20.037/20.037 NO 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (VAR vNonEmpty:S x:S) 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 f(x:S) -> x:S | x:S ->* c, d ->* x:S 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Inlining of Conditions Processor [STERN17]: 20.037/20.037 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (VAR vNonEmpty:S x:S) 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 f(x:S) -> x:S | d ->* x:S, x:S ->* c 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Clean CTRS Processor: 20.037/20.037 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 20.037/20.037 CRule InfChecker Info: 20.037/20.037 a -> c 20.037/20.037 Rule remains 20.037/20.037 Proof: 20.037/20.037 NO_CONDS 20.037/20.037 20.037/20.037 CRule InfChecker Info: 20.037/20.037 a -> d 20.037/20.037 Rule remains 20.037/20.037 Proof: 20.037/20.037 NO_CONDS 20.037/20.037 20.037/20.037 CRule InfChecker Info: 20.037/20.037 f(x:S) -> x:S | d ->* x:S, x:S ->* c 20.037/20.037 Rule deleted 20.037/20.037 Proof: 20.037/20.037 YES 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Infeasibility Problem: 20.037/20.037 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 f(x:S:S) -> x:S:S | d ->* x:S:S, x:S:S ->* c 20.037/20.037 )] 20.037/20.037 20.037/20.037 Infeasibility Conditions: 20.037/20.037 d ->* x:S:S, x:S:S ->* c 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Obtaining a model using Mace4: 20.037/20.037 20.037/20.037 -> Usable Rules: 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 f(x:S:S) -> x:S:S | d ->* x:S:S, x:S:S ->* c 20.037/20.037 20.037/20.037 -> Mace4 Output: 20.037/20.037 ============================== Mace4 ================================= 20.037/20.037 Mace4 (64) version 2009-11A, November 2009. 20.037/20.037 Process 109574 was started by ubuntu on ubuntu, 20.037/20.037 Fri Jul 16 15:05:03 2021 20.037/20.037 The command was "./mace4 -c -f /tmp/mace4109562-2.in". 20.037/20.037 ============================== end of head =========================== 20.037/20.037 20.037/20.037 ============================== INPUT ================================= 20.037/20.037 20.037/20.037 % Reading from file /tmp/mace4109562-2.in 20.037/20.037 20.037/20.037 assign(max_seconds,10). 20.037/20.037 20.037/20.037 formulas(assumptions). 20.037/20.037 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 20.037/20.037 ->(a,c) # label(replacement). 20.037/20.037 ->(a,d) # label(replacement). 20.037/20.037 ->*(d,x2) & ->*(x2,c) -> ->(f(x2),x2) # label(replacement). 20.037/20.037 ->*(x,x) # label(reflexivity). 20.037/20.037 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.037/20.037 end_of_list. 20.037/20.037 20.037/20.037 formulas(goals). 20.037/20.037 (exists x2 (->*(d,x2) & ->*(x2,c))) # label(goal). 20.037/20.037 end_of_list. 20.037/20.037 20.037/20.037 ============================== end of input ========================== 20.037/20.037 20.037/20.037 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.037/20.037 20.037/20.037 % Formulas that are not ordinary clauses: 20.037/20.037 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.037/20.037 2 ->*(d,x2) & ->*(x2,c) -> ->(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 20.037/20.037 3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.037/20.037 4 (exists x2 (->*(d,x2) & ->*(x2,c))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.037/20.037 20.037/20.037 ============================== end of process non-clausal formulas === 20.037/20.037 20.037/20.037 ============================== CLAUSES FOR SEARCH ==================== 20.037/20.037 20.037/20.037 formulas(mace4_clauses). 20.037/20.037 -->(x,y) | ->(f(x),f(y)) # label(congruence). 20.037/20.037 ->(a,c) # label(replacement). 20.037/20.037 ->(a,d) # label(replacement). 20.037/20.037 -->*(d,x) | -->*(x,c) | ->(f(x),x) # label(replacement). 20.037/20.037 ->*(x,x) # label(reflexivity). 20.037/20.037 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.037/20.037 -->*(d,x) | -->*(x,c) # label(goal). 