0.00/0.24 YES 0.00/0.24 0.00/0.24 Problem 1: 0.00/0.24 0.00/0.24 (VAR v_NonEmpty:S x:S y:S) 0.00/0.24 (RULES 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 ) 0.00/0.24 (STRATEGY INNERMOST) 0.00/0.24 0.00/0.24 Problem 1: 0.00/0.24 0.00/0.24 Dependency Pairs Processor: 0.00/0.24 -> Pairs: 0.00/0.24 F(0,1,x:S) -> H(x:S,x:S) 0.00/0.24 H(x:S,y:S) -> F(x:S,y:S,x:S) 0.00/0.24 -> Rules: 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 0.00/0.24 Problem 1: 0.00/0.24 0.00/0.24 SCC Processor: 0.00/0.24 -> Pairs: 0.00/0.24 F(0,1,x:S) -> H(x:S,x:S) 0.00/0.24 H(x:S,y:S) -> F(x:S,y:S,x:S) 0.00/0.24 -> Rules: 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 ->Strongly Connected Components: 0.00/0.24 ->->Cycle: 0.00/0.24 ->->-> Pairs: 0.00/0.24 F(0,1,x:S) -> H(x:S,x:S) 0.00/0.24 H(x:S,y:S) -> F(x:S,y:S,x:S) 0.00/0.24 ->->-> Rules: 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 0.00/0.24 Problem 1: 0.00/0.24 0.00/0.24 Reduction Pair Processor: 0.00/0.24 -> Pairs: 0.00/0.24 F(0,1,x:S) -> H(x:S,x:S) 0.00/0.24 H(x:S,y:S) -> F(x:S,y:S,x:S) 0.00/0.24 -> Rules: 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 -> Usable rules: 0.00/0.24 Empty 0.00/0.24 ->Mace4 Output: 0.00/0.24 ============================== Mace4 ================================= 0.00/0.24 Mace4 (64) version 2009-11A, November 2009. 0.00/0.24 Process 6449 was started by sandbox on n067.star.cs.uiowa.edu, 0.00/0.24 Thu Mar 28 22:24:27 2019 0.00/0.24 The command was "./mace4 -c -f /tmp/mace41497983152038664370.in". 0.00/0.24 ============================== end of head =========================== 0.00/0.24 0.00/0.24 ============================== INPUT ================================= 0.00/0.24 0.00/0.24 % Reading from file /tmp/mace41497983152038664370.in 0.00/0.24 0.00/0.24 assign(max_seconds,20). 0.00/0.24 0.00/0.24 formulas(assumptions). 0.00/0.24 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.24 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.24 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.24 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2,x3),f2(y,x2,x3)) # label(congruence). 0.00/0.24 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,y,x3)) # label(congruence). 0.00/0.24 arrow_s0(x3,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,x2,y)) # label(congruence). 0.00/0.24 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence). 0.00/0.24 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence). 0.00/0.24 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence). 0.00/0.24 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence). 0.00/0.24 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence). 0.00/0.24 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence). 0.00/0.24 arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence). 0.00/0.24 arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence). 0.00/0.24 arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence). 0.00/0.24 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.24 sqsupset_s0(f9(f5,f6,x1),f10(x1,x1)) # label(replacement). 0.00/0.24 succeq_s0(f10(x1,x2),f9(x1,x2,x1)) # label(replacement). 0.00/0.24 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.24 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.24 end_of_list. 0.00/0.24 0.00/0.24 formulas(goals). 0.00/0.24 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.24 end_of_list. 0.00/0.24 0.00/0.24 ============================== end of input ========================== 0.00/0.24 0.00/0.24 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.24 0.00/0.24 % Formulas that are not ordinary clauses: 0.00/0.24 1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.24 2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.24 3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.24 4 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2,x3),f2(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 5 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 6 arrow_s0(x3,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 7 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 8 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 9 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 10 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 11 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 12 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 13 arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 14 arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 15 arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.24 16 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.24 17 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.24 18 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.24 19 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.24 0.00/0.24 ============================== end of process non-clausal formulas === 0.00/0.24 0.00/0.24 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.24 0.00/0.24 formulas(mace4_clauses). 