20.019/20.019 NO 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR vNonEmpty x y z) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(x) | a ->* x 20.019/20.019 f(k(z),a) -> g(x,x) | h(z) ->* x, x ->* b 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Inlining of Conditions Processor [STERN17]: 20.019/20.019 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR vNonEmpty x y z) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 f(k(z),a) -> g(h(z),h(z)) | h(z) ->* b 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Clean CTRS Processor: 20.019/20.019 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR x) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 a -> b 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 f(k(z),a) -> g(h(z),h(z)) | h(z) ->* b 20.019/20.019 Rule deleted 20.019/20.019 Proof: 20.019/20.019 YES 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Infeasibility Problem: 20.019/20.019 [(VAR vNonEmpty x y z vNonEmpty z) 20.019/20.019 (STRATEGY CONTEXTSENSITIVE 20.019/20.019 (a) 20.019/20.019 (f 1 2) 20.019/20.019 (g 1 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 f(k(z),a) -> g(h(z),h(z)) | h(z) ->* b 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 )] 20.019/20.019 20.019/20.019 Infeasibility Conditions: 20.019/20.019 h(z) ->* b 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Obtaining a model using Mace4: 20.019/20.019 20.019/20.019 -> Usable Rules: 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 f(k(z),a) -> g(h(z),h(z)) | h(z) ->* b 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 20.019/20.019 -> Mace4 Output: 20.019/20.019 ============================== Mace4 ================================= 20.019/20.019 Mace4 (64) version 2009-11A, November 2009. 20.019/20.019 Process 81947 was started by ubuntu on ubuntu, 20.019/20.019 Wed Mar 9 10:29:57 2022 20.019/20.019 The command was "./mace4 -c -f /tmp/mace481936-2.in". 20.019/20.019 ============================== end of head =========================== 20.019/20.019 20.019/20.019 ============================== INPUT ================================= 20.019/20.019 20.019/20.019 % Reading from file /tmp/mace481936-2.in 20.019/20.019 20.019/20.019 assign(max_seconds,20). 20.019/20.019 20.019/20.019 formulas(assumptions). 20.019/20.019 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.019/20.019 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.019/20.019 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 20.019/20.019 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 20.019/20.019 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence). 20.019/20.019 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 20.019/20.019 ->(a,b) # label(replacement). 20.019/20.019 ->(f(k(a),h(a)),k(a)) # label(replacement). 20.019/20.019 ->*(h(x3),b) -> ->(f(k(x3),a),g(h(x3),h(x3))) # label(replacement). 20.019/20.019 ->(g(x1,x1),a) # label(replacement). 20.019/20.019 ->(k(x1),a) # label(replacement). 20.019/20.019 ->(k(x1),b) # label(replacement). 20.019/20.019 ->(k(x1),h(x1)) # label(replacement). 20.019/20.019 ->*(x,x) # label(reflexivity). 20.019/20.019 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.019/20.019 end_of_list. 20.019/20.019 20.019/20.019 formulas(goals). 20.019/20.019 (exists x5 ->*(h(x5),b)) # label(goal). 20.019/20.019 end_of_list. 20.019/20.019 20.019/20.019 ============================== end of input ========================== 20.019/20.019 20.019/20.019 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.019/20.019 20.019/20.019 % Formulas that are not ordinary clauses: 20.019/20.019 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 5 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 6 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.019/20.019 7 ->*(h(x3),b) -> ->(f(k(x3),a),g(h(x3),h(x3))) # label(replacement) # label(non_clause). [assumption]. 