0.00/0.07 YES 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 (VAR v_NonEmpty:S x:S) 0.00/0.07 (RULES 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 ) 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 Valid CTRS Processor: 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 -> The system is a deterministic 3-CTRS. 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 Dependency Pairs Processor: 0.00/0.07 0.00/0.07 Conditional Termination Problem 1: 0.00/0.07 -> Pairs: 0.00/0.07 G(x:S) -> A | f(x:S) ->* x:S 0.00/0.07 G(x:S) -> G(a) | f(x:S) ->* x:S 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 0.00/0.07 Conditional Termination Problem 2: 0.00/0.07 -> Pairs: 0.00/0.07 G(x:S) -> F(x:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 0.00/0.07 0.00/0.07 The problem is decomposed in 2 subproblems. 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 G(x:S) -> A | f(x:S) ->* x:S 0.00/0.07 G(x:S) -> G(a) | f(x:S) ->* x:S 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 G(x:S) -> G(a) | f(x:S) ->* x:S 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 ->->-> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 Reduction Pair Processor: 0.00/0.07 -> Pairs: 0.00/0.07 G(x:S) -> G(a) | f(x:S) ->* x:S 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 -> Needed rules: 0.00/0.07 a -> b 0.00/0.07 -> Usable rules: 0.00/0.07 f(a) -> b 0.00/0.07 ->Mace4 Output: 0.00/0.07 ============================== Mace4 ================================= 0.00/0.07 Mace4 (64) version 2009-11A, November 2009. 0.00/0.07 Process 58828 was started by sandbox on n140.star.cs.uiowa.edu, 0.00/0.07 Fri Mar 29 01:43:41 2019 0.00/0.07 The command was "./mace4 -c -f /tmp/mace41957747793424238335.in". 0.00/0.07 ============================== end of head =========================== 0.00/0.07 0.00/0.07 ============================== INPUT ================================= 0.00/0.07 0.00/0.07 % Reading from file /tmp/mace41957747793424238335.in 0.00/0.07 0.00/0.07 assign(max_seconds,20). 0.00/0.07 0.00/0.07 formulas(assumptions). 0.00/0.07 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.07 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility). 0.00/0.07 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f12(x1,x2),f12(y,x2)) # label(congruence). 0.00/0.07 arrow_s0(x2,y) -> arrow_s0(f12(x1,x2),f12(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f4(x1),f4(y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f10(x1),f10(y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence). 0.00/0.07 arrow_s0(f3(f2),f5) # label(replacement). 0.00/0.07 arrow_s0(f12(x2,x3),x2) # label(replacement). 0.00/0.07 arrow_s0(f12(x2,x3),x3) # label(replacement). 0.00/0.07 arrowN_s0(f2,f5) # label(replacement). 0.00/0.07 arrowN_s0(f12(x2,x3),x2) # label(replacement). 0.00/0.07 arrowN_s0(f12(x2,x3),x3) # label(replacement). 0.00/0.07 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.07 arrowStar_s0(f3(x1),x1) -> sqsupset_s0(f11(x1),f11(f2)) # label(replacement). 0.00/0.07 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.07 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 formulas(goals). 0.00/0.07 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 ============================== end of input ========================== 0.00/0.07 0.00/0.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.07 0.00/0.07 % Formulas that are not ordinary clauses: 0.00/0.07 1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 5 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 6 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 7 arrow_s0(x1,y) -> arrow_s0(f12(x1,x2),f12(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 8 arrow_s0(x2,y) -> arrow_s0(f12(x1,x2),f12(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 9 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 10 arrowN_s0(x1,y) -> arrowN_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 11 arrowN_s0(x1,y) -> arrowN_s0(f10(x1),f10(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 12 arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 13 arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 14 arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 15 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.07 16 arrowStar_s0(f3(x1),x1) -> sqsupset_s0(f11(x1),f11(f2)) # label(replacement) # label(non_clause). [assumption]. 