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 23 -->*_s0(x,y) | -->*_s0(z,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 24 -->*_s0(x,y) # answer(goal). [resolve(23,a,12,a)]. 0.01/0.01 25 $F # answer(goal). [resolve(24,a,12,a)]. 0.01/0.01 0.01/0.01 ============================== end of proof ========================== 0.01/0.01 0.01/0.01 ============================== STATISTICS ============================ 0.01/0.01 0.01/0.01 Given=10. Generated=14. Kept=13. proofs=1. 0.01/0.01 Usable=10. Sos=0. Demods=0. Limbo=0, Disabled=14. Hints=0. 0.01/0.01 Kept_by_rule=0, Deleted_by_rule=0. 0.01/0.01 Forward_subsumed=1. Back_subsumed=2. 0.01/0.01 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.01/0.01 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.01/0.01 Demod_attempts=0. Demod_rewrites=0. 0.01/0.01 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.01/0.01 Nonunit_fsub_feature_tests=6. Nonunit_bsub_feature_tests=24. 0.01/0.01 Megabytes=0.07. 0.01/0.01 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.01/0.01 0.01/0.01 ============================== end of statistics ===================== 0.01/0.01 0.01/0.01 ============================== end of search ========================= 0.01/0.01 0.01/0.01 THEOREM PROVED 0.01/0.01 0.01/0.01 Exiting with 1 proof. 0.01/0.01 0.01/0.01 Process 44597 exit (max_proofs) Wed Jul 14 10:32:35 2021 0.01/0.01 0.01/0.01 0.01/0.01 The problem is feasible. 0.01/0.01 0.01/0.01 0.01/0.01 CRule InfChecker Info: 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 Rule remains 0.01/0.01 Proof: 0.01/0.01 NO 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Infeasibility Problem: 0.01/0.01 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S x':S:S x'':S:S y:S:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S:S,x':S:S) -> g(y:S:S,y:S:S) | x:S:S ->* y:S:S, x':S:S ->* y:S:S 0.01/0.01 h(x:S:S,x':S:S,x'':S:S) -> c | x:S:S ->* y:S:S, x':S:S ->* y:S:S, x'':S:S ->* y:S:S 0.01/0.01 )] 0.01/0.01 0.01/0.01 Infeasibility Conditions: 0.01/0.01 x:S:S ->* y:S:S, x':S:S ->* y:S:S, x'':S:S ->* y:S:S 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 Obtaining a proof using Prover9: 0.01/0.01 0.01/0.01 -> Prover9 Output: 0.01/0.01 ============================== Prover9 =============================== 0.01/0.01 Prover9 (64) version 2009-11A, November 2009. 0.01/0.01 Process 44620 was started by ubuntu on ubuntu, 0.01/0.01 Wed Jul 14 10:32:35 2021 0.01/0.01 The command was "./prover9 -f /tmp/prover944610-0.in". 0.01/0.01 ============================== end of head =========================== 0.01/0.01 0.01/0.01 ============================== INPUT ================================= 0.01/0.01 0.01/0.01 % Reading from file /tmp/prover944610-0.in 0.01/0.01 0.01/0.01 assign(max_seconds,20). 0.01/0.01 0.01/0.01 formulas(assumptions). 0.01/0.01 ->*_s0(x,x) # label(reflexivity). 0.01/0.01 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.01/0.01 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 0.01/0.01 ->_s0(x1,y) -> ->_s0(h(x1,x2,x3),h(y,x2,x3)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(h(x1,x2,x3),h(x1,y,x3)) # label(congruence). 0.01/0.01 ->_s0(x3,y) -> ->_s0(h(x1,x2,x3),h(x1,x2,y)) # label(congruence). 0.01/0.01 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 0.01/0.01 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 0.01/0.01 ->*_s0(x2,x5) & ->*_s0(x3,x5) -> ->_s0(f(x2,x3),g(x5,x5)) # label(replacement). 0.01/0.01 ->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5) -> ->_s0(h(x2,x3,x4),c) # label(replacement). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(goals). 0.01/0.01 (exists x2 exists x3 exists x4 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5))) # label(goal). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== end of input ========================== 0.01/0.01 0.01/0.