0.00/0.08 YES 0.00/0.08 0.00/0.08 Problem 1: 0.00/0.08 0.00/0.08 (VAR v_NonEmpty:S x:S) 0.00/0.08 (RULES 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ) 0.00/0.08 0.00/0.08 Problem 1: 0.00/0.08 Valid CTRS Processor: 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 -> The system is a deterministic 3-CTRS. 0.00/0.08 0.00/0.08 Problem 1: 0.00/0.08 0.00/0.08 Dependency Pairs Processor: 0.00/0.08 0.00/0.08 Conditional Termination Problem 1: 0.00/0.08 -> Pairs: 0.00/0.08 P(q(x:S)) -> P(r(x:S)) 0.00/0.08 P(q(x:S)) -> R(x:S) 0.00/0.08 Q(h(x:S)) -> R(x:S) 0.00/0.08 R(x:S) -> R(h(x:S)) | s(x:S) ->* 0 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 0.00/0.08 Conditional Termination Problem 2: 0.00/0.08 -> Pairs: 0.00/0.08 R(x:S) -> S(x:S) 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 0.00/0.08 0.00/0.08 The problem is decomposed in 2 subproblems. 0.00/0.08 0.00/0.08 Problem 1.1: 0.00/0.08 0.00/0.08 SCC Processor: 0.00/0.08 -> Pairs: 0.00/0.08 P(q(x:S)) -> P(r(x:S)) 0.00/0.08 P(q(x:S)) -> R(x:S) 0.00/0.08 Q(h(x:S)) -> R(x:S) 0.00/0.08 R(x:S) -> R(h(x:S)) | s(x:S) ->* 0 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Strongly Connected Components: 0.00/0.08 ->->Cycle: 0.00/0.08 ->->-> Pairs: 0.00/0.08 R(x:S) -> R(h(x:S)) | s(x:S) ->* 0 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 ->->-> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->->Cycle: 0.00/0.08 ->->-> Pairs: 0.00/0.08 P(q(x:S)) -> P(r(x:S)) 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 ->->-> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 0.00/0.08 0.00/0.08 The problem is decomposed in 2 subproblems. 0.00/0.08 0.00/0.08 Problem 1.1.1: 0.00/0.08 0.00/0.08 Reduction Pair Processor: 0.00/0.08 -> Pairs: 0.00/0.08 R(x:S) -> R(h(x:S)) | s(x:S) ->* 0 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 -> Needed rules: 0.00/0.08 Empty 0.00/0.08 -> Usable rules: 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Mace4 Output: 0.00/0.08 ============================== Mace4 ================================= 0.00/0.08 Mace4 (64) version 2009-11A, November 2009. 0.00/0.08 Process 20827 was started by sandbox on n166.star.cs.uiowa.edu, 0.00/0.08 Fri Mar 29 01:51:28 2019 0.00/0.08 The command was "./mace4 -c -f /tmp/mace41957747793424238335.in". 0.00/0.08 ============================== end of head =========================== 0.00/0.08 0.00/0.08 ============================== INPUT ================================= 0.00/0.08 0.00/0.08 % Reading from file /tmp/mace41957747793424238335.in 0.00/0.08 0.00/0.08 assign(max_seconds,20). 0.00/0.08 0.00/0.08 formulas(assumptions). 0.00/0.08 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.08 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility). 0.00/0.08 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.08 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.08 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f9(x1),f9(y)) # label(congruence). 0.00/0.08 arrow_s0(x1,y) -> arrow_s0(f16(x1,x2),f16(y,x2)) # label(congruence). 0.00/0.08 arrow_s0(x2,y) -> arrow_s0(f16(x1,x2),f16(x1,y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f4(x1),f4(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f5(x1),f5(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f9(x1),f9(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f13(x1),f13(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f14(x1),f14(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f15(x1),f15(y)) # label(congruence). 0.00/0.08 arrowN_s0(x1,y) -> arrowN_s0(f16(x1,x2),f16(y,x2)) # label(congruence). 