0.00/0.07 17 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.07 18 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 19 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.07 0.00/0.07 ============================== end of process non-clausal formulas === 0.00/0.07 0.00/0.07 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.07 0.00/0.07 formulas(mace4_clauses). 0.00/0.07 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.07 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility). 0.00/0.07 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f12(x,z),f12(y,z)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f12(z,x),f12(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f4(x),f4(y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f10(x),f10(y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f11(x),f11(y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f12(x,z),f12(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f12(z,x),f12(z,y)) # label(congruence). 0.00/0.07 arrow_s0(f3(f2),f5) # label(replacement). 0.00/0.07 arrow_s0(f12(x,y),x) # label(replacement). 0.00/0.07 arrow_s0(f12(x,y),y) # label(replacement). 0.00/0.07 arrowN_s0(f2,f5) # label(replacement). 0.00/0.07 arrowN_s0(f12(x,y),x) # label(replacement). 0.00/0.07 arrowN_s0(f12(x,y),y) # label(replacement). 0.00/0.07 -arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.07 -arrowStar_s0(f3(x),x) | sqsupset_s0(f11(x),f11(f2)) # label(replacement). 0.00/0.07 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.07 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.07 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 ============================== end of clauses for search ============= 0.00/0.07 0.00/0.07 % There are no natural numbers in the input. 0.00/0.07 0.00/0.07 ============================== DOMAIN SIZE 2 ========================= 0.00/0.07 0.00/0.07 ============================== STATISTICS ============================ 0.00/0.07 0.00/0.07 For domain size 2. 0.00/0.07 0.00/0.07 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.07 Ground clauses: seen=128, kept=124. 0.00/0.07 Selections=8, assignments=15, propagations=95, current_models=0. 0.00/0.07 Rewrite_terms=286, rewrite_bools=384, indexes=66. 0.00/0.07 Rules_from_neg_clauses=28, cross_offs=28. 0.00/0.07 0.00/0.07 ============================== end of statistics ===================== 0.00/0.07 0.00/0.07 ============================== DOMAIN SIZE 3 ========================= 0.00/0.07 0.00/0.07 ============================== MODEL ================================= 0.00/0.07 0.00/0.07 interpretation( 3, [number=1, seconds=0], [ 0.00/0.07 0.00/0.07 function(f2, [ 0 ]), 0.00/0.07 0.00/0.07 function(f5, [ 1 ]), 0.00/0.07 0.00/0.07 function(f10(_), [ 0, 0, 0 ]), 0.00/0.07 0.00/0.07 function(f11(_), [ 0, 0, 2 ]), 0.00/0.07 0.00/0.07 function(f3(_), [ 1, 0, 2 ]), 0.00/0.07 0.00/0.07 function(f4(_), [ 0, 0, 0 ]), 0.00/0.07 0.00/0.07 function(f12(_,_), [ 0.00/0.07 2, 2, 2, 0.00/0.07 2, 2, 2, 0.00/0.07 2, 2, 2 ]), 0.00/0.07 0.00/0.07 relation(arrowN_s0(_,_), [ 0.00/0.07 1, 1, 0, 0.00/0.07 1, 1, 0, 0.00/0.07 1, 1, 1 ]), 0.00/0.07 0.00/0.07 relation(arrowStar_s0(_,_), [ 0.00/0.07 1, 0, 0, 0.00/0.07 0, 1, 0, 0.00/0.07 1, 1, 1 ]), 0.00/0.07 0.00/0.07 relation(arrow_s0(_,_), [ 0.00/0.07 1, 0, 0, 0.00/0.07 0, 1, 0, 0.00/0.07 1, 1, 1 ]), 0.00/0.07 0.00/0.07 relation(gtrsim_s0(_,_), [ 0.00/0.07 1, 1, 0, 0.00/0.07 1, 1, 0, 0.00/0.07 1, 1, 1 ]), 0.00/0.07 0.00/0.07 relation(sqsupsetStar_s0(_,_), [ 0.00/0.07 0, 0, 0, 0.00/0.07 0, 0, 0, 0.00/0.07 1, 0, 0 ]), 0.00/0.07 0.00/0.07 relation(sqsupset_s0(_,_), [ 0.00/0.07 0, 0, 0, 0.00/0.07 0, 0, 0, 0.00/0.07 1, 0, 0 ]), 0.00/0.07 0.00/0.07 relation(succeq_s0(_,_), [ 0.00/0.07 0, 0, 0, 0.00/0.07 0, 0, 0, 0.00/0.07 0, 0, 0 ]) 0.00/0.07 ]). 