20.019/20.019 8 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.019/20.019 9 (exists x5 ->*(h(x5),b)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.019/20.019 20.019/20.019 ============================== end of process non-clausal formulas === 20.019/20.019 20.019/20.019 ============================== CLAUSES FOR SEARCH ==================== 20.019/20.019 20.019/20.019 formulas(mace4_clauses). 20.019/20.019 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.019/20.019 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.019/20.019 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 20.019/20.019 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 20.019/20.019 -->(x,y) | ->(k(x),k(y)) # label(congruence). 20.019/20.019 -->(x,y) | ->(h(x),h(y)) # label(congruence). 20.019/20.019 ->(a,b) # label(replacement). 20.019/20.019 ->(f(k(a),h(a)),k(a)) # label(replacement). 20.019/20.019 -->*(h(x),b) | ->(f(k(x),a),g(h(x),h(x))) # label(replacement). 20.019/20.019 ->(g(x,x),a) # label(replacement). 20.019/20.019 ->(k(x),a) # label(replacement). 20.019/20.019 ->(k(x),b) # label(replacement). 20.019/20.019 ->(k(x),h(x)) # label(replacement). 20.019/20.019 ->*(x,x) # label(reflexivity). 20.019/20.019 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.019/20.019 -->*(h(x),b) # label(goal). 20.019/20.019 end_of_list. 20.019/20.019 20.019/20.019 ============================== end of clauses for search ============= 20.019/20.019 20.019/20.019 % There are no natural numbers in the input. 20.019/20.019 20.019/20.019 ============================== DOMAIN SIZE 2 ========================= 20.019/20.019 20.019/20.019 ============================== MODEL ================================= 20.019/20.019 20.019/20.019 interpretation( 2, [number=1, seconds=0], [ 20.019/20.019 20.019/20.019 function(a, [ 0 ]), 20.019/20.019 20.019/20.019 function(b, [ 0 ]), 20.019/20.019 20.019/20.019 function(k(_), [ 0, 0 ]), 20.019/20.019 20.019/20.019 function(h(_), [ 1, 1 ]), 20.019/20.019 20.019/20.019 function(f(_,_), [ 20.019/20.019 0, 0, 20.019/20.019 0, 0 ]), 20.019/20.019 20.019/20.019 function(g(_,_), [ 20.019/20.019 0, 0, 20.019/20.019 0, 0 ]), 20.019/20.019 20.019/20.019 relation(->*(_,_), [ 20.019/20.019 1, 1, 20.019/20.019 0, 1 ]), 20.019/20.019 20.019/20.019 relation(->(_,_), [ 20.019/20.019 1, 1, 20.019/20.019 0, 1 ]) 20.019/20.019 ]). 20.019/20.019 20.019/20.019 ============================== end of model ========================== 20.019/20.019 20.019/20.019 ============================== STATISTICS ============================ 20.019/20.019 20.019/20.019 For domain size 2. 20.019/20.019 20.019/20.019 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.019/20.019 Ground clauses: seen=64, kept=60. 20.019/20.019 Selections=4, assignments=4, propagations=18, current_models=1. 20.019/20.019 Rewrite_terms=125, rewrite_bools=94, indexes=11. 20.019/20.019 Rules_from_neg_clauses=10, cross_offs=10. 20.019/20.019 20.019/20.019 ============================== end of statistics ===================== 20.019/20.019 20.019/20.019 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.019/20.019 20.019/20.019 Exiting with 1 model. 20.019/20.019 20.019/20.019 Process 81947 exit (max_models) Wed Mar 9 10:29:57 2022 20.019/20.019 The process finished Wed Mar 9 10:29:57 2022 20.019/20.019 20.019/20.019 20.019/20.019 Mace4 cooked interpretation: 20.019/20.019 20.019/20.019 20.019/20.019 20.019/20.019 The problem is infeasible. 