/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ) Problem 1: Dependency Pairs Processor: -> Pairs: B(y:S,z:S) -> C(c(y:S,z:S,z:S),a,a) B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(f(b(x:S,z:S)),c(z:S,y:S,a),a) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) Problem 1: SCC Processor: -> Pairs: B(y:S,z:S) -> C(c(y:S,z:S,z:S),a,a) B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(f(b(x:S,z:S)),c(z:S,y:S,a),a) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(f(b(x:S,z:S)),c(z:S,y:S,a),a) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) ->->-> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) Problem 1: Reduction Pair Processor: -> Pairs: B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(f(b(x:S,z:S)),c(z:S,y:S,a),a) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) -> Usable rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 25435 was started by sandbox on n174.star.cs.uiowa.edu, Tue Jul 13 17:26:35 2021 The command was "./mace4 -c -f /tmp/mace41330573317603570492.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/mace41330573317603570492.in assign(max_seconds,20). formulas(assumptions). gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f3(x1,x2,x3),f3(y,x2,x3)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f3(x1,x2,x3),f3(x1,y,x3)) # label(congruence). arrow_s0(x3,y) -> arrow_s0(f3(x1,x2,x3),f3(x1,x2,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f8(x1,x2),f8(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f8(x1,x2),f8(x1,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence). arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence). arrow_s0(f2(f2(x3,x2),f4),x3) # label(replacement). arrow_s0(f2(x2,x3),f5(f3(f3(x2,x3,x3),f4,f4))) # label(replacement). arrow_s0(f3(f5(x3),f5(f3(f4,x1,f4)),x2),f3(f5(f2(x1,x3)),f3(x3,x2,f4),f4)) # label(replacement). arrow_s0(f10(x4,x5),x4) # label(replacement). arrow_s0(f10(x4,x5),x5) # label(replacement). arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f9(f5(x3),f5(f3(f4,x1,f4)),x2),f9(f5(f2(x1,x3)),f3(x3,x2,f4),f4)) # label(replacement). succeq_s0(f8(x2,x3),f9(x2,x3,x3)) # label(replacement). succeq_s0(f9(f5(x3),f5(f3(f4,x1,f4)),x2),f8(x1,x3)) # label(replacement). succeq_s0(f9(f5(x3),f5(f3(f4,x1,f4)),x2),f9(x3,x2,f4)) # label(replacement). sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). end_of_list. formulas(goals). (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 4 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 5 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 6 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2,x3),f3(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 7 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2,x3),f3(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 8 arrow_s0(x3,y) -> arrow_s0(f3(x1,x2,x3),f3(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 9 arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence) # label(non_clause). [assumption]. 10 arrow_s0(x1,y) -> arrow_s0(f8(x1,x2),f8(y,x2)) # label(congruence) # label(non_clause). [assumption]. 11 arrow_s0(x2,y) -> arrow_s0(f8(x1,x2),f8(x1,y)) # label(congruence) # label(non_clause). [assumption]. 12 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 13 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 14 arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 15 arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence) # label(non_clause). [assumption]. 16 arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 18 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 19 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 20 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== CLAUSES FOR SEARCH ==================== formulas(mace4_clauses). -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). -arrow_s0(x,y) | arrow_s0(f2(x,z),f2(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f2(z,x),f2(z,y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f3(x,z,u),f3(y,z,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f3(z,x,u),f3(z,y,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f3(z,u,x),f3(z,u,y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f5(x),f5(y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f8(x,z),f8(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f8(z,x),f8(z,y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f9(x,z,u),f