/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) (RULES f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x: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(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) ->->-> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: Reduction Pairs Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) -> Usable rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 2 [a] = 1 [fSNonEmpty] = 0 [F](X1,X2) = 2.X1 + 2.X2 Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) ->->-> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: Reduction Pair Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) -> Usable rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 10000 was started by sandbox on n090.star.cs.uiowa.edu, Tue Jul 13 15:10:56 2021 The command was "./mace4 -c -f /tmp/mace41315634022635723058.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/mace41315634022635723058.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(f6(x1,x2),f6(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f6(x1,x2),f6(x1,y)) # label(congruence). arrow_s0(f2(x1,f2(f3,f2(f2(f3,f3),f3))),f2(f2(f3,x1),x1)) # label(replacement). arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f6(x1,f2(f3,f2(f2(f3,f3),f3))),f6(f2(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),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(f6(x1,x2),f6(y,x2)) # label(congruence) # label(non_clause). [assumption]. 7 arrow_s0(x2,y) -> arrow_s0(f6(x1,x2),f6(x1,y)) # label(congruence) # label(non_clause). [assumption]. 8 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 9 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 10 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 11 (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(f6(x,z),f6(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f6(z,x),f6(z,y)) # label(congruence). arrow_s0(f2(x,f2(f3,f2(f2(f3,f3),f3))),f2(f2(f3,x),x)) # label(replacement). -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f6(x,f2(f3,f2(f2(f3,f3),f3))),f6(f2(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 ========================= ============================== STATISTICS ============================ For domain size 2. Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). Ground clauses: seen=78, kept=78. Selections=118, assignments=235, propagations=402, current_models=0. Rewrite_terms=2314, rewrite_bools=2398, indexes=413. Rules_from_neg_clauses=68, cross_offs=68. ============================== end of statistics ===================== ============================== DOMAIN SIZE 3 ========================= ============================== MODEL ================================= interpretation( 3, [number=1, seconds=7], [ function(f3, [ 0 ]), function(f2(_,_), [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]), function(f6(_,_), [ 0, 0, 0, 1, 2, 0, 0, 2, 0 ]), relation(arrow_s0(_,_), [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]), relation(gtrsim_s0(_,_), [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]), relation(sqsupsetStar_s0(_,_), [ 0, 1, 0, 0, 0, 0, 1, 1, 0 ]), relation(sqsupset_s0(_,_), [ 0, 1, 0, 0, 0, 0, 1, 0, 0 ]), relation(succeq_s0(_,_), [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) ]). ============================== end of model ========================== ============================== STATISTICS ============================ For domain size 3. Current CPU time: 0.00 seconds (total CPU time: 7.83 seconds). Ground clauses: seen=243, kept=243. Selections=1397672, assignments=3967299, propagations=4337686, current_models=1. Rewrite_terms=37016097, rewrite_bools=23868482, indexes=5025239. Rules_from_neg_clauses=930895, cross_offs=2046879. ============================== end of statistics ===================== User_CPU=7.83, System_CPU=1.06, Wall_clock=9. Exiting with 1 model. Process 10000 exit (max_models) Tue Jul 13 15:11:05 2021 The process finished Tue Jul 13 15:11:05 2021 Mace4 cooked interpretation: % number = 1 % seconds = 7 % Interpretation of size 3 f3 = 0. f2(0,0) = 1. f2(0,1) = 0. f2(0,2) = 0. f2(1,0) = 0. f2(1,1) = 0. f2(1,2) = 0. f2(2,0) = 0. f2(2,1) = 0. f2(2,2) = 0. f6(0,0) = 0. f6(0,1) = 0. f6(0,2) = 0. f6(1,0) = 1. f6(1,1) = 2. f6(1,2) = 0. f6(2,0) = 0. f6(2,1) = 2. f6(2,2) = 0. arrow_s0(0,0). - arrow_s0(0,1). - arrow_s0(0,2). - arrow_s0(1,0). arrow_s0(1,1). - arrow_s0(1,2). - arrow_s0(2,0). - arrow_s0(2,1). arrow_s0(2,2). gtrsim_s0(0,0). - gtrsim_s0(0,1). - gtrsim_s0(0,2). - gtrsim_s0(1,0). gtrsim_s0(1,1). - gtrsim_s0(1,2). - gtrsim_s0(2,0). - gtrsim_s0(2,1). gtrsim_s0(2,2). - sqsupsetStar_s0(0,0). sqsupsetStar_s0(0,1). - sqsupsetStar_s0(0,2). - sqsupsetStar_s0(1,0). - sqsupsetStar_s0(1,1). - sqsupsetStar_s0(1,2). sqsupsetStar_s0(2,0). sqsupsetStar_s0(2,1). - sqsupsetStar_s0(2,2). - sqsupset_s0(0,0). sqsupset_s0(0,1). - sqsupset_s0(0,2). - sqsupset_s0(1,0). - sqsupset_s0(1,1). - sqsupset_s0(1,2). sqsupset_s0(2,0). - sqsupset_s0(2,1). - sqsupset_s0(2,2). - succeq_s0(0,0). - succeq_s0(0,1). - succeq_s0(0,2). - succeq_s0(1,0). - succeq_s0(1,1). - succeq_s0(1,2). - succeq_s0(2,0). - succeq_s0(2,1). - succeq_s0(2,2). Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.