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.01/0.01 0.01/0.01 % Formulas that are not ordinary clauses: 0.01/0.01 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.01/0.01 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 4 ->_s0(x1,y) -> ->_s0(h(x1,x2,x3),h(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 5 ->_s0(x2,y) -> ->_s0(h(x1,x2,x3),h(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 6 ->_s0(x3,y) -> ->_s0(h(x1,x2,x3),h(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 7 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 8 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.01/0.01 9 ->*_s0(x2,x5) & ->*_s0(x3,x5) -> ->_s0(f(x2,x3),g(x5,x5)) # label(replacement) # label(non_clause). [assumption]. 0.01/0.01 10 ->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5) -> ->_s0(h(x2,x3,x4),c) # label(replacement) # label(non_clause). [assumption]. 0.01/0.01 11 (exists x2 exists x3 exists x4 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.01/0.01 0.01/0.01 ============================== end of process non-clausal formulas === 0.01/0.01 0.01/0.01 ============================== PROCESS INITIAL CLAUSES =============== 0.01/0.01 0.01/0.01 % Clauses before input processing: 0.01/0.01 0.01/0.01 formulas(usable). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(sos). 0.01/0.01 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) | ->_s0(h(x,z,u),c) # label(replacement). [clausify(10)]. 0.01/0.01 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) # label(goal). [deny(11)]. 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(demodulators). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== PREDICATE ELIMINATION ================= 0.01/0.01 0.01/0.01 No predicates eliminated. 0.01/0.01 0.01/0.01 ============================== end predicate elimination ============= 0.01/0.01 0.01/0.01 Auto_denials: 0.01/0.01 % copying label goal to answer in negative clause 0.01/0.01 0.01/0.01 Term ordering decisions: 0.01/0.01 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.01/0.01 Function symbol precedence: function_order([ c, f, g, h ]). 0.01/0.01 After inverse_order: (no changes). 0.01/0.01 Unfolding symbols: (none). 0.01/0.01 0.01/0.01 Auto_inference settings: 0.01/0.01 % set(neg_binary_resolution). % (HNE depth_diff=-9) 0.01/0.01 % clear(ordered_res). % (HNE depth_diff=-9) 0.01/0.01 % set(ur_resolution). % (HNE depth_diff=-9) 0.01/0.01 % set(ur_resolution) -> set(pos_ur_resolution). 0.01/0.01 % set(ur_resolution) -> set(neg_ur_resolution). 0.01/0.01 0.01/0.01 Auto_process settings: 0.01/0.01 % set(unit_deletion). % (Horn set with negative nonunits) 0.01/0.01 0.01/0.01 kept: 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 kept: 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 kept: 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 kept: 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 kept: 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 kept: 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 kept: 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 kept: 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 kept: 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 kept: 21 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 kept: 22 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) | ->_s0(h(x,z,u),c) # label(replacement). [clausify(10)]. 0.01/0.01 kept: 23 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 0.01/0.01 ============================== end of process initial clauses ======== 0.01/0.01 0.01/0.01 ============================== CLAUSES FOR SEARCH ==================== 0.01/0.01 0.01/0.01 % Clauses after input processing: 0.01/0.01 0.01/0.01 formulas(usable). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(sos). 0.01/0.01 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 21 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 23 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 formulas(demodulators). 0.01/0.01 end_of_list. 0.01/0.01 0.01/0.01 ============================== end of clauses for search ============= 0.01/0.01 0.01/0.01 ============================== SEARCH ================================ 0.01/0.01 0.01/0.01 % Starting search at 0.00 seconds. 