20.037/20.037 end_of_list. 20.037/20.037 20.037/20.037 ============================== end of clauses for search ============= 20.037/20.037 20.037/20.037 % There are no natural numbers in the input. 20.037/20.037 20.037/20.037 ============================== DOMAIN SIZE 2 ========================= 20.037/20.037 20.037/20.037 ============================== MODEL ================================= 20.037/20.037 20.037/20.037 interpretation( 2, [number=1, seconds=0], [ 20.037/20.037 20.037/20.037 function(a, [ 0 ]), 20.037/20.037 20.037/20.037 function(c, [ 0 ]), 20.037/20.037 20.037/20.037 function(d, [ 1 ]), 20.037/20.037 20.037/20.037 function(f(_), [ 0, 0 ]), 20.037/20.037 20.037/20.037 relation(->*(_,_), [ 20.037/20.037 1, 1, 20.037/20.037 0, 1 ]), 20.037/20.037 20.037/20.037 relation(->(_,_), [ 20.037/20.037 1, 1, 20.037/20.037 0, 0 ]) 20.037/20.037 ]). 20.037/20.037 20.037/20.037 ============================== end of model ========================== 20.037/20.037 20.037/20.037 ============================== STATISTICS ============================ 20.037/20.037 20.037/20.037 For domain size 2. 20.037/20.037 20.037/20.037 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.037/20.037 Ground clauses: seen=20, kept=16. 20.037/20.037 Selections=5, assignments=5, propagations=8, current_models=1. 20.037/20.037 Rewrite_terms=22, rewrite_bools=26, indexes=4. 20.037/20.037 Rules_from_neg_clauses=1, cross_offs=1. 20.037/20.037 20.037/20.037 ============================== end of statistics ===================== 20.037/20.037 20.037/20.037 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.037/20.037 20.037/20.037 Exiting with 1 model. 20.037/20.037 20.037/20.037 Process 109574 exit (max_models) Fri Jul 16 15:05:03 2021 20.037/20.037 The process finished Fri Jul 16 15:05:03 2021 20.037/20.037 20.037/20.037 20.037/20.037 Mace4 cooked interpretation: 20.037/20.037 20.037/20.037 20.037/20.037 20.037/20.037 The problem is infeasible. 20.037/20.037 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Transform No Conds CTRS Processor: 20.037/20.037 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Resulting R: 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 ) 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 CleanTRS Processor: 20.037/20.037 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 20.037/20.037 Modular Confluence Combinations Decomposition Processor: 20.037/20.037 20.037/20.037 No usable combinations 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 Confluence Problem: 20.037/20.037 (STRATEGY CONTEXTSENSITIVE 20.037/20.037 (a) 20.037/20.037 (f 1) 20.037/20.037 (c) 20.037/20.037 (d) 20.037/20.037 (fSNonEmpty) 20.037/20.037 ) 20.037/20.037 (RULES 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 ) 20.037/20.037 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.037/20.037 20.037/20.037 Huet Levy Processor: 20.037/20.037 -> Rules: 20.037/20.037 a -> c 20.037/20.037 a -> d 20.037/20.037 -> Vars: 20.037/20.037 20.037/20.037 -> FVars: 20.037/20.037 20.037/20.037 -> PVars: 20.037/20.037 20.037/20.037 20.037/20.037 -> Rlps: 20.037/20.037 (rule: a -> c, id: 1, possubterms: a->[]) 20.037/20.037 (rule: a -> d, id: 2, possubterms: a->[]) 20.037/20.037 20.037/20.037 -> Unifications: 20.037/20.037 (R2 unifies with R1 at p: [], l: a, lp: a, sig: {}, l': a, r: d, r': c) 20.037/20.037 20.037/20.037 -> Critical pairs info: 20.037/20.037 => Not trivial, Overlay, N1 20.037/20.037 20.037/20.037 -> Problem conclusions: 20.037/20.037 Left linear, Right linear, Linear 20.037/20.037 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.037/20.037 Not Huet-Levy confluent, Not Newman confluent 20.037/20.037 R is a TRS 20.037/20.037 20.037/20.037 20.037/20.037 Problem 1: 20.037/20.037 Different Normal CP Terms Processor: 20.037/20.037 => Not trivial, Overlay, N1, Normal and not trivial cp 20.037/20.037 20.037/20.037 The problem is not joinable. 20.037/20.037 22.69user 0.44system 0:20.37elapsed 113%CPU (0avgtext+0avgdata 135840maxresident)k 20.037/20.037 8inputs+0outputs (0major+76969minor)pagefaults 0swaps