20.082/20.082 YES 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 Confluence Problem: 20.082/20.082 (VAR vNonEmpty x y z) 20.082/20.082 (REPLACEMENT-MAP 20.082/20.082 (f 1, 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 g(x) -> c | d ->* c 20.082/20.082 ) 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Inlining of Conditions Processor [STERN17]: 20.082/20.082 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 Confluence Problem: 20.082/20.082 (VAR vNonEmpty x y z) 20.082/20.082 (REPLACEMENT-MAP 20.082/20.082 (f 1, 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 g(x) -> c | d ->* c 20.082/20.082 ) 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Clean CTRS Processor: 20.082/20.082 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 Confluence Problem: 20.082/20.082 (VAR x y z) 20.082/20.082 (REPLACEMENT-MAP 20.082/20.082 (f 1, 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 ) 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 20.082/20.082 CRule InfChecker Info: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 Rule remains 20.082/20.082 Proof: 20.082/20.082 NO 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Infeasibility Problem: 20.082/20.082 [(VAR vNonEmpty x y z vNonEmpty x y z) 20.082/20.082 (STRATEGY CONTEXTSENSITIVE 20.082/20.082 (f 1 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 g(x) -> c | d ->* c 20.082/20.082 )] 20.082/20.082 20.082/20.082 Infeasibility Conditions: 20.082/20.082 g(x) ->* z, g(y) ->* z 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Obtaining a proof using Prover9: 20.082/20.082 20.082/20.082 -> Prover9 Output: 20.082/20.082 ============================== Prover9 =============================== 20.082/20.082 Prover9 (64) version 2009-11A, November 2009. 20.082/20.082 Process 11223 was started by ubuntu on ubuntu, 20.082/20.082 Wed Mar 9 09:16:16 2022 20.082/20.082 The command was "./prover9 -f /tmp/prover911214-0.in". 20.082/20.082 ============================== end of head =========================== 20.082/20.082 20.082/20.082 ============================== INPUT ================================= 20.082/20.082 20.082/20.082 % Reading from file /tmp/prover911214-0.in 20.082/20.082 20.082/20.082 assign(max_seconds,20). 20.082/20.082 20.082/20.082 formulas(assumptions). 20.082/20.082 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.082/20.082 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.082/20.082 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 20.082/20.082 ->*_s0(g(x1),x3) & ->*_s0(g(x2),x3) -> ->_s0(f(x1,x2),x1) # label(replacement). 20.082/20.082 ->*_s0(d,c) -> ->_s0(g(x1),c) # label(replacement). 20.082/20.082 ->*_s0(x,x) # label(reflexivity). 20.082/20.082 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(goals). 20.082/20.082 (exists x5 exists x6 exists x7 (->*_s0(g(x5),x7) & ->*_s0(g(x6),x7))) # label(goal). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 ============================== end of input ========================== 20.082/20.082 20.082/20.082 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.082/20.082 20.082/20.082 % Formulas that are not ordinary clauses: 20.082/20.082 1 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 2 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 3 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 4 ->*_s0(g(x1),x3) & ->*_s0(g(x2),x3) -> ->_s0(f(x1,x2),x1) # label(replacement) # label(non_clause). [assumption]. 20.082/20.082 5 ->*_s0(d,c) -> ->_s0(g(x1),c) # label(replacement) # label(non_clause). [assumption]. 20.082/20.082 6 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.082/20.082 7 (exists x5 exists x6 exists x7 (->*_s0(g(x5),x7) & ->*_s0(g(x6),x7))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.082/20.082 20.082/20.082 ============================== end of process non-clausal formulas === 20.082/20.082 20.082/20.082 ============================== PROCESS INITIAL CLAUSES =============== 20.082/20.082 20.082/20.082 % Clauses before input processing: 20.082/20.082 20.082/20.082 formulas(usable). