25.03/25.03 YES 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 25.03/25.03 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 Confluence Problem: 25.03/25.03 (VAR vNonEmpty:S x:S) 25.03/25.03 (STRATEGY CONTEXTSENSITIVE 25.03/25.03 (c) 25.03/25.03 (g 1) 25.03/25.03 (h 1) 25.03/25.03 (a) 25.03/25.03 (b) 25.03/25.03 (fSNonEmpty) 25.03/25.03 ) 25.03/25.03 (RULES 25.03/25.03 c -> c 25.03/25.03 g(x:S) -> a | h(x:S) ->* b 25.03/25.03 g(x:S) -> x:S 25.03/25.03 h(x:S) -> a 25.03/25.03 ) 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 25.03/25.03 Inlining of Conditions Processor [STERN17]: 25.03/25.03 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 Confluence Problem: 25.03/25.03 (VAR vNonEmpty:S x:S) 25.03/25.03 (STRATEGY CONTEXTSENSITIVE 25.03/25.03 (c) 25.03/25.03 (g 1) 25.03/25.03 (h 1) 25.03/25.03 (a) 25.03/25.03 (b) 25.03/25.03 (fSNonEmpty) 25.03/25.03 ) 25.03/25.03 (RULES 25.03/25.03 c -> c 25.03/25.03 g(x:S) -> a | h(x:S) ->* b 25.03/25.03 g(x:S) -> x:S 25.03/25.03 h(x:S) -> a 25.03/25.03 ) 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 25.03/25.03 Clean CTRS Processor: 25.03/25.03 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 Confluence Problem: 25.03/25.03 (VAR x:S) 25.03/25.03 (STRATEGY CONTEXTSENSITIVE 25.03/25.03 (c) 25.03/25.03 (g 1) 25.03/25.03 (h 1) 25.03/25.03 (a) 25.03/25.03 (b) 25.03/25.03 (fSNonEmpty) 25.03/25.03 ) 25.03/25.03 (RULES 25.03/25.03 g(x:S) -> x:S 25.03/25.03 h(x:S) -> a 25.03/25.03 ) 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 25.03/25.03 CRule InfChecker Info: 25.03/25.03 c -> c 25.03/25.03 Rule deleted 25.03/25.03 Proof: 25.03/25.03 SAME_LHS_AND_RHS 25.03/25.03 25.03/25.03 CRule InfChecker Info: 25.03/25.03 g(x:S) -> a | h(x:S) ->* b 25.03/25.03 Rule deleted 25.03/25.03 Proof: 25.03/25.03 YES 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 25.03/25.03 Infeasibility Problem: 25.03/25.03 [(VAR vNonEmpty:S x:S:S) 25.03/25.03 (STRATEGY CONTEXTSENSITIVE 25.03/25.03 (g 1) 25.03/25.03 (h 1) 25.03/25.03 (a) 25.03/25.03 (b) 25.03/25.03 (fSNonEmpty) 25.03/25.03 ) 25.03/25.03 (RULES 25.03/25.03 g(x:S:S) -> a | h(x:S:S) ->* b 25.03/25.03 g(x:S:S) -> x:S:S 25.03/25.03 h(x:S:S) -> a 25.03/25.03 )] 25.03/25.03 25.03/25.03 Infeasibility Conditions: 25.03/25.03 h(x:S:S) ->* b 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 25.03/25.03 Obtaining a model using Mace4: 25.03/25.03 25.03/25.03 -> Usable Rules: 25.03/25.03 g(x:S:S) -> a | h(x:S:S) ->* b 25.03/25.03 g(x:S:S) -> x:S:S 25.03/25.03 h(x:S:S) -> a 25.03/25.03 25.03/25.03 -> Mace4 Output: 25.03/25.03 ============================== Mace4 ================================= 25.03/25.03 Mace4 (64) version 2009-11A, November 2009. 25.03/25.03 Process 58025 was started by ubuntu on ubuntu, 25.03/25.03 Wed Jul 14 11:24:40 2021 25.03/25.03 The command was "./mace4 -c -f /tmp/mace458013-2.in". 25.03/25.03 ============================== end of head =========================== 25.03/25.03 25.03/25.03 ============================== INPUT ================================= 25.03/25.03 25.03/25.03 % Reading from file /tmp/mace458013-2.in 25.03/25.03 25.03/25.03 assign(max_seconds,20). 25.03/25.03 25.03/25.03 formulas(assumptions). 25.03/25.03 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence). 25.03/25.03 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 25.03/25.03 ->*(h(x1),b) -> ->(g(x1),a) # label(replacement). 25.03/25.03 ->(g(x1),x1) # label(replacement). 25.03/25.03 ->(h(x1),a) # label(replacement). 25.03/25.03 ->*(x,x) # label(reflexivity). 25.03/25.03 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.03/25.03 end_of_list. 25.03/25.03 25.03/25.03 formulas(goals). 25.03/25.03 (exists x1 ->*(h(x1),b)) # label(goal). 25.03/25.03 end_of_list. 25.03/25.03 25.03/25.03 ============================== end of input ========================== 25.03/25.03 25.03/25.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.03/25.03 25.03/25.03 % Formulas that are not ordinary clauses: 25.03/25.03 1 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 25.03/25.03 2 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 25.03/25.03 3 ->*(h(x1),b) -> ->(g(x1),a) # label(replacement) # label(non_clause). [assumption]. 25.03/25.03 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.03/25.03 5 (exists x1 ->*(h(x1),b)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.03/25.03 25.03/25.03 ============================== end of process non-clausal formulas === 25.03/25.03 25.03/25.03 ============================== CLAUSES FOR SEARCH ==================== 25.03/25.03 25.03/25.03 formulas(mace4_clauses). 