0.00/0.24 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.24 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.24 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f2(x,z,u),f2(y,z,u)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f2(z,x,u),f2(z,y,u)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f2(z,u,x),f2(z,u,y)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f3(x,z),f3(y,z)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f3(z,x),f3(z,y)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f4(x,z),f4(y,z)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f4(z,x),f4(z,y)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f9(x,z,u),f9(y,z,u)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f9(z,x,u),f9(z,y,u)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f9(z,u,x),f9(z,u,y)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f10(x,z),f10(y,z)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | arrow_s0(f10(z,x),f10(z,y)) # label(congruence). 0.00/0.24 -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.24 sqsupset_s0(f9(f5,f6,x),f10(x,x)) # label(replacement). 0.00/0.24 succeq_s0(f10(x,y),f9(x,y,x)) # label(replacement). 0.00/0.24 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.24 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.24 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.24 end_of_list. 0.00/0.24 0.00/0.24 ============================== end of clauses for search ============= 0.00/0.24 0.00/0.24 % There are no natural numbers in the input. 0.00/0.24 0.00/0.24 ============================== DOMAIN SIZE 2 ========================= 0.00/0.24 0.00/0.24 ============================== MODEL ================================= 0.00/0.24 0.00/0.24 interpretation( 2, [number=1, seconds=0], [ 0.00/0.24 0.00/0.24 function(f5, [ 0 ]), 0.00/0.24 0.00/0.24 function(f6, [ 1 ]), 0.00/0.24 0.00/0.24 function(f10(_,_), [ 0.00/0.24 0, 1, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 function(f3(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 function(f4(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 function(f2(_,_,_), [ 0.00/0.24 0, 0, 0.00/0.24 0, 0, 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 function(f9(_,_,_), [ 0.00/0.24 0, 0, 0.00/0.24 1, 1, 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 relation(arrow_s0(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 relation(gtrsim_s0(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 0, 0 ]), 0.00/0.24 0.00/0.24 relation(sqsupsetStar_s0(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 1, 0 ]), 0.00/0.24 0.00/0.24 relation(sqsupset_s0(_,_), [ 0.00/0.24 0, 0, 0.00/0.24 1, 0 ]), 0.00/0.24 0.00/0.24 relation(succeq_s0(_,_), [ 0.00/0.24 1, 0, 0.00/0.24 0, 1 ]) 0.00/0.24 ]). 0.00/0.24 0.00/0.24 ============================== end of model ========================== 0.00/0.24 0.00/0.24 ============================== STATISTICS ============================ 0.00/0.24 0.00/0.24 For domain size 2. 0.00/0.24 0.00/0.24 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.24 Ground clauses: seen=192, kept=192. 0.00/0.24 Selections=30, assignments=32, propagations=27, current_models=1. 0.00/0.24 Rewrite_terms=354, rewrite_bools=250, indexes=40. 0.00/0.24 Rules_from_neg_clauses=8, cross_offs=8. 0.00/0.24 0.00/0.24 ============================== end of statistics ===================== 0.00/0.24 0.00/0.24 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.00/0.24 0.00/0.24 Exiting with 1 model. 0.00/0.24 0.00/0.24 Process 6449 exit (max_models) Thu Mar 28 22:24:27 2019 0.00/0.24 The process finished Thu Mar 28 22:24:27 2019 0.00/0.24 0.00/0.24 0.00/0.24 Mace4 cooked interpretation: 0.00/0.24 0.00/0.24 % number = 1 0.00/0.24 % seconds = 0 0.00/0.24 0.00/0.24 % Interpretation of size 2 0.00/0.24 0.00/0.24 f5 = 0. 0.00/0.24 0.00/0.24 f6 = 1. 0.00/0.24 0.00/0.24 f10(0,0) = 0. 0.00/0.24 f10(0,1) = 1. 0.00/0.24 f10(1,0) = 0. 0.00/0.24 f10(1,1) = 0. 0.00/0.24 0.00/0.24 f3(0,0) = 0. 0.00/0.24 f3(0,1) = 0. 0.00/0.24 f3(1,0) = 0. 0.00/0.24 f3(1,1) = 0. 0.00/0.24 0.00/0.24 f4(0,0) = 0. 0.00/0.24 f4(0,1) = 0. 0.00/0.24 f4(1,0) = 0. 0.00/0.24 f4(1,1) = 0. 0.00/0.24 0.00/0.24 f2(0,0,0) = 0. 0.00/0.24 f2(0,0,1) = 0. 0.00/0.24 f2(0,1,0) = 0. 0.00/0.24 f2(0,1,1) = 0. 0.00/0.24 f2(1,0,0) = 0. 0.00/0.24 f2(1,0,1) = 0. 0.00/0.24 f2(1,1,0) = 0. 0.00/0.24 f2(1,1,1) = 0. 0.00/0.24 0.00/0.24 f9(0,0,0) = 0. 0.00/0.24 f9(0,0,1) = 0. 0.00/0.24 f9(0,1,0) = 1. 0.00/0.24 f9(0,1,1) = 1. 0.00/0.24 f9(1,0,0) = 0. 0.00/0.24 f9(1,0,1) = 0. 0.00/0.24 f9(1,1,0) = 0. 0.00/0.24 f9(1,1,1) = 0. 0.00/0.24 0.00/0.24 - arrow_s0(0,0). 0.00/0.24 - arrow_s0(0,1). 0.00/0.24 - arrow_s0(1,0). 0.00/0.24 - arrow_s0(1,1). 0.00/0.24 0.00/0.24 - gtrsim_s0(0,0). 0.00/0.24 - gtrsim_s0(0,1). 0.00/0.24 - gtrsim_s0(1,0). 0.00/0.24 - gtrsim_s0(1,1). 0.00/0.24 0.00/0.24 - sqsupsetStar_s0(0,0). 0.00/0.24 - sqsupsetStar_s0(0,1). 0.00/0.24 sqsupsetStar_s0(1,0). 0.00/0.24 - sqsupsetStar_s0(1,1). 0.00/0.24 0.00/0.24 - sqsupset_s0(0,0). 0.00/0.24 - sqsupset_s0(0,1). 0.00/0.24 sqsupset_s0(1,0). 0.00/0.24 - sqsupset_s0(1,1). 0.00/0.24 0.00/0.24 succeq_s0(0,0). 0.00/0.24 - succeq_s0(0,1). 0.00/0.24 - succeq_s0(1,0). 0.00/0.24 succeq_s0(1,1). 0.00/0.24 0.00/0.24 0.00/0.24 Problem 1: 0.00/0.24 0.00/0.24 SCC Processor: 0.00/0.24 -> Pairs: 0.00/0.24 H(x:S,y:S) -> F(x:S,y:S,x:S) 0.00/0.24 -> Rules: 0.00/0.24 f(0,1,x:S) -> h(x:S,x:S) 0.00/0.24 g(x:S,y:S) -> x:S 0.00/0.24 g(x:S,y:S) -> y:S 0.00/0.24 h(x:S,y:S) -> f(x:S,y:S,x:S) 0.00/0.24 ->Strongly Connected Components: 0.00/0.24 There is no strongly connected component 0.00/0.24 0.00/0.24 The problem is finite. 0.00/0.24 EOF