20.033/20.033 NO 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (VAR vNonEmpty x) 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 f(x) -> x | x ->* c, d ->* x 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Inlining of Conditions Processor [STERN17]: 20.033/20.033 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (VAR vNonEmpty x) 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 f(x) -> x | d ->* x, x ->* c 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Clean CTRS Processor: 20.033/20.033 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 20.033/20.033 CRule InfChecker Info: 20.033/20.033 a -> c 20.033/20.033 Rule remains 20.033/20.033 Proof: 20.033/20.033 NO_CONDS 20.033/20.033 20.033/20.033 CRule InfChecker Info: 20.033/20.033 a -> d 20.033/20.033 Rule remains 20.033/20.033 Proof: 20.033/20.033 NO_CONDS 20.033/20.033 20.033/20.033 CRule InfChecker Info: 20.033/20.033 f(x) -> x | d ->* x, x ->* c 20.033/20.033 Rule deleted 20.033/20.033 Proof: 20.033/20.033 YES 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Infeasibility Problem: 20.033/20.033 [(VAR vNonEmpty x vNonEmpty x) 20.033/20.033 (STRATEGY CONTEXTSENSITIVE 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 f(x) -> x | d ->* x, x ->* c 20.033/20.033 )] 20.033/20.033 20.033/20.033 Infeasibility Conditions: 20.033/20.033 d ->* x, x ->* c 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Obtaining a model using Mace4: 20.033/20.033 20.033/20.033 -> Usable Rules: 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 f(x) -> x | d ->* x, x ->* c 20.033/20.033 20.033/20.033 -> Mace4 Output: 20.033/20.033 ============================== Mace4 ================================= 20.033/20.033 Mace4 (64) version 2009-11A, November 2009. 20.033/20.033 Process 59787 was started by ubuntu on ubuntu, 20.033/20.033 Wed Mar 9 09:43:07 2022 20.033/20.033 The command was "./mace4 -c -f /tmp/mace459774-2.in". 20.033/20.033 ============================== end of head =========================== 20.033/20.033 20.033/20.033 ============================== INPUT ================================= 20.033/20.033 20.033/20.033 % Reading from file /tmp/mace459774-2.in 20.033/20.033 20.033/20.033 assign(max_seconds,20). 20.033/20.033 20.033/20.033 formulas(assumptions). 20.033/20.033 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 20.033/20.033 ->(a,c) # label(replacement). 20.033/20.033 ->(a,d) # label(replacement). 20.033/20.033 ->*(d,x1) & ->*(x1,c) -> ->(f(x1),x1) # label(replacement). 20.033/20.033 ->*(x,x) # label(reflexivity). 20.033/20.033 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.033/20.033 end_of_list. 20.033/20.033 20.033/20.033 formulas(goals). 20.033/20.033 (exists x3 (->*(d,x3) & ->*(x3,c))) # label(goal). 20.033/20.033 end_of_list. 20.033/20.033 20.033/20.033 ============================== end of input ========================== 20.033/20.033 20.033/20.033 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.033/20.033 20.033/20.033 % Formulas that are not ordinary clauses: 20.033/20.033 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.033/20.033 2 ->*(d,x1) & ->*(x1,c) -> ->(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 20.033/20.033 3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.033/20.033 4 (exists x3 (->*(d,x3) & ->*(x3,c))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.033/20.033 20.033/20.033 ============================== end of process non-clausal formulas === 20.033/20.033 20.033/20.033 ============================== CLAUSES FOR SEARCH ==================== 20.033/20.033 20.033/20.033 formulas(mace4_clauses). 20.033/20.033 -->(x,y) | ->(f(x),f(y)) # label(congruence). 20.033/20.033 ->(a,c) # label(replacement). 20.033/20.033 ->(a,d) # label(replacement). 20.033/20.033 -->*(d,x) | -->*(x,c) | ->(f(x),x) # label(replacement). 20.033/20.033 ->*(x,x) # label(reflexivity). 20.033/20.033 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.033/20.033 -->*(d,x) | -->*(x,c) # label(goal). 