9(y,z,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f9(z,x,u),f9(z,y,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f9(z,u,x),f9(z,u,y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f10(x,z),f10(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f10(z,x),f10(z,y)) # label(congruence). arrow_s0(f2(f2(x,y),f4),x) # label(replacement). arrow_s0(f2(x,y),f5(f3(f3(x,y,y),f4,f4))) # label(replacement). arrow_s0(f3(f5(x),f5(f3(f4,y,f4)),z),f3(f5(f2(y,x)),f3(x,z,f4),f4)) # label(replacement). arrow_s0(f10(x,y),x) # label(replacement). arrow_s0(f10(x,y),y) # label(replacement). -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f9(f5(x),f5(f3(f4,y,f4)),z),f9(f5(f2(y,x)),f3(x,z,f4),f4)) # label(replacement). succeq_s0(f8(x,y),f9(x,y,y)) # label(replacement). succeq_s0(f9(f5(x),f5(f3(f4,y,f4)),z),f8(y,x)) # label(replacement). succeq_s0(f9(f5(x),f5(f3(f4,y,f4)),z),f9(x,z,f4)) # label(replacement). -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). -sqsupsetStar_s0(x,x) # label(wellfoundedness). end_of_list. ============================== end of clauses for search ============= % There are no natural numbers in the input. ============================== DOMAIN SIZE 2 ========================= ============================== MODEL ================================= interpretation( 2, [number=1, seconds=0], [ function(f4, [ 0 ]), function(f5(_), [ 0, 0 ]), function(f10(_,_), [ 0, 0, 0, 0 ]), function(f2(_,_), [ 0, 0, 0, 0 ]), function(f8(_,_), [ 0, 0, 0, 0 ]), function(f3(_,_,_), [ 1, 1, 1, 1, 1, 1, 1, 1 ]), function(f9(_,_,_), [ 0, 0, 1, 1, 0, 0, 1, 1 ]), relation(arrow_s0(_,_), [ 1, 1, 0, 1 ]), relation(gtrsim_s0(_,_), [ 1, 1, 0, 1 ]), relation(sqsupsetStar_s0(_,_), [ 0, 1, 0, 0 ]), relation(sqsupset_s0(_,_), [ 0, 1, 0, 0 ]), relation(succeq_s0(_,_), [ 1, 1, 0, 0 ]) ]). ============================== end of model ========================== ============================== STATISTICS ============================ For domain size 2. Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). Ground clauses: seen=242, kept=242. Selections=17, assignments=19, propagations=37, current_models=1. Rewrite_terms=721, rewrite_bools=386, indexes=110. Rules_from_neg_clauses=16, cross_offs=16. ============================== end of statistics ===================== User_CPU=0.00, System_CPU=0.00, Wall_clock=0. Exiting with 1 model. Process 25435 exit (max_models) Tue Jul 13 17:26:35 2021 The process finished Tue Jul 13 17:26:35 2021 Mace4 cooked interpretation: % number = 1 % seconds = 0 % Interpretation of size 2 f4 = 0. f5(0) = 0. f5(1) = 0. f10(0,0) = 0. f10(0,1) = 0. f10(1,0) = 0. f10(1,1) = 0. f2(0,0) = 0. f2(0,1) = 0. f2(1,0) = 0. f2(1,1) = 0. f8(0,0) = 0. f8(0,1) = 0. f8(1,0) = 0. f8(1,1) = 0. f3(0,0,0) = 1. f3(0,0,1) = 1. f3(0,1,0) = 1. f3(0,1,1) = 1. f3(1,0,0) = 1. f3(1,0,1) = 1. f3(1,1,0) = 1. f3(1,1,1) = 1. f9(0,0,0) = 0. f9(0,0,1) = 0. f9(0,1,0) = 1. f9(0,1,1) = 1. f9(1,0,0) = 0. f9(1,0,1) = 0. f9(1,1,0) = 1. f9(1,1,1) = 1. arrow_s0(0,0). arrow_s0(0,1). - arrow_s0(1,0). arrow_s0(1,1). gtrsim_s0(0,0). gtrsim_s0(0,1). - gtrsim_s0(1,0). gtrsim_s0(1,1). - sqsupsetStar_s0(0,0). sqsupsetStar_s0(0,1). - sqsupsetStar_s0(1,0). - sqsupsetStar_s0(1,1). - sqsupset_s0(0,0). sqsupset_s0(0,1). - sqsupset_s0(1,0). - sqsupset_s0(1,1). succeq_s0(0,0). succeq_s0(0,1). - succeq_s0(1,0). - succeq_s0(1,1). Problem 1: SCC Processor: -> Pairs: B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) ->->-> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) Problem 1: Reduction Pair Processor: -> Pairs: B(y:S,z:S) -> C(y:S,z:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [c](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [a] = 1 [f](X) = X + 2 [B](X1,X2) = 2.X1 + 2.X2 + 2 [C](X1,X2,X3) = 2.X1 + X2 + X3 + 1 Problem 1: SCC Processor: -> Pairs: C(f(z:S),f(c(a,x:S,a)),y:S) -> B(x:S,z:S) C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) ->->-> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) Problem 1: Subterm Processor: -> Pairs: C(f(z:S),f(c(a,x:S,a)),y:S) -> C(z:S,y:S,a) -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Projection: pi(C) = 1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: b(b(z:S,y:S),a) -> z:S b(y:S,z:S) -> f(c(c(y:S,z:S,z:S),a,a)) c(f(z:S),f(c(a,x:S,a)),y:S) -> c(f(b(x:S,z:S)),c(z:S,y:S,a),a) ->Strongly Connected Components: There is no strongly connected component The problem is finite.