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(sos). 20.082/20.082 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.082/20.082 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.082/20.082 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.082/20.082 -->*_s0(g(x),y) | -->*_s0(g(z),y) | ->_s0(f(x,z),x) # label(replacement). [clausify(4)]. 20.082/20.082 -->*_s0(d,c) | ->_s0(g(x),c) # label(replacement). [clausify(5)]. 20.082/20.082 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.082/20.082 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(6)]. 20.082/20.082 -->*_s0(g(x),y) | -->*_s0(g(z),y) # label(goal). [deny(7)]. 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(demodulators). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 ============================== PREDICATE ELIMINATION ================= 20.082/20.082 20.082/20.082 No predicates eliminated. 20.082/20.082 20.082/20.082 ============================== end predicate elimination ============= 20.082/20.082 20.082/20.082 Auto_denials: 20.082/20.082 % copying label goal to answer in negative clause 20.082/20.082 20.082/20.082 Term ordering decisions: 20.082/20.082 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.082/20.082 Function symbol precedence: function_order([ c, d, f, g ]). 20.082/20.082 After inverse_order: (no changes). 20.082/20.082 Unfolding symbols: (none). 20.082/20.082 20.082/20.082 Auto_inference settings: 20.082/20.082 % set(neg_binary_resolution). % (HNE depth_diff=-4) 20.082/20.082 % clear(ordered_res). % (HNE depth_diff=-4) 20.082/20.082 % set(ur_resolution). % (HNE depth_diff=-4) 20.082/20.082 % set(ur_resolution) -> set(pos_ur_resolution). 20.082/20.082 % set(ur_resolution) -> set(neg_ur_resolution). 20.082/20.082 20.082/20.082 Auto_process settings: 20.082/20.082 % set(unit_deletion). % (Horn set with negative nonunits) 20.082/20.082 20.082/20.082 kept: 8 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.082/20.082 kept: 9 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.082/20.082 kept: 10 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.082/20.082 kept: 11 -->*_s0(g(x),y) | -->*_s0(g(z),y) | ->_s0(f(x,z),x) # label(replacement). [clausify(4)]. 20.082/20.082 kept: 12 -->*_s0(d,c) | ->_s0(g(x),c) # label(replacement). [clausify(5)]. 20.082/20.082 kept: 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.082/20.082 kept: 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(6)]. 20.082/20.082 kept: 15 -->*_s0(g(x),y) | -->*_s0(g(z),y) # label(goal) # answer(goal). [deny(7)]. 20.082/20.082 20.082/20.082 ============================== end of process initial clauses ======== 20.082/20.082 20.082/20.082 ============================== CLAUSES FOR SEARCH ==================== 20.082/20.082 20.082/20.082 % Clauses after input processing: 20.082/20.082 20.082/20.082 formulas(usable). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(sos). 20.082/20.082 8 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.082/20.082 9 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.082/20.082 10 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.082/20.082 12 -->*_s0(d,c) | ->_s0(g(x),c) # label(replacement). [clausify(5)]. 20.082/20.082 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.082/20.082 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(6)]. 20.082/20.082 15 -->*_s0(g(x),y) | -->*_s0(g(z),y) # label(goal) # answer(goal). [deny(7)]. 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(demodulators). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 ============================== end of clauses for search ============= 20.082/20.082 20.082/20.082 ============================== SEARCH ================================ 20.082/20.082 20.082/20.082 % Starting search at 0.00 seconds. 20.082/20.082 20.082/20.082 given #1 (I,wt=10): 8 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 20.082/20.082 20.082/20.082 given #2 (I,wt=10): 9 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 20.082/20.082 20.082/20.082 given #3 (I,wt=8): 10 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(3)]. 