0.00/0.08 arrowN_s0(x2,y) -> arrowN_s0(f16(x1,x2),f16(x1,y)) # label(congruence). 0.00/0.08 arrow_s0(f5(x1),f7) # label(replacement). 0.00/0.08 arrow_s0(f16(x2,x3),x2) # label(replacement). 0.00/0.08 arrow_s0(f16(x2,x3),x3) # label(replacement). 0.00/0.08 arrowN_s0(f16(x2,x3),x2) # label(replacement). 0.00/0.08 arrowN_s0(f16(x2,x3),x3) # label(replacement). 0.00/0.08 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.08 arrowStar_s0(f5(x1),f6) -> sqsupset_s0(f14(x1),f14(f9(x1))) # label(replacement). 0.00/0.08 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.08 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.08 end_of_list. 0.00/0.08 0.00/0.08 formulas(goals). 0.00/0.08 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.08 end_of_list. 0.00/0.08 0.00/0.08 ============================== end of input ========================== 0.00/0.08 0.00/0.08 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.08 0.00/0.08 % Formulas that are not ordinary clauses: 0.00/0.08 1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.08 2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.08 3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.08 4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.08 5 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 7 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 8 arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 9 arrow_s0(x1,y) -> arrow_s0(f9(x1),f9(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 10 arrow_s0(x1,y) -> arrow_s0(f16(x1,x2),f16(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 11 arrow_s0(x2,y) -> arrow_s0(f16(x1,x2),f16(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 12 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 13 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 14 arrowN_s0(x1,y) -> arrowN_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 15 arrowN_s0(x1,y) -> arrowN_s0(f5(x1),f5(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 16 arrowN_s0(x1,y) -> arrowN_s0(f9(x1),f9(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 17 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 18 arrowN_s0(x1,y) -> arrowN_s0(f13(x1),f13(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 19 arrowN_s0(x1,y) -> arrowN_s0(f14(x1),f14(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 20 arrowN_s0(x1,y) -> arrowN_s0(f15(x1),f15(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 21 arrowN_s0(x1,y) -> arrowN_s0(f16(x1,x2),f16(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 22 arrowN_s0(x2,y) -> arrowN_s0(f16(x1,x2),f16(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.08 23 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.08 24 arrowStar_s0(f5(x1),f6) -> sqsupset_s0(f14(x1),f14(f9(x1))) # label(replacement) # label(non_clause). [assumption]. 0.00/0.08 25 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.08 26 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.08 27 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.08 0.00/0.08 ============================== end of process non-clausal formulas === 0.00/0.08 0.00/0.08 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.08 0.00/0.08 formulas(mace4_clauses). 0.00/0.08 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.08 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility). 0.00/0.08 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.08 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.08 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f5(x),f5(y)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f9(x),f9(y)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f16(x,z),f16(y,z)) # label(congruence). 