/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) F(0,1,x:S) -> H(x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S Problem 1: SCC Processor: -> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) F(0,1,x:S) -> H(x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) ->->-> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S Problem 1: Reduction Pair Processor: -> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S -> Usable rules: h(0) -> 0 h(g(x:S,y:S)) -> y:S ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 26944 was started by sandbox2 on n081.star.cs.uiowa.edu, Tue Jul 13 15:01:54 2021 The command was "./mace4 -c -f /tmp/mace4336465782861021530.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/mace4336465782861021530.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,x3),f2(y,x2,x3)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,y,x3)) # label(congruence). arrow_s0(x3,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,x2,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(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),f10(y)) # label(congruence). arrow_s0(f3(f4),f4) # label(replacement). arrow_s0(f3(f7(x1,x2)),x2) # label(replacement). arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f9(f4,f5,x1),f9(f3(x1),f3(x1),x1)) # 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,x3),f2(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 5 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 6 arrow_s0(x3,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 7 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 8 arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence) # label(non_clause). [assumption]. 9 arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence) # label(non_clause). [assumption]. 10 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 11 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 12 arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 13 arrow_s0(x1,y) -> arrow_s0(f10(x1),f10(y)) # label(congruence) # label(non_clause). [assumption]. 14 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 15 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 16 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 17 (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,u),f2(y,z,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f2(z,x,u),f2(z,y,u)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f2(z,u,x),f2(z,u,y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f7(x,z),f7(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f7(z,x),f7(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),f10(y)) # label(congruence). arrow_s0(f3(f4),f4) # label(replacement). arrow_s0(f3(f7(x,y)),y) # label(replacement). -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f9(f4,f5,x),f9(f3(x),f3(x),x)) # 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, [ 1 ]), function(f10(_), [ 0, 0 ]), function(f3(_), [ 0, 1 ]), function(f7(_,_), [ 0, 1, 0, 1 ]), function(f2(_,_,_), [ 0, 0, 0, 0, 0, 0, 0, 0 ]), function(f9(_,_,_), [ 0, 0, 1, 1, 0, 0, 0, 0 ]), relation(arrow_s0(_,_), [ 1, 0, 0, 1 ]), relation(gtrsim_s0(_,_), [ 1, 0, 0, 1 ]), relation(sqsupsetStar_s0(_,_), [ 0, 0, 1, 0 ]), relation(sqsupset_s0(_,_), [ 0, 0, 1, 0 ]), relation(succeq_s0(_,_), [ 0, 0, 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=169, kept=169. Selections=59, assignments=96, propagations=157, current_models=1. Rewrite_terms=940, rewrite_bools=969, indexes=148. Rules_from_neg_clauses=75, cross_offs=75. ============================== end of statistics ===================== User_CPU=0.00, System_CPU=0.00, Wall_clock=0. Exiting with 1 model. Process 26944 exit (max_models) Tue Jul 13 15:01:54 2021 The process finished Tue Jul 13 15:01:54 2021 Mace4 cooked interpretation: % number = 1 % seconds = 0 % Interpretation of size 2 f4 = 0. f5 = 1. f10(0) = 0. f10(1) = 0. f3(0) = 0. f3(1) = 1. f7(0,0) = 0. f7(0,1) = 1. f7(1,0) = 0. f7(1,1) = 1. f2(0,0,0) = 0. f2(0,0,1) = 0. f2(0,1,0) = 0. f2(0,1,1) = 0. f2(1,0,0) = 0. f2(1,0,1) = 0. f2(1,1,0) = 0. f2(1,1,1) = 0. 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) = 0. f9(1,1,1) = 0. 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: Empty -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S ->Strongly Connected Components: There is no strongly connected component The problem is finite.