25.03/25.03 -->(x,y) | ->(g(x),g(y)) # label(congruence). 25.03/25.03 -->(x,y) | ->(h(x),h(y)) # label(congruence). 25.03/25.03 -->*(h(x),b) | ->(g(x),a) # label(replacement). 25.03/25.03 ->(g(x),x) # label(replacement). 25.03/25.03 ->(h(x),a) # label(replacement). 25.03/25.03 ->*(x,x) # label(reflexivity). 25.03/25.03 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.03/25.03 -->*(h(x),b) # label(goal). 25.03/25.03 end_of_list. 25.03/25.03 25.03/25.03 ============================== end of clauses for search ============= 25.03/25.03 25.03/25.03 % There are no natural numbers in the input. 25.03/25.03 25.03/25.03 ============================== DOMAIN SIZE 2 ========================= 25.03/25.03 25.03/25.03 ============================== MODEL ================================= 25.03/25.03 25.03/25.03 interpretation( 2, [number=1, seconds=0], [ 25.03/25.03 25.03/25.03 function(a, [ 0 ]), 25.03/25.03 25.03/25.03 function(b, [ 1 ]), 25.03/25.03 25.03/25.03 function(g(_), [ 0, 1 ]), 25.03/25.03 25.03/25.03 function(h(_), [ 0, 0 ]), 25.03/25.03 25.03/25.03 relation(->*(_,_), [ 25.03/25.03 1, 0, 25.03/25.03 0, 1 ]), 25.03/25.03 25.03/25.03 relation(->(_,_), [ 25.03/25.03 1, 0, 25.03/25.03 0, 1 ]) 25.03/25.03 ]). 25.03/25.03 25.03/25.03 ============================== end of model ========================== 25.03/25.03 25.03/25.03 ============================== STATISTICS ============================ 25.03/25.03 25.03/25.03 For domain size 2. 25.03/25.03 25.03/25.03 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.03/25.03 Ground clauses: seen=26, kept=22. 25.03/25.03 Selections=4, assignments=5, propagations=13, current_models=1. 25.03/25.03 Rewrite_terms=45, rewrite_bools=34, indexes=8. 25.03/25.03 Rules_from_neg_clauses=4, cross_offs=4. 25.03/25.03 25.03/25.03 ============================== end of statistics ===================== 25.03/25.03 25.03/25.03 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.03/25.03 25.03/25.03 Exiting with 1 model. 25.03/25.03 25.03/25.03 Process 58025 exit (max_models) Wed Jul 14 11:24:40 2021 25.03/25.03 The process finished Wed Jul 14 11:24:40 2021 25.03/25.03 25.03/25.03 25.03/25.03 Mace4 cooked interpretation: 25.03/25.03 25.03/25.03 25.03/25.03 25.03/25.03 The problem is infeasible. 25.03/25.03 25.03/25.03 25.03/25.03 CRule InfChecker Info: 25.03/25.03 g(x:S) -> x:S 25.03/25.03 Rule remains 25.03/25.03 Proof: 25.03/25.03 NO_CONDS 25.03/25.03 25.03/25.03 CRule InfChecker Info: 25.03/25.03 h(x:S) -> a 25.03/25.03 Rule remains 25.03/25.03 Proof: 25.03/25.03 NO_CONDS 25.03/25.03 25.03/25.03 Problem 1: 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 Confluence Problem: 25.03/25.03 (VAR x:S) 25.03/25.03 (STRATEGY CONTEXTSENSITIVE 25.03/25.03 (c) 25.03/25.03 (g 1) 25.03/25.03 (h 1) 25.03/25.03 (a) 25.03/25.03 (b) 25.03/25.03 (fSNonEmpty) 25.03/25.03 ) 25.03/25.03 (RULES 25.03/25.03 g(x:S) -> x:S 25.03/25.03 h(x:S) -> a 25.03/25.03 ) 25.03/25.03 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.03/25.03 25.03/25.03 Critical Pairs Processor: 25.03/25.03 -> Rules: 25.03/25.03 g(x:S) -> x:S 25.03/25.03 h(x:S) -> a 25.03/25.03 -> Vars: 25.03/25.03 "x", "x" 25.03/25.03 -> FVars: 25.03/25.03 "x2", "x3" 25.03/25.03 -> PVars: 25.03/25.03 "x": ["x2", "x3"] 25.03/25.03 25.03/25.03 -> Rlps: 25.03/25.03 crule: g(x2:S) -> x2:S, id: 1, possubterms: g(x2:S)-> [] 25.03/25.03 crule: h(x3:S) -> a, id: 2, possubterms: h(x3:S)-> [] 25.03/25.03 25.03/25.03 -> Unifications: 25.03/25.03 25.03/25.03 25.03/25.03 -> Critical pairs info: 25.03/25.03 25.03/25.03 25.03/25.03 -> Problem conclusions: 25.03/25.03 Left linear, Right linear, Linear 25.03/25.03 Weakly orthogonal, Almost orthogonal, Orthogonal 25.03/25.03 CTRS Type: 1 25.03/25.03 Deterministic, Strongly deterministic 25.03/25.03 Oriented CTRS, Properly oriented CTRS, Join CTRS 25.03/25.03 Maybe right-stable CTRS, Overlay CTRS 25.03/25.03 Normal CTRS, Almost normal CTRS 25.03/25.03 Maybe terminating CTRS, Joinable CCPs 25.03/25.03 Level confluent 25.03/25.03 Confluent 25.03/25.03 25.03/25.03 The problem is joinable. 25.03/25.03 25.40user 0.56system 0:25.30elapsed 102%CPU (0avgtext+0avgdata 210640maxresident)k 25.03/25.03 8inputs+0outputs (0major+151364minor)pagefaults 0swaps