20.082/20.082 20.082/20.082 given #4 (I,wt=7): 12 -->*_s0(d,c) | ->_s0(g(x),c) # label(replacement). [clausify(5)]. 20.082/20.082 20.082/20.082 given #5 (I,wt=3): 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.082/20.082 20.082/20.082 given #6 (I,wt=9): 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(6)]. 20.082/20.082 20.082/20.082 given #7 (I,wt=8): 15 -->*_s0(g(x),y) | -->*_s0(g(z),y) # label(goal) # answer(goal). [deny(7)]. 20.082/20.082 20.082/20.082 ============================== PROOF ================================= 20.082/20.082 20.082/20.082 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.082/20.082 % Length of proof is 5. 20.082/20.082 % Level of proof is 3. 20.082/20.082 % Maximum clause weight is 8.000. 20.082/20.082 % Given clauses 7. 20.082/20.082 20.082/20.082 7 (exists x5 exists x6 exists x7 (->*_s0(g(x5),x7) & ->*_s0(g(x6),x7))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.082/20.082 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.082/20.082 15 -->*_s0(g(x),y) | -->*_s0(g(z),y) # label(goal) # answer(goal). [deny(7)]. 20.082/20.082 16 -->*_s0(g(x),g(y)) # answer(goal). [resolve(15,a,13,a)]. 20.082/20.082 17 $F # answer(goal). [resolve(16,a,13,a)]. 20.082/20.082 20.082/20.082 ============================== end of proof ========================== 20.082/20.082 20.082/20.082 ============================== STATISTICS ============================ 20.082/20.082 20.082/20.082 Given=7. Generated=10. Kept=9. proofs=1. 20.082/20.082 Usable=7. Sos=0. Demods=0. Limbo=0, Disabled=9. Hints=0. 20.082/20.082 Kept_by_rule=0, Deleted_by_rule=0. 20.082/20.082 Forward_subsumed=1. Back_subsumed=1. 20.082/20.082 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.082/20.082 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.082/20.082 Demod_attempts=0. Demod_rewrites=0. 20.082/20.082 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.082/20.082 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=11. 20.082/20.082 Megabytes=0.06. 20.082/20.082 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.082/20.082 20.082/20.082 ============================== end of statistics ===================== 20.082/20.082 20.082/20.082 ============================== end of search ========================= 20.082/20.082 20.082/20.082 THEOREM PROVED 20.082/20.082 20.082/20.082 Exiting with 1 proof. 20.082/20.082 20.082/20.082 Process 11223 exit (max_proofs) Wed Mar 9 09:16:16 2022 20.082/20.082 20.082/20.082 20.082/20.082 The problem is feasible. 20.082/20.082 20.082/20.082 20.082/20.082 CRule InfChecker Info: 20.082/20.082 g(x) -> c | d ->* c 20.082/20.082 Rule deleted 20.082/20.082 Proof: 20.082/20.082 YES 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Infeasibility Problem: 20.082/20.082 [(VAR vNonEmpty x y z vNonEmpty) 20.082/20.082 (STRATEGY CONTEXTSENSITIVE 20.082/20.082 (f 1 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 g(x) -> c | d ->* c 20.082/20.082 )] 20.082/20.082 20.082/20.082 Infeasibility Conditions: 20.082/20.082 d ->* c 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 Obtaining a model using Mace4: 20.082/20.082 20.082/20.082 -> Usable Rules: 20.082/20.082 Empty 20.082/20.082 20.082/20.082 -> Mace4 Output: 20.082/20.082 ============================== Mace4 ================================= 20.082/20.082 Mace4 (64) version 2009-11A, November 2009. 20.082/20.082 Process 11251 was started by ubuntu on ubuntu, 20.082/20.082 Wed Mar 9 09:16:17 2022 20.082/20.082 The command was "./mace4 -c -f /tmp/mace411236-2.in". 20.082/20.082 ============================== end of head =========================== 20.082/20.082 20.082/20.082 ============================== INPUT ================================= 20.082/20.082 20.082/20.082 % Reading from file /tmp/mace411236-2.in 20.082/20.082 20.082/20.082 assign(max_seconds,20). 20.082/20.082 20.082/20.082 formulas(assumptions). 