20.033/20.033 end_of_list. 20.033/20.033 20.033/20.033 ============================== end of clauses for search ============= 20.033/20.033 20.033/20.033 % There are no natural numbers in the input. 20.033/20.033 20.033/20.033 ============================== DOMAIN SIZE 2 ========================= 20.033/20.033 20.033/20.033 ============================== MODEL ================================= 20.033/20.033 20.033/20.033 interpretation( 2, [number=1, seconds=0], [ 20.033/20.033 20.033/20.033 function(a, [ 0 ]), 20.033/20.033 20.033/20.033 function(c, [ 0 ]), 20.033/20.033 20.033/20.033 function(d, [ 1 ]), 20.033/20.033 20.033/20.033 function(f(_), [ 0, 0 ]), 20.033/20.033 20.033/20.033 relation(->*(_,_), [ 20.033/20.033 1, 1, 20.033/20.033 0, 1 ]), 20.033/20.033 20.033/20.033 relation(->(_,_), [ 20.033/20.033 1, 1, 20.033/20.033 0, 0 ]) 20.033/20.033 ]). 20.033/20.033 20.033/20.033 ============================== end of model ========================== 20.033/20.033 20.033/20.033 ============================== STATISTICS ============================ 20.033/20.033 20.033/20.033 For domain size 2. 20.033/20.033 20.033/20.033 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.033/20.033 Ground clauses: seen=20, kept=16. 20.033/20.033 Selections=5, assignments=5, propagations=8, current_models=1. 20.033/20.033 Rewrite_terms=22, rewrite_bools=26, indexes=4. 20.033/20.033 Rules_from_neg_clauses=1, cross_offs=1. 20.033/20.033 20.033/20.033 ============================== end of statistics ===================== 20.033/20.033 20.033/20.033 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.033/20.033 20.033/20.033 Exiting with 1 model. 20.033/20.033 20.033/20.033 Process 59787 exit (max_models) Wed Mar 9 09:43:07 2022 20.033/20.033 The process finished Wed Mar 9 09:43:07 2022 20.033/20.033 20.033/20.033 20.033/20.033 Mace4 cooked interpretation: 20.033/20.033 20.033/20.033 20.033/20.033 20.033/20.033 The problem is infeasible. 20.033/20.033 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Transform No Conds CTRS Processor: 20.033/20.033 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Resulting R: 20.033/20.033 (STRATEGY CONTEXTSENSITIVE 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 ) 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 CleanTRS Processor: 20.033/20.033 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 20.033/20.033 Modular Confluence Combinations Decomposition Processor: 20.033/20.033 20.033/20.033 No usable combinations 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 Confluence Problem: 20.033/20.033 (REPLACEMENT-MAP 20.033/20.033 (a) 20.033/20.033 (f 1) 20.033/20.033 (c) 20.033/20.033 (d) 20.033/20.033 (fSNonEmpty) 20.033/20.033 ) 20.033/20.033 (RULES 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 ) 20.033/20.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.033/20.033 20.033/20.033 Huet Levy Processor: 20.033/20.033 -> Rules: 20.033/20.033 a -> c 20.033/20.033 a -> d 20.033/20.033 -> Vars: 20.033/20.033 20.033/20.033 20.033/20.033 -> Rlps: 20.033/20.033 (rule: a -> c, id: 1, possubterms: a->[]) 20.033/20.033 (rule: a -> d, id: 2, possubterms: a->[]) 20.033/20.033 20.033/20.033 -> Unifications: 20.033/20.033 (R2 unifies with R1 at p: [], l: a, lp: a, sig: {}, l': a, r: d, r': c) 20.033/20.033 20.033/20.033 -> Critical pairs info: 20.033/20.033 => Not trivial, Overlay, NW0, N1 20.033/20.033 20.033/20.033 -> Problem conclusions: 20.033/20.033 Left linear, Right linear, Linear 20.033/20.033 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.033/20.033 Not Huet-Levy confluent, Not Newman confluent 20.033/20.033 R is a TRS 20.033/20.033 20.033/20.033 20.033/20.033 Problem 1: 20.033/20.033 Different Normal CP Terms Processor: 20.033/20.033 => Not trivial, Overlay, NW0, N1, Normal and not trivial cp 20.033/20.033 20.033/20.033 The problem is not joinable. 20.033/20.033 26.59user 0.47system 0:20.33elapsed 133%CPU (0avgtext+0avgdata 135860maxresident)k 20.033/20.033 8inputs+0outputs (0major+79280minor)pagefaults 0swaps