0.00/0.08 -arrow_s0(x,y) | arrow_s0(f16(z,x),f16(z,y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f2(x),f2(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f4(x),f4(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f5(x),f5(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f9(x),f9(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f13(x),f13(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f14(x),f14(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f15(x),f15(y)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f16(x,z),f16(y,z)) # label(congruence). 0.00/0.08 -arrowN_s0(x,y) | arrowN_s0(f16(z,x),f16(z,y)) # label(congruence). 0.00/0.08 arrow_s0(f5(x),f7) # label(replacement). 0.00/0.08 arrow_s0(f16(x,y),x) # label(replacement). 0.00/0.08 arrow_s0(f16(x,y),y) # label(replacement). 0.00/0.08 arrowN_s0(f16(x,y),x) # label(replacement). 0.00/0.08 arrowN_s0(f16(x,y),y) # label(replacement). 0.00/0.08 -arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.08 -arrowStar_s0(f5(x),f6) | sqsupset_s0(f14(x),f14(f9(x))) # label(replacement). 0.00/0.08 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.08 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.08 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.08 end_of_list. 0.00/0.08 0.00/0.08 ============================== end of clauses for search ============= 0.00/0.08 0.00/0.08 % There are no natural numbers in the input. 0.00/0.08 0.00/0.08 ============================== DOMAIN SIZE 2 ========================= 0.00/0.08 0.00/0.08 ============================== MODEL ================================= 0.00/0.08 0.00/0.08 interpretation( 2, [number=1, seconds=0], [ 0.00/0.08 0.00/0.08 function(f6, [ 0 ]), 0.00/0.08 0.00/0.08 function(f7, [ 1 ]), 0.00/0.08 0.00/0.08 function(f12(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f13(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f14(_), [ 0, 1 ]), 0.00/0.08 0.00/0.08 function(f15(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f2(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f3(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f4(_), [ 0, 0 ]), 0.00/0.08 0.00/0.08 function(f5(_), [ 0, 1 ]), 0.00/0.08 0.00/0.08 function(f9(_), [ 1, 1 ]), 0.00/0.08 0.00/0.08 function(f16(_,_), [ 0.00/0.08 0, 0, 0.00/0.08 0, 0 ]), 0.00/0.08 0.00/0.08 relation(arrowN_s0(_,_), [ 0.00/0.08 1, 1, 0.00/0.08 0, 1 ]), 0.00/0.08 0.00/0.08 relation(arrowStar_s0(_,_), [ 0.00/0.08 1, 1, 0.00/0.08 0, 1 ]), 0.00/0.08 0.00/0.08 relation(arrow_s0(_,_), [ 0.00/0.08 1, 1, 0.00/0.08 0, 1 ]), 0.00/0.08 0.00/0.08 relation(gtrsim_s0(_,_), [ 0.00/0.08 1, 1, 0.00/0.08 0, 1 ]), 0.00/0.08 0.00/0.08 relation(sqsupsetStar_s0(_,_), [ 0.00/0.08 0, 1, 0.00/0.08 0, 0 ]), 0.00/0.08 0.00/0.08 relation(sqsupset_s0(_,_), [ 0.00/0.08 0, 1, 0.00/0.08 0, 0 ]), 0.00/0.08 0.00/0.08 relation(succeq_s0(_,_), [ 0.00/0.08 0, 0, 0.00/0.08 0, 0 ]) 0.00/0.08 ]). 0.00/0.08 0.00/0.08 ============================== end of model ========================== 0.00/0.08 0.00/0.08 ============================== STATISTICS ============================ 0.00/0.08 0.00/0.08 For domain size 2. 0.00/0.08 0.00/0.08 Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds). 0.00/0.08 Ground clauses: seen=160, kept=156. 0.00/0.08 Selections=532, assignments=1045, propagations=4959, current_models=1. 0.00/0.08 Rewrite_terms=15314, rewrite_bools=25971, indexes=3527. 0.00/0.08 Rules_from_neg_clauses=1478, cross_offs=1478. 0.00/0.08 0.00/0.08 ============================== end of statistics ===================== 0.00/0.08 0.00/0.08 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. 