0.98/1.03 YES 0.98/1.03 0.98/1.03 Problem 1: 0.98/1.03 0.98/1.03 (VAR v_NonEmpty:S x:S y:S z:S) 0.98/1.03 (RULES 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 ) 0.98/1.03 0.98/1.03 Problem 1: 0.98/1.03 Valid CTRS Processor: 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 -> The system is a deterministic 3-CTRS. 0.98/1.03 0.98/1.03 Problem 1: 0.98/1.03 0.98/1.03 Dependency Pairs Processor: 0.98/1.03 0.98/1.03 Conditional Termination Problem 1: 0.98/1.03 -> Pairs: 0.98/1.03 Empty 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 0.98/1.03 Conditional Termination Problem 2: 0.98/1.03 -> Pairs: 0.98/1.03 TC(x:S) -> PIN(x:S) 0.98/1.03 TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 0.98/1.03 0.98/1.03 The problem is decomposed in 2 subproblems. 0.98/1.03 0.98/1.03 Problem 1.1: 0.98/1.03 0.98/1.03 SCC Processor: 0.98/1.03 -> Pairs: 0.98/1.03 Empty 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 ->Strongly Connected Components: 0.98/1.03 There is no strongly connected component 0.98/1.03 0.98/1.03 The problem is finite. 0.98/1.03 0.98/1.03 Problem 1.2: 0.98/1.03 0.98/1.03 SCC Processor: 0.98/1.03 -> Pairs: 0.98/1.03 TC(x:S) -> PIN(x:S) 0.98/1.03 TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 ->Strongly Connected Components: 0.98/1.03 ->->Cycle: 0.98/1.03 ->->-> Pairs: 0.98/1.03 TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 ->->-> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 0.98/1.03 Problem 1.2: 0.98/1.03 0.98/1.03 Reduction Pair Processor: 0.98/1.03 -> Pairs: 0.98/1.03 TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 -> Needed rules: 0.98/1.03 Empty 0.98/1.03 -> Usable rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 ->Mace4 Output: 0.98/1.03 ============================== Mace4 ================================= 0.98/1.03 Mace4 (64) version 2009-11A, November 2009. 0.98/1.03 Process 5309 was started by sandbox on n057.star.cs.uiowa.edu, 0.98/1.03 Fri Mar 29 01:49:42 2019 0.98/1.03 The command was "./mace4 -c -f /tmp/mace41804289383846930886.in". 0.98/1.03 ============================== end of head =========================== 0.98/1.03 0.98/1.03 ============================== INPUT ================================= 0.98/1.03 0.98/1.03 % Reading from file /tmp/mace41804289383846930886.in 0.98/1.03 0.98/1.03 assign(max_seconds,20). 0.98/1.03 0.98/1.03 formulas(assumptions). 0.98/1.03 arrowStar_s0(x,x) # label(reflexivity). 0.98/1.03 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility). 0.98/1.03 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.98/1.03 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.98/1.03 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.98/1.03 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence). 0.98/1.03 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). 0.98/1.03 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence). 0.98/1.03 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence). 0.98/1.03 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence). 0.98/1.03 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence). 0.98/1.03 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence). 0.98/1.03 arrow_s0(f2(f4),f8(f5)) # label(replacement). 0.98/1.03 arrow_s0(f2(f5),f8(f6)) # label(replacement). 0.98/1.03 arrow_s0(f13(x4,x5),x4) # label(replacement). 0.98/1.03 arrow_s0(f13(x4,x5),x5) # label(replacement). 0.98/1.03 arrowN_s0(f13(x4,x5),x4) # label(replacement). 0.98/1.03 arrowN_s0(f13(x4,x5),x5) # label(replacement). 0.98/1.03 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.98/1.03 arrowStar_s0(f2(x1),f8(x3)) -> sqsupset_s0(f12(x1),f12(x3)) # label(replacement). 0.98/1.03 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.98/1.03 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.98/1.03 end_of_list. 0.98/1.03 0.98/1.03 formulas(goals). 