20.082/20.082 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.082/20.082 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.082/20.082 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence). 20.082/20.082 ->*(x,x) # label(reflexivity). 20.082/20.082 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 formulas(goals). 20.082/20.082 ->*(d,c) # label(goal). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 ============================== end of input ========================== 20.082/20.082 20.082/20.082 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.082/20.082 20.082/20.082 % Formulas that are not ordinary clauses: 20.082/20.082 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 3 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 20.082/20.082 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.082/20.082 5 ->*(d,c) # label(goal) # label(non_clause) # label(goal). [goal]. 20.082/20.082 20.082/20.082 ============================== end of process non-clausal formulas === 20.082/20.082 20.082/20.082 ============================== CLAUSES FOR SEARCH ==================== 20.082/20.082 20.082/20.082 formulas(mace4_clauses). 20.082/20.082 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.082/20.082 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.082/20.082 -->(x,y) | ->(g(x),g(y)) # label(congruence). 20.082/20.082 ->*(x,x) # label(reflexivity). 20.082/20.082 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.082/20.082 -->*(d,c) # label(goal). 20.082/20.082 end_of_list. 20.082/20.082 20.082/20.082 ============================== end of clauses for search ============= 20.082/20.082 20.082/20.082 % There are no natural numbers in the input. 20.082/20.082 20.082/20.082 ============================== DOMAIN SIZE 2 ========================= 20.082/20.082 20.082/20.082 ============================== MODEL ================================= 20.082/20.082 20.082/20.082 interpretation( 2, [number=1, seconds=0], [ 20.082/20.082 20.082/20.082 function(c, [ 0 ]), 20.082/20.082 20.082/20.082 function(d, [ 1 ]), 20.082/20.082 20.082/20.082 function(g(_), [ 0, 0 ]), 20.082/20.082 20.082/20.082 function(f(_,_), [ 20.082/20.082 0, 0, 20.082/20.082 0, 0 ]), 20.082/20.082 20.082/20.082 relation(->*(_,_), [ 20.082/20.082 1, 0, 20.082/20.082 0, 1 ]), 20.082/20.082 20.082/20.082 relation(->(_,_), [ 20.082/20.082 0, 0, 20.082/20.082 0, 0 ]) 20.082/20.082 ]). 20.082/20.082 20.082/20.082 ============================== end of model ========================== 20.082/20.082 20.082/20.082 ============================== STATISTICS ============================ 20.082/20.082 20.082/20.082 For domain size 2. 20.082/20.082 20.082/20.082 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.082/20.082 Ground clauses: seen=31, kept=27. 20.082/20.082 Selections=9, assignments=9, propagations=7, current_models=1. 20.082/20.082 Rewrite_terms=42, rewrite_bools=34, indexes=4. 20.082/20.082 Rules_from_neg_clauses=1, cross_offs=1. 20.082/20.082 20.082/20.082 ============================== end of statistics ===================== 20.082/20.082 20.082/20.082 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.082/20.082 20.082/20.082 Exiting with 1 model. 20.082/20.082 20.082/20.082 Process 11251 exit (max_models) Wed Mar 9 09:16:17 2022 20.082/20.082 The process finished Wed Mar 9 09:16:17 2022 20.082/20.082 20.082/20.082 20.082/20.082 Mace4 cooked interpretation: 20.082/20.082 20.082/20.082 20.082/20.082 20.082/20.082 The problem is infeasible. 