20.019/20.019 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 g(x,x) -> a 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 k(x) -> a 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 k(x) -> b 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 CRule InfChecker Info: 20.019/20.019 k(x) -> h(x) 20.019/20.019 Rule remains 20.019/20.019 Proof: 20.019/20.019 NO_CONDS 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Transform No Conds CTRS Processor: 20.019/20.019 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR x) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Resulting R: 20.019/20.019 (VAR x) 20.019/20.019 (STRATEGY CONTEXTSENSITIVE 20.019/20.019 (a) 20.019/20.019 (f 1 2) 20.019/20.019 (g 1 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 CleanTRS Processor: 20.019/20.019 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR x) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 20.019/20.019 Modular Confluence Combinations Decomposition Processor: 20.019/20.019 20.019/20.019 No usable combinations 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 Confluence Problem: 20.019/20.019 (VAR x) 20.019/20.019 (REPLACEMENT-MAP 20.019/20.019 (a) 20.019/20.019 (f 1, 2) 20.019/20.019 (g 1, 2) 20.019/20.019 (k 1) 20.019/20.019 (b) 20.019/20.019 (fSNonEmpty) 20.019/20.019 (h 1) 20.019/20.019 ) 20.019/20.019 (RULES 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 ) 20.019/20.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.019/20.019 20.019/20.019 Huet Levy Processor: 20.019/20.019 -> Rules: 20.019/20.019 a -> b 20.019/20.019 f(k(a),h(a)) -> k(a) 20.019/20.019 g(x,x) -> a 20.019/20.019 k(x) -> a 20.019/20.019 k(x) -> b 20.019/20.019 k(x) -> h(x) 20.019/20.019 -> Vars: 20.019/20.019 x, x, x, x 20.019/20.019 20.019/20.019 -> Rlps: 20.019/20.019 (rule: a -> b, id: 1, possubterms: a->[]) 20.019/20.019 (rule: f(k(a),h(a)) -> k(a), id: 2, possubterms: f(k(a),h(a))->[], k(a)->[1], a->[1, 1], h(a)->[2], a->[2, 1]) 20.019/20.019 (rule: g(x,x) -> a, id: 3, possubterms: g(x,x)->[]) 20.019/20.019 (rule: k(x) -> a, id: 4, possubterms: k(x)->[]) 20.019/20.019 (rule: k(x) -> b, id: 5, possubterms: k(x)->[]) 20.019/20.019 (rule: k(x) -> h(x), id: 6, possubterms: k(x)->[]) 20.019/20.019 20.019/20.019 -> Unifications: 20.019/20.019 (R2 unifies with R4 at p: [1], l: f(k(a),h(a)), lp: k(a), sig: {x -> a}, l': k(x), r: k(a), r': a) 20.019/20.019 (R2 unifies with R5 at p: [1], l: f(k(a),h(a)), lp: k(a), sig: {x -> a}, l': k(x), r: k(a), r': b) 20.019/20.019 (R2 unifies with R6 at p: [1], l: f(k(a),h(a)), lp: k(a), sig: {x -> a}, l': k(x), r: k(a), r': h(x)) 20.019/20.019 (R2 unifies with R1 at p: [1,1], l: f(k(a),h(a)), lp: a, sig: {}, l': a, r: k(a), r': b) 20.019/20.019 (R2 unifies with R1 at p: [2,1], l: f(k(a),h(a)), lp: a, sig: {}, l': a, r: k(a), r': b) 20.019/20.019 (R5 unifies with R4 at p: [], l: k(x), lp: k(x), sig: {x -> x'}, l': k(x'), r: b, r': a) 20.019/20.019 (R6 unifies with R4 at p: [], l: k(x), lp: k(x), sig: {x -> x'}, l': k(x'), r: h(x), r': a) 20.019/20.019 (R6 unifies with R5 at p: [], l: k(x), lp: k(x), sig: {x -> x'}, l': k(x'), r: h(x), r': b) 20.019/20.019 20.019/20.019 -> Critical pairs info: 20.019/20.019 => Not trivial, Overlay, NW0, N1 20.019/20.019 => Not trivial, Not overlay, NW0, N2 20.019/20.019 => Not trivial, Not overlay, NW0, N3 20.019/20.019 => Not trivial, Overlay, NW0, N4 20.019/20.019 => Not trivial, Not overlay, NW0, N5 20.019/20.019 => Not trivial, Not overlay, NW0, N6 20.019/20.019 => Not trivial, Overlay, NW0, N7 20.019/20.019 => Not trivial, Not overlay, NW0, N8 20.019/20.019 20.019/20.019 -> Problem conclusions: 20.019/20.019 Not left linear, Right linear, Not linear 20.019/20.019 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.019/20.019 Not Huet-Levy confluent, Not Newman confluent 20.019/20.019 R is a TRS 20.019/20.019 20.019/20.019 20.019/20.019 Problem 1: 20.019/20.019 Different Normal CP Terms Processor: 20.019/20.019 => Not trivial, Overlay, NW0, N1, Normal and not trivial cp 20.019/20.019 20.019/20.019 The problem is not joinable. 20.019/20.019 18.71user 1.65system 0:20.19elapsed 100%CPU (0avgtext+0avgdata 62376maxresident)k 20.019/20.019 8inputs+0outputs (0major+29723minor)pagefaults 0swaps