0.00/0.08 0.00/0.08 Exiting with 1 model. 0.00/0.08 0.00/0.08 Process 20827 exit (max_models) Fri Mar 29 01:51:28 2019 0.00/0.08 The process finished Fri Mar 29 01:51:28 2019 0.00/0.08 0.00/0.08 0.00/0.08 Mace4 cooked interpretation: 0.00/0.08 0.00/0.08 % number = 1 0.00/0.08 % seconds = 0 0.00/0.08 0.00/0.08 % Interpretation of size 2 0.00/0.08 0.00/0.08 f6 = 0. 0.00/0.08 0.00/0.08 f7 = 1. 0.00/0.08 0.00/0.08 f12(0) = 0. 0.00/0.08 f12(1) = 0. 0.00/0.08 0.00/0.08 f13(0) = 0. 0.00/0.08 f13(1) = 0. 0.00/0.08 0.00/0.08 f14(0) = 0. 0.00/0.08 f14(1) = 1. 0.00/0.08 0.00/0.08 f15(0) = 0. 0.00/0.08 f15(1) = 0. 0.00/0.08 0.00/0.08 f2(0) = 0. 0.00/0.08 f2(1) = 0. 0.00/0.08 0.00/0.08 f3(0) = 0. 0.00/0.08 f3(1) = 0. 0.00/0.08 0.00/0.08 f4(0) = 0. 0.00/0.08 f4(1) = 0. 0.00/0.08 0.00/0.08 f5(0) = 0. 0.00/0.08 f5(1) = 1. 0.00/0.08 0.00/0.08 f9(0) = 1. 0.00/0.08 f9(1) = 1. 0.00/0.08 0.00/0.08 f16(0,0) = 0. 0.00/0.08 f16(0,1) = 0. 0.00/0.08 f16(1,0) = 0. 0.00/0.08 f16(1,1) = 0. 0.00/0.08 0.00/0.08 arrowN_s0(0,0). 0.00/0.08 arrowN_s0(0,1). 0.00/0.08 - arrowN_s0(1,0). 0.00/0.08 arrowN_s0(1,1). 0.00/0.08 0.00/0.08 arrowStar_s0(0,0). 0.00/0.08 arrowStar_s0(0,1). 0.00/0.08 - arrowStar_s0(1,0). 0.00/0.08 arrowStar_s0(1,1). 0.00/0.08 0.00/0.08 arrow_s0(0,0). 0.00/0.08 arrow_s0(0,1). 0.00/0.08 - arrow_s0(1,0). 0.00/0.08 arrow_s0(1,1). 0.00/0.08 0.00/0.08 gtrsim_s0(0,0). 0.00/0.08 gtrsim_s0(0,1). 0.00/0.08 - gtrsim_s0(1,0). 0.00/0.08 gtrsim_s0(1,1). 0.00/0.08 0.00/0.08 - sqsupsetStar_s0(0,0). 0.00/0.08 sqsupsetStar_s0(0,1). 0.00/0.08 - sqsupsetStar_s0(1,0). 0.00/0.08 - sqsupsetStar_s0(1,1). 0.00/0.08 0.00/0.08 - sqsupset_s0(0,0). 0.00/0.08 sqsupset_s0(0,1). 0.00/0.08 - sqsupset_s0(1,0). 0.00/0.08 - sqsupset_s0(1,1). 0.00/0.08 0.00/0.08 - succeq_s0(0,0). 0.00/0.08 - succeq_s0(0,1). 0.00/0.08 - succeq_s0(1,0). 0.00/0.08 - succeq_s0(1,1). 0.00/0.08 0.00/0.08 0.00/0.08 Problem 1.1.1: 0.00/0.08 0.00/0.08 SCC Processor: 0.00/0.08 -> Pairs: 0.00/0.08 Empty 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Strongly Connected Components: 0.00/0.08 There is no strongly connected component 0.00/0.08 0.00/0.08 The problem is finite. 0.00/0.08 0.00/0.08 Problem 1.1.2: 0.00/0.08 0.00/0.08 Reduction Triple Processor: 0.00/0.08 -> Pairs: 0.00/0.08 P(q(x:S)) -> P(r(x:S)) 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 -> Usable rules: 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Interpretation type: 0.00/0.08 Linear 0.00/0.08 ->Coefficients: 0.00/0.08 Natural Numbers 0.00/0.08 ->Dimension: 0.00/0.08 1 0.00/0.08 ->Bound: 0.00/0.08 2 0.00/0.08 ->Interpretation: 0.00/0.08 0.00/0.08 [p](X) = 0 0.00/0.08 [q](X) = 2.X + 2 0.00/0.08 [r](X) = 0 0.00/0.08 [s](X) = 0 0.00/0.08 [0] = 0 0.00/0.08 [1] = 0 0.00/0.08 [fSNonEmpty] = 0 0.00/0.08 [h](X) = 0 0.00/0.08 [P](X) = 2.X 0.00/0.08 [Q](X) = 0 0.00/0.08 [R](X) = 0 0.00/0.08 [S](X) = 0 0.00/0.08 0.00/0.08 Problem 1.1.2: 0.00/0.08 0.00/0.08 SCC Processor: 0.00/0.08 -> Pairs: 0.00/0.08 Empty 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Strongly Connected Components: 0.00/0.08 There is no strongly connected component 0.00/0.08 0.00/0.08 The problem is finite. 0.00/0.08 0.00/0.08 Problem 1.2: 0.00/0.08 0.00/0.08 SCC Processor: 0.00/0.08 -> Pairs: 0.00/0.08 R(x:S) -> S(x:S) 0.00/0.08 -> QPairs: 0.00/0.08 Empty 0.00/0.08 -> Rules: 0.00/0.08 p(q(x:S)) -> p(r(x:S)) 0.00/0.08 q(h(x:S)) -> r(x:S) 0.00/0.08 r(x:S) -> r(h(x:S)) | s(x:S) ->* 0 0.00/0.08 s(x:S) -> 1 0.00/0.08 ->Strongly Connected Components: 0.00/0.08 There is no strongly connected component 0.00/0.08 0.00/0.08 The problem is finite. 0.00/0.08 EOF