0.00/0.07 0.00/0.07 ============================== end of model ========================== 0.00/0.07 0.00/0.07 ============================== STATISTICS ============================ 0.00/0.07 0.00/0.07 For domain size 3. 0.00/0.07 0.00/0.07 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.07 Ground clauses: seen=362, kept=353. 0.00/0.07 Selections=87, assignments=210, propagations=1141, current_models=1. 0.00/0.07 Rewrite_terms=4572, rewrite_bools=7264, indexes=597. 0.00/0.07 Rules_from_neg_clauses=281, cross_offs=602. 0.00/0.07 0.00/0.07 ============================== end of statistics ===================== 0.00/0.07 0.00/0.07 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.00/0.07 0.00/0.07 Exiting with 1 model. 0.00/0.07 0.00/0.07 Process 58828 exit (max_models) Fri Mar 29 01:43:41 2019 0.00/0.07 The process finished Fri Mar 29 01:43:41 2019 0.00/0.07 0.00/0.07 0.00/0.07 Mace4 cooked interpretation: 0.00/0.07 0.00/0.07 % number = 1 0.00/0.07 % seconds = 0 0.00/0.07 0.00/0.07 % Interpretation of size 3 0.00/0.07 0.00/0.07 f2 = 0. 0.00/0.07 0.00/0.07 f5 = 1. 0.00/0.07 0.00/0.07 f10(0) = 0. 0.00/0.07 f10(1) = 0. 0.00/0.07 f10(2) = 0. 0.00/0.07 0.00/0.07 f11(0) = 0. 0.00/0.07 f11(1) = 0. 0.00/0.07 f11(2) = 2. 0.00/0.07 0.00/0.07 f3(0) = 1. 0.00/0.07 f3(1) = 0. 0.00/0.07 f3(2) = 2. 0.00/0.07 0.00/0.07 f4(0) = 0. 0.00/0.07 f4(1) = 0. 0.00/0.07 f4(2) = 0. 0.00/0.07 0.00/0.07 f12(0,0) = 2. 0.00/0.07 f12(0,1) = 2. 0.00/0.07 f12(0,2) = 2. 0.00/0.07 f12(1,0) = 2. 0.00/0.07 f12(1,1) = 2. 0.00/0.07 f12(1,2) = 2. 0.00/0.07 f12(2,0) = 2. 0.00/0.07 f12(2,1) = 2. 0.00/0.07 f12(2,2) = 2. 0.00/0.07 0.00/0.07 arrowN_s0(0,0). 0.00/0.07 arrowN_s0(0,1). 0.00/0.07 - arrowN_s0(0,2). 0.00/0.07 arrowN_s0(1,0). 0.00/0.07 arrowN_s0(1,1). 0.00/0.07 - arrowN_s0(1,2). 0.00/0.07 arrowN_s0(2,0). 0.00/0.07 arrowN_s0(2,1). 0.00/0.07 arrowN_s0(2,2). 0.00/0.07 0.00/0.07 arrowStar_s0(0,0). 0.00/0.07 - arrowStar_s0(0,1). 0.00/0.07 - arrowStar_s0(0,2). 0.00/0.07 - arrowStar_s0(1,0). 0.00/0.07 arrowStar_s0(1,1). 0.00/0.07 - arrowStar_s0(1,2). 0.00/0.07 arrowStar_s0(2,0). 0.00/0.07 arrowStar_s0(2,1). 0.00/0.07 arrowStar_s0(2,2). 0.00/0.07 0.00/0.07 arrow_s0(0,0). 0.00/0.07 - arrow_s0(0,1). 0.00/0.07 - arrow_s0(0,2). 0.00/0.07 - arrow_s0(1,0). 0.00/0.07 arrow_s0(1,1). 0.00/0.07 - arrow_s0(1,2). 0.00/0.07 arrow_s0(2,0). 0.00/0.07 arrow_s0(2,1). 0.00/0.07 arrow_s0(2,2). 0.00/0.07 0.00/0.07 gtrsim_s0(0,0). 0.00/0.07 gtrsim_s0(0,1). 0.00/0.07 - gtrsim_s0(0,2). 0.00/0.07 gtrsim_s0(1,0). 0.00/0.07 gtrsim_s0(1,1). 0.00/0.07 - gtrsim_s0(1,2). 0.00/0.07 gtrsim_s0(2,0). 0.00/0.07 gtrsim_s0(2,1). 0.00/0.07 gtrsim_s0(2,2). 0.00/0.07 0.00/0.07 - sqsupsetStar_s0(0,0). 0.00/0.07 - sqsupsetStar_s0(0,1). 0.00/0.07 - sqsupsetStar_s0(0,2). 0.00/0.07 - sqsupsetStar_s0(1,0). 0.00/0.07 - sqsupsetStar_s0(1,1). 0.00/0.07 - sqsupsetStar_s0(1,2). 0.00/0.07 sqsupsetStar_s0(2,0). 0.00/0.07 - sqsupsetStar_s0(2,1). 0.00/0.07 - sqsupsetStar_s0(2,2). 0.00/0.07 0.00/0.07 - sqsupset_s0(0,0). 0.00/0.07 - sqsupset_s0(0,1). 0.00/0.07 - sqsupset_s0(0,2). 0.00/0.07 - sqsupset_s0(1,0). 0.00/0.07 - sqsupset_s0(1,1). 0.00/0.07 - sqsupset_s0(1,2). 0.00/0.07 sqsupset_s0(2,0). 0.00/0.07 - sqsupset_s0(2,1). 0.00/0.07 - sqsupset_s0(2,2). 0.00/0.07 0.00/0.07 - succeq_s0(0,0). 0.00/0.07 - succeq_s0(0,1). 0.00/0.07 - succeq_s0(0,2). 0.00/0.07 - succeq_s0(1,0). 0.00/0.07 - succeq_s0(1,1). 0.00/0.07 - succeq_s0(1,2). 0.00/0.07 - succeq_s0(2,0). 0.00/0.07 - succeq_s0(2,1). 0.00/0.07 - succeq_s0(2,2). 0.00/0.07 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 G(x:S) -> F(x:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a -> b 0.00/0.07 f(a) -> b 0.00/0.07 g(x:S) -> g(a) | f(x:S) ->* x:S 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 EOF