0.98/1.03 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.98/1.03 end_of_list. 0.98/1.03 0.98/1.03 ============================== end of input ========================== 0.98/1.03 0.98/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.98/1.03 0.98/1.03 % Formulas that are not ordinary clauses: 0.98/1.03 1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.98/1.03 2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.98/1.03 3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.98/1.03 4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.98/1.03 5 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 7 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 8 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 9 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 10 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 12 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 13 arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 14 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 15 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 16 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.98/1.03 17 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.98/1.03 18 arrowStar_s0(f2(x1),f8(x3)) -> sqsupset_s0(f12(x1),f12(x3)) # label(replacement) # label(non_clause). [assumption]. 0.98/1.03 19 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.98/1.03 20 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.98/1.03 21 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.98/1.03 0.98/1.03 ============================== end of process non-clausal formulas === 0.98/1.03 0.98/1.03 ============================== CLAUSES FOR SEARCH ==================== 0.98/1.03 0.98/1.03 formulas(mace4_clauses). 0.98/1.03 arrowStar_s0(x,x) # label(reflexivity). 0.98/1.03 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility). 0.98/1.03 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.98/1.03 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.98/1.03 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.98/1.03 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence). 0.98/1.03 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). 0.98/1.03 -arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence). 0.98/1.03 -arrow_s0(x,y) | arrow_s0(f13(x,z),f13(y,z)) # label(congruence). 0.98/1.03 -arrow_s0(x,y) | arrow_s0(f13(z,x),f13(z,y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f2(x),f2(y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f11(x),f11(y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence). 0.98/1.03 -arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence). 0.98/1.03 arrow_s0(f2(f4),f8(f5)) # label(replacement). 0.98/1.03 arrow_s0(f2(f5),f8(f6)) # label(replacement). 0.98/1.03 arrow_s0(f13(x,y),x) # label(replacement). 0.98/1.03 arrow_s0(f13(x,y),y) # label(replacement). 0.98/1.03 arrowN_s0(f13(x,y),x) # label(replacement). 0.98/1.03 arrowN_s0(f13(x,y),y) # label(replacement). 0.98/1.03 -arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.98/1.03 -arrowStar_s0(f2(x),f8(y)) | sqsupset_s0(f12(x),f12(y)) # label(replacement). 0.98/1.03 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.98/1.03 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.98/1.03 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.98/1.03 end_of_list. 0.98/1.03 0.98/1.03 ============================== end of clauses for search ============= 0.98/1.03 0.98/1.03 % There are no natural numbers in the input. 0.98/1.03 0.98/1.03 ============================== DOMAIN SIZE 2 ========================= 0.98/1.03 0.98/1.03 ============================== STATISTICS ============================ 0.98/1.03 0.98/1.03 For domain size 2. 0.98/1.03 0.98/1.03 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.98/1.03 Ground clauses: seen=138, kept=134. 