20.082/20.082 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 Confluence Problem: 20.082/20.082 (VAR x y z) 20.082/20.082 (REPLACEMENT-MAP 20.082/20.082 (f 1, 2) 20.082/20.082 (g 1) 20.082/20.082 (c) 20.082/20.082 (d) 20.082/20.082 (fSNonEmpty) 20.082/20.082 ) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 ) 20.082/20.082 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.082/20.082 20.082/20.082 Critical Pairs Processor: 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 -> Vars: 20.082/20.082 "x", "y", "z" 20.082/20.082 20.082/20.082 -> Rlps: 20.082/20.082 crule: f(x,y) -> x | g(x) ->* z, g(y) ->* z, id: 1, possubterms: f(x,y)-> [] 20.082/20.082 20.082/20.082 -> Unifications: 20.082/20.082 20.082/20.082 20.082/20.082 -> Critical pairs info: 20.082/20.082 20.082/20.082 20.082/20.082 -> Problem conclusions: 20.082/20.082 Left linear, Right linear, Linear 20.082/20.082 Weakly orthogonal, Almost orthogonal, Orthogonal 20.082/20.082 CTRS Type: 2 20.082/20.082 Deterministic, Strongly deterministic 20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.082/20.082 Maybe right-stable CTRS, Overlay CTRS 20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS 20.082/20.082 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.082/20.082 Maybe level confluent 20.082/20.082 Maybe confluent 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 Clean Infeasible CCPs Processor: 20.082/20.082 20.082/20.082 20.082/20.082 -> Problem conclusions: 20.082/20.082 Left linear, Right linear, Linear 20.082/20.082 Weakly orthogonal, Almost orthogonal, Orthogonal 20.082/20.082 CTRS Type: 2 20.082/20.082 Deterministic, Strongly deterministic 20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.082/20.082 Maybe right-stable CTRS, Overlay CTRS 20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS 20.082/20.082 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.082/20.082 Maybe level confluent 20.082/20.082 Maybe confluent 20.082/20.082 20.082/20.082 Resulting CCPs: 20.082/20.082 No CCPs left 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 Operation Termination Processor: 20.082/20.082 Operational terminating? 20.082/20.082 YES 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 (VAR vu95NonEmpty x y z) 20.082/20.082 (RULES 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 ) 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 Valid CTRS Processor: 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 -> The system is a deterministic 3-CTRS. 20.082/20.082 20.082/20.082 Problem 1: 20.082/20.082 20.082/20.082 2D Dependency Pair Processor: 20.082/20.082 20.082/20.082 Conditional Termination Problem 1: 20.082/20.082 -> Pairs: 20.082/20.082 Empty 20.082/20.082 -> QPairs: 20.082/20.082 Empty 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 20.082/20.082 Conditional Termination Problem 2: 20.082/20.082 -> Pairs: 20.082/20.082 Empty 20.082/20.082 -> QPairs: 20.082/20.082 Empty 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 20.082/20.082 20.082/20.082 The problem is decomposed in 2 subproblems. 20.082/20.082 20.082/20.082 Problem 1.1: 20.082/20.082 20.082/20.082 SCC Processor: 20.082/20.082 -> Pairs: 20.082/20.082 Empty 20.082/20.082 -> QPairs: 20.082/20.082 Empty 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 ->Strongly Connected Components: 20.082/20.082 There is no strongly connected component 20.082/20.082 20.082/20.082 The problem is finite. 20.082/20.082 20.082/20.082 Problem 1.2: 20.082/20.082 20.082/20.082 SCC Processor: 20.082/20.082 -> Pairs: 20.082/20.082 Empty 20.082/20.082 -> QPairs: 20.082/20.082 Empty 20.082/20.082 -> Rules: 20.082/20.082 f(x,y) -> x | g(x) ->* z, g(y) ->* z 20.082/20.082 ->Strongly Connected Components: 20.082/20.082 There is no strongly connected component 20.082/20.082 20.082/20.082 The problem is finite. 20.082/20.082 20.082/20.082 20.082/20.082 -> Problem conclusions: 20.082/20.082 Left linear, Right linear, Linear 20.082/20.082 Weakly orthogonal, Almost orthogonal, Orthogonal 20.082/20.082 CTRS Type: 2 20.082/20.082 Deterministic, Strongly deterministic 20.082/20.082 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.082/20.082 Maybe right-stable CTRS, Overlay CTRS 20.082/20.082 Maybe normal CTRS, Maybe almost normal CTRS 20.082/20.082 Terminating CTRS, Operational terminating CTRS, Joinable CCPs 20.082/20.082 Maybe level confluent 20.082/20.082 Confluent 20.082/20.082 20.082/20.082 The problem is joinable. 20.082/20.082 22.09user 0.33system 0:20.82elapsed 107%CPU (0avgtext+0avgdata 261816maxresident)k 20.082/20.082 8inputs+0outputs (0major+102974minor)pagefaults 0swaps