0.01/0.01 0.01/0.01 given #1 (I,wt=3): 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 0.01/0.01 given #2 (I,wt=9): 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 0.01/0.01 0.01/0.01 given #3 (I,wt=10): 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 0.01/0.01 0.01/0.01 given #4 (I,wt=10): 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 0.01/0.01 0.01/0.01 given #5 (I,wt=12): 16 -->_s0(x,y) | ->_s0(h(x,z,u),h(y,z,u)) # label(congruence). [clausify(4)]. 0.01/0.01 0.01/0.01 given #6 (I,wt=12): 17 -->_s0(x,y) | ->_s0(h(z,x,u),h(z,y,u)) # label(congruence). [clausify(5)]. 0.01/0.01 0.01/0.01 given #7 (I,wt=12): 18 -->_s0(x,y) | ->_s0(h(z,u,x),h(z,u,y)) # label(congruence). [clausify(6)]. 0.01/0.01 0.01/0.01 given #8 (I,wt=10): 19 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(7)]. 0.01/0.01 0.01/0.01 given #9 (I,wt=10): 20 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(8)]. 0.01/0.01 0.01/0.01 given #10 (I,wt=13): 21 -->*_s0(x,y) | -->*_s0(z,y) | ->_s0(f(x,z),g(y,y)) # label(replacement). [clausify(9)]. 0.01/0.01 0.01/0.01 given #11 (I,wt=9): 23 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 0.01/0.01 ============================== PROOF ================================= 0.01/0.01 0.01/0.01 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.01/0.01 % Length of proof is 5. 0.01/0.01 % Level of proof is 3. 0.01/0.01 % Maximum clause weight is 9.000. 0.01/0.01 % Given clauses 11. 0.01/0.01 0.01/0.01 11 (exists x2 exists x3 exists x4 exists x5 (->*_s0(x2,x5) & ->*_s0(x3,x5) & ->*_s0(x4,x5))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.01/0.01 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.01/0.01 23 -->*_s0(x,y) | -->*_s0(z,y) | -->*_s0(u,y) # label(goal) # answer(goal). [deny(11)]. 0.01/0.01 26 -->*_s0(x,y) # answer(goal). [ur(23,b,12,a,c,12,a)]. 0.01/0.01 27 $F # answer(goal). [resolve(26,a,12,a)]. 0.01/0.01 0.01/0.01 ============================== end of proof ========================== 0.01/0.01 0.01/0.01 ============================== STATISTICS ============================ 0.01/0.01 0.01/0.01 Given=11. Generated=20. Kept=15. proofs=1. 0.01/0.01 Usable=11. Sos=1. Demods=0. Limbo=1, Disabled=13. Hints=0. 0.01/0.01 Kept_by_rule=0, Deleted_by_rule=0. 0.01/0.01 Forward_subsumed=5. Back_subsumed=1. 0.01/0.01 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.01/0.01 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.01/0.01 Demod_attempts=0. Demod_rewrites=0. 0.01/0.01 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.01/0.01 Nonunit_fsub_feature_tests=10. Nonunit_bsub_feature_tests=24. 0.01/0.01 Megabytes=0.08. 0.01/0.01 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.01/0.01 0.01/0.01 ============================== end of statistics ===================== 0.01/0.01 0.01/0.01 ============================== end of search ========================= 0.01/0.01 0.01/0.01 THEOREM PROVED 0.01/0.01 0.01/0.01 Exiting with 1 proof. 0.01/0.01 0.01/0.01 Process 44620 exit (max_proofs) Wed Jul 14 10:32:35 2021 0.01/0.01 0.01/0.01 0.01/0.01 The problem is feasible. 0.01/0.01 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 Confluence Problem: 0.01/0.01 (VAR x:S x':S x'':S y:S) 0.01/0.01 (STRATEGY CONTEXTSENSITIVE 0.01/0.01 (f 1 2) 0.01/0.01 (h 1 2 3) 0.01/0.01 (c) 0.01/0.01 (fSNonEmpty) 0.01/0.01 (g 1 2) 0.01/0.01 ) 0.01/0.01 (RULES 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 ) 0.01/0.01 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.01/0.01 0.01/0.01 Critical Pairs Processor: 0.01/0.01 -> Rules: 0.01/0.01 f(x:S,x':S) -> g(y:S,y:S) | x:S ->* y:S, x':S ->* y:S 0.01/0.01 h(x:S,x':S,x'':S) -> c | x:S ->* y:S, x':S ->* y:S, x'':S ->* y:S 0.01/0.01 -> Vars: 0.01/0.01 "x", "x'", "y", "x", "x'", "x''", "y" 0.01/0.01 -> FVars: 0.01/0.01 "x5", "x6", "x7", "x8", "x9", "x10", "x11" 0.01/0.01 -> PVars: 0.01/0.01 "x": ["x5", "x8"], "x'": ["x6", "x9"], "y": ["x7", "x11"], "x''": ["x10"] 0.01/0.01 0.01/0.01 -> Rlps: 0.01/0.01 crule: f(x5:S,x6:S) -> g(x7:S,x7:S) | x5:S ->* x7:S, x6:S ->* x7:S, id: 