25.029/25.029 YES 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR vNonEmpty:S x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 c -> c 25.029/25.029 g(x:S) -> a | h(x:S) ->* b 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Inlining of Conditions Processor [STERN17]: 25.029/25.029 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR vNonEmpty:S x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 c -> c 25.029/25.029 g(x:S) -> a | h(x:S) ->* b 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Clean CTRS Processor: 25.029/25.029 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 CRule InfChecker Info: 25.029/25.029 c -> c 25.029/25.029 Rule deleted 25.029/25.029 Proof: 25.029/25.029 SAME_LHS_AND_RHS 25.029/25.029 25.029/25.029 CRule InfChecker Info: 25.029/25.029 g(x:S) -> a | h(x:S) ->* b 25.029/25.029 Rule deleted 25.029/25.029 Proof: 25.029/25.029 YES 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Infeasibility Problem: 25.029/25.029 [(VAR vNonEmpty:S x:S:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S:S) -> a | h(x:S:S) ->* b 25.029/25.029 g(x:S:S) -> x:S:S 25.029/25.029 h(x:S:S) -> a 25.029/25.029 )] 25.029/25.029 25.029/25.029 Infeasibility Conditions: 25.029/25.029 h(x:S:S) ->* b 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Obtaining a model using Mace4: 25.029/25.029 25.029/25.029 -> Usable Rules: 25.029/25.029 g(x:S:S) -> a | h(x:S:S) ->* b 25.029/25.029 g(x:S:S) -> x:S:S 25.029/25.029 h(x:S:S) -> a 25.029/25.029 25.029/25.029 -> Mace4 Output: 25.029/25.029 ============================== Mace4 ================================= 25.029/25.029 Mace4 (64) version 2009-11A, November 2009. 25.029/25.029 Process 118048 was started by ubuntu on ubuntu, 25.029/25.029 Fri Jul 16 15:31:10 2021 25.029/25.029 The command was "./mace4 -c -f /tmp/mace4118036-2.in". 25.029/25.029 ============================== end of head =========================== 25.029/25.029 25.029/25.029 ============================== INPUT ================================= 25.029/25.029 25.029/25.029 % Reading from file /tmp/mace4118036-2.in 25.029/25.029 25.029/25.029 assign(max_seconds,10). 25.029/25.029 25.029/25.029 formulas(assumptions). 25.029/25.029 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence). 25.029/25.029 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 25.029/25.029 ->*(h(x1),b) -> ->(g(x1),a) # label(replacement). 25.029/25.029 ->(g(x1),x1) # label(replacement). 25.029/25.029 ->(h(x1),a) # label(replacement). 25.029/25.029 ->*(x,x) # label(reflexivity). 25.029/25.029 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.029/25.029 end_of_list. 25.029/25.029 25.029/25.029 formulas(goals). 25.029/25.029 (exists x1 ->*(h(x1),b)) # label(goal). 25.029/25.029 end_of_list. 25.029/25.029 25.029/25.029 ============================== end of input ========================== 25.029/25.029 25.029/25.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.029/25.029 25.029/25.029 % Formulas that are not ordinary clauses: 25.029/25.029 1 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 25.029/25.029 2 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 25.029/25.029 3 ->*(h(x1),b) -> ->(g(x1),a) # label(replacement) # label(non_clause). [assumption]. 25.029/25.029 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.029/25.029 5 (exists x1 ->*(h(x1),b)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.029/25.029 25.029/25.029 ============================== end of process non-clausal formulas === 25.029/25.029 25.029/25.029 ============================== CLAUSES FOR SEARCH ==================== 25.029/25.029 25.029/25.029 formulas(mace4_clauses). 25.029/25.029 -->(x,y) | ->(g(x),g(y)) # label(congruence). 25.029/25.029 -->(x,y) | ->(h(x),h(y)) # label(congruence). 25.029/25.029 -->*(h(x),b) | ->(g(x),a) # label(replacement). 25.029/25.029 ->(g(x),x) # label(replacement). 25.029/25.029 ->(h(x),a) # label(replacement). 25.029/25.029 ->*(x,x) # label(reflexivity). 25.029/25.029 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.029/25.029 -->*(h(x),b) # label(goal). 25.029/25.029 end_of_list. 25.029/25.029 25.029/25.029 ============================== end of clauses for search ============= 25.029/25.029 25.029/25.029 % There are no natural numbers in the input. 25.029/25.029 25.029/25.029 ============================== DOMAIN SIZE 2 ========================= 25.029/25.029 25.029/25.029 ============================== MODEL ================================= 25.029/25.029 25.029/25.029 interpretation( 2, [number=1, seconds=0], [ 25.029/25.029 25.029/25.029 function(a, [ 0 ]), 25.029/25.029 25.029/25.029 function(b, [ 1 ]), 25.029/25.029 25.029/25.029 function(g(_), [ 0, 1 ]), 25.029/25.029 25.029/25.029 function(h(_), [ 0, 0 ]), 25.029/25.029 25.029/25.029 relation(->*(_,_), [ 25.029/25.029 1, 0, 25.029/25.029 0, 1 ]), 25.029/25.029 25.029/25.029 relation(->(_,_), [ 25.029/25.029 1, 0, 25.029/25.029 0, 1 ]) 25.029/25.029 ]). 