0.98/1.03 Selections=32, assignments=63, propagations=272, current_models=0. 0.98/1.03 Rewrite_terms=1141, rewrite_bools=670, indexes=321. 0.98/1.03 Rules_from_neg_clauses=122, cross_offs=122. 0.98/1.03 0.98/1.03 ============================== end of statistics ===================== 0.98/1.03 0.98/1.03 ============================== DOMAIN SIZE 3 ========================= 0.98/1.03 0.98/1.03 ============================== STATISTICS ============================ 0.98/1.03 0.98/1.03 For domain size 3. 0.98/1.03 0.98/1.03 Current CPU time: 0.00 seconds (total CPU time: 0.02 seconds). 0.98/1.03 Ground clauses: seen=386, kept=377. 0.98/1.03 Selections=582, assignments=1738, propagations=13178, current_models=0. 0.98/1.03 Rewrite_terms=61642, rewrite_bools=89397, indexes=9661. 0.98/1.03 Rules_from_neg_clauses=2977, cross_offs=6832. 0.98/1.03 0.98/1.03 ============================== end of statistics ===================== 0.98/1.03 0.98/1.03 ============================== DOMAIN SIZE 4 ========================= 0.98/1.03 0.98/1.03 ============================== MODEL ================================= 0.98/1.03 0.98/1.03 interpretation( 4, [number=1, seconds=0], [ 0.98/1.03 0.98/1.03 function(f4, [ 0 ]), 0.98/1.03 0.98/1.03 function(f5, [ 1 ]), 0.98/1.03 0.98/1.03 function(f6, [ 2 ]), 0.98/1.03 0.98/1.03 function(f11(_), [ 0, 0, 0, 0 ]), 0.98/1.03 0.98/1.03 function(f12(_), [ 0, 1, 2, 0 ]), 0.98/1.03 0.98/1.03 function(f2(_), [ 0, 1, 2, 0 ]), 0.98/1.03 0.98/1.03 function(f3(_), [ 0, 0, 0, 0 ]), 0.98/1.03 0.98/1.03 function(f8(_), [ 3, 0, 1, 3 ]), 0.98/1.03 0.98/1.03 function(f13(_,_), [ 0.98/1.03 0, 0, 0, 3, 0.98/1.03 0, 0, 0, 3, 0.98/1.03 0, 0, 0, 3, 0.98/1.03 3, 3, 3, 3 ]), 0.98/1.03 0.98/1.03 relation(arrowN_s0(_,_), [ 0.98/1.03 1, 1, 1, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 1, 1, 1, 1 ]), 0.98/1.03 0.98/1.03 relation(arrowStar_s0(_,_), [ 0.98/1.03 1, 1, 1, 0, 0.98/1.03 0, 1, 0, 0, 0.98/1.03 0, 0, 1, 0, 0.98/1.03 1, 1, 1, 1 ]), 0.98/1.03 0.98/1.03 relation(arrow_s0(_,_), [ 0.98/1.03 1, 1, 1, 0, 0.98/1.03 0, 1, 0, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 1, 1, 1, 1 ]), 0.98/1.03 0.98/1.03 relation(gtrsim_s0(_,_), [ 0.98/1.03 1, 1, 1, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 1, 1, 1, 1 ]), 0.98/1.03 0.98/1.03 relation(sqsupsetStar_s0(_,_), [ 0.98/1.03 0, 1, 1, 0, 0.98/1.03 0, 0, 1, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 1, 1, 0 ]), 0.98/1.03 0.98/1.03 relation(sqsupset_s0(_,_), [ 0.98/1.03 0, 1, 1, 0, 0.98/1.03 0, 0, 1, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 1, 1, 0 ]), 0.98/1.03 0.98/1.03 relation(succeq_s0(_,_), [ 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 0, 0, 0, 0.98/1.03 0, 0, 0, 0 ]) 0.98/1.03 ]). 0.98/1.03 0.98/1.03 ============================== end of model ========================== 0.98/1.03 0.98/1.03 ============================== STATISTICS ============================ 0.98/1.03 0.98/1.03 For domain size 4. 0.98/1.03 0.98/1.03 Current CPU time: 0.00 seconds (total CPU time: 0.96 seconds). 0.98/1.03 Ground clauses: seen=826, kept=810. 0.98/1.03 Selections=44683, assignments=178483, propagations=476301, current_models=1. 0.98/1.03 Rewrite_terms=3194403, rewrite_bools=4688761, indexes=312025. 0.98/1.03 Rules_from_neg_clauses=40104, cross_offs=237067. 0.98/1.03 0.98/1.03 ============================== end of statistics ===================== 0.98/1.03 0.98/1.03 User_CPU=0.96, System_CPU=0.03, Wall_clock=1. 0.98/1.03 0.98/1.03 Exiting with 1 model. 0.98/1.03 0.98/1.03 Process 5309 exit (max_models) Fri Mar 29 01:49:43 2019 0.98/1.03 The process finished Fri Mar 29 01:49:43 2019 0.98/1.03 0.98/1.03 0.98/1.03 Mace4 cooked interpretation: 0.98/1.03 0.98/1.03 % number = 1 0.98/1.03 % seconds = 0 0.98/1.03 0.98/1.03 % Interpretation of size 4 0.98/1.03 0.98/1.03