1, possubterms: f(x5:S,x6:S)-> [] 0.01/0.01 crule: h(x8:S,x9:S,x10:S) -> c | x8:S ->* x11:S, x9:S ->* x11:S, x10:S ->* x11:S, id: 2, possubterms: h(x8:S,x9:S,x10:S)-> [] 0.01/0.01 0.01/0.01 -> Unifications: 0.01/0.01 0.01/0.01 0.01/0.01 -> Critical pairs info: 0.01/0.01 0.01/0.01 0.01/0.01 -> Problem conclusions: 0.01/0.01 Left linear, Not right linear, Not linear 0.01/0.01 Weakly orthogonal, Almost orthogonal, Orthogonal 0.01/0.01 CTRS Type: 3 0.01/0.01 Deterministic, Strongly deterministic 0.01/0.01 Oriented CTRS, Properly oriented CTRS, Not join CTRS 0.01/0.01 Maybe right-stable CTRS, Overlay CTRS 0.01/0.01 Maybe normal CTRS, Maybe almost normal CTRS 0.01/0.01 Maybe terminating CTRS, Joinable CCPs 0.01/0.01 Maybe level confluent 0.01/0.01 Maybe confluent 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 Clean Infeasible CCPs Processor: 0.01/0.01 0.01/0.01 0.01/0.01 -> Problem conclusions: 0.01/0.01 Left linear, Not right linear, Not linear 0.01/0.01 Weakly orthogonal, Almost orthogonal, Orthogonal 0.01/0.01 CTRS Type: 3 0.01/0.01 Deterministic, Strongly deterministic 0.01/0.01 Oriented CTRS, Properly oriented CTRS, Not join CTRS 0.01/0.01 Maybe right-stable CTRS, Overlay CTRS 0.01/0.01 Maybe normal CTRS, Maybe almost normal CTRS 0.01/0.01 Maybe terminating CTRS, Joinable CCPs 0.01/0.01 Maybe level confluent 0.01/0.01 Maybe confluent 0.01/0.01 0.01/0.01 Resulting CCPs: 0.01/0.01 No CCPs left 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 Operation Termination Processor: 0.01/0.01 Operational terminating? 0.01/0.01 YES 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 (VAR vu95NonEmpty:S xu58S:S xu39u58S:S xu39u39u58S:S yu58S:S) 0.01/0.01 (RULES 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 ) 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 Valid CTRS Processor: 0.01/0.01 -> Rules: 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 -> The system is a deterministic 3-CTRS. 0.01/0.01 0.01/0.01 Problem 1: 0.01/0.01 0.01/0.01 2D Dependency Pair Processor: 0.01/0.01 0.01/0.01 Conditional Termination Problem 1: 0.01/0.01 -> Pairs: 0.01/0.01 Empty 0.01/0.01 -> QPairs: 0.01/0.01 Empty 0.01/0.01 -> Rules: 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 0.01/0.01 Conditional Termination Problem 2: 0.01/0.01 -> Pairs: 0.01/0.01 Empty 0.01/0.01 -> QPairs: 0.01/0.01 Empty 0.01/0.01 -> Rules: 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 0.01/0.01 0.01/0.01 The problem is decomposed in 2 subproblems. 0.01/0.01 0.01/0.01 Problem 1.1: 0.01/0.01 0.01/0.01 SCC Processor: 0.01/0.01 -> Pairs: 0.01/0.01 Empty 0.01/0.01 -> QPairs: 0.01/0.01 Empty 0.01/0.01 -> Rules: 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 ->Strongly Connected Components: 0.01/0.01 There is no strongly connected component 0.01/0.01 0.01/0.01 The problem is finite. 0.01/0.01 0.01/0.01 Problem 1.2: 0.01/0.01 0.01/0.01 SCC Processor: 0.01/0.01 -> Pairs: 0.01/0.01 Empty 0.01/0.01 -> QPairs: 0.01/0.01 Empty 0.01/0.01 -> Rules: 0.01/0.01 f(xu58S:S,xu39u58S:S) -> g(yu58S:S,yu58S:S) | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S 0.01/0.01 h(xu58S:S,xu39u58S:S,xu39u39u58S:S) -> c | xu58S:S ->* yu58S:S, xu39u58S:S ->* yu58S:S, xu39u39u58S:S ->* yu58S:S 0.01/0.01 ->Strongly Connected Components: 0.01/0.01 There is no strongly connected component 0.01/0.01 0.01/0.01 The problem is finite. 0.01/0.01 0.01/0.01 0.01/0.01 -> Problem conclusions: 0.01/0.01 Left linear, Not right linear, Not linear 0.01/0.01 Weakly orthogonal, Almost orthogonal, Orthogonal 0.01/0.01 CTRS Type: 3 0.01/0.01 Deterministic, Strongly deterministic 0.01/0.01 Oriented CTRS, Properly oriented CTRS, Not join CTRS 0.01/0.01 Maybe right-stable CTRS, Overlay CTRS 0.01/0.01 Maybe normal CTRS, Maybe almost normal CTRS 0.01/0.01 Terminating CTRS, Joinable CCPs 0.01/0.01 Maybe level confluent 0.01/0.01 Confluent 0.01/0.01 0.01/0.01 The problem is joinable. 0.01/0.01 0.07user 0.01system 0:00.10elapsed 94%CPU (0avgtext+0avgdata 11840maxresident)k 0.01/0.01 0inputs+0outputs (0major+8931minor)pagefaults 0swaps