25.029/25.029 25.029/25.029 ============================== end of model ========================== 25.029/25.029 25.029/25.029 ============================== STATISTICS ============================ 25.029/25.029 25.029/25.029 For domain size 2. 25.029/25.029 25.029/25.029 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.029/25.029 Ground clauses: seen=26, kept=22. 25.029/25.029 Selections=4, assignments=5, propagations=13, current_models=1. 25.029/25.029 Rewrite_terms=45, rewrite_bools=34, indexes=8. 25.029/25.029 Rules_from_neg_clauses=4, cross_offs=4. 25.029/25.029 25.029/25.029 ============================== end of statistics ===================== 25.029/25.029 25.029/25.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.029/25.029 25.029/25.029 Exiting with 1 model. 25.029/25.029 25.029/25.029 Process 118048 exit (max_models) Fri Jul 16 15:31:10 2021 25.029/25.029 The process finished Fri Jul 16 15:31:10 2021 25.029/25.029 25.029/25.029 25.029/25.029 Mace4 cooked interpretation: 25.029/25.029 25.029/25.029 25.029/25.029 25.029/25.029 The problem is infeasible. 25.029/25.029 25.029/25.029 25.029/25.029 CRule InfChecker Info: 25.029/25.029 g(x:S) -> x:S 25.029/25.029 Rule remains 25.029/25.029 Proof: 25.029/25.029 NO_CONDS 25.029/25.029 25.029/25.029 CRule InfChecker Info: 25.029/25.029 h(x:S) -> a 25.029/25.029 Rule remains 25.029/25.029 Proof: 25.029/25.029 NO_CONDS 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Transform No Conds CTRS Processor: 25.029/25.029 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Resulting R: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 CleanTRS Processor: 25.029/25.029 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (c) 25.029/25.029 (g 1) 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 (b) 25.029/25.029 (fSNonEmpty) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 25.029/25.029 Problem 1: 25.029/25.029 25.029/25.029 Modular Confluence Combinations Decomposition Processor: 25.029/25.029 25.029/25.029 TRS combination: 25.029/25.029 {g(x:S) -> x:S} 25.029/25.029 {h(x:S) -> a} 25.029/25.029 Disjoint 25.029/25.029 Constructor-sharing 25.029/25.029 Left linear 25.029/25.029 Not layer-preserving 25.029/25.029 TRS1 25.029/25.029 Just (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (g 1) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 ) 25.029/25.029 25.029/25.029 TRS2 25.029/25.029 Just (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 25.029/25.029 25.029/25.029 The problem is decomposed in 2 subproblems. 25.029/25.029 25.029/25.029 Problem 1.1: 25.029/25.029 Linearity Processor: 25.029/25.029 Linear? 25.029/25.029 YES 25.029/25.029 Problem 1.1.1: 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (g 1) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 g(x:S) -> x:S 25.029/25.029 ) 25.029/25.029 Linear:YES 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 Huet Levy Processor: 25.029/25.029 -> Rules: 25.029/25.029 g(x:S) -> x:S 25.029/25.029 -> Vars: 25.029/25.029 x 25.029/25.029 -> FVars: 25.029/25.029 x2 25.029/25.029 -> PVars: 25.029/25.029 x: [x2] 25.029/25.029 25.029/25.029 -> Rlps: 25.029/25.029 (rule: g(x2:S) -> x2:S, id: 1, possubterms: g(x2:S)->[]) 25.029/25.029 25.029/25.029 -> Unifications: 25.029/25.029 25.029/25.029 25.029/25.029 -> Critical pairs info: 25.029/25.029 25.029/25.029 25.029/25.029 -> Problem conclusions: 25.029/25.029 Left linear, Right linear, Linear 25.029/25.029 Weakly orthogonal, Almost orthogonal, Orthogonal 25.029/25.029 Huet-Levy confluent, Not Newman confluent 25.029/25.029 R is a TRS 25.029/25.029 25.029/25.029 25.029/25.029 The problem is joinable. 25.029/25.029 25.029/25.029 Problem 1.2: 25.029/25.029 Linearity Processor: 25.029/25.029 Linear? 25.029/25.029 YES 25.029/25.029 Problem 1.2.1: 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 Confluence Problem: 25.029/25.029 (VAR x:S) 25.029/25.029 (STRATEGY CONTEXTSENSITIVE 25.029/25.029 (h 1) 25.029/25.029 (a) 25.029/25.029 ) 25.029/25.029 (RULES 25.029/25.029 h(x:S) -> a 25.029/25.029 ) 25.029/25.029 Linear:YES 25.029/25.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.029/25.029 25.029/25.029 Huet Levy Processor: 25.029/25.029 -> Rules: 25.029/25.029 h(x:S) -> a 25.029/25.029 -> Vars: 25.029/25.029 x 25.029/25.029 -> FVars: 25.029/25.029 x2 25.029/25.029 -> PVars: 25.029/25.029 x: [x2] 25.029/25.029 25.029/25.029 -> Rlps: 25.029/25.029 (rule: h(x2:S) -> a, id: 1, possubterms: h(x2:S)->[]) 25.029/25.029 25.029/25.029 -> Unifications: 25.029/25.029 25.029/25.029 25.029/25.029 -> Critical pairs info: 25.029/25.029 25.029/25.029 25.029/25.029 -> Problem conclusions: 25.029/25.029 Left linear, Right linear, Linear 25.029/25.029 Weakly orthogonal, Almost orthogonal, Orthogonal 25.029/25.029 Huet-Levy confluent, Not Newman confluent 25.029/25.029 R is a TRS 25.029/25.029 25.029/25.029 25.029/25.029 The problem is joinable. 25.029/25.029 24.89user 0.44system 0:25.29elapsed 100%CPU (0avgtext+0avgdata 210700maxresident)k 25.029/25.029 8inputs+0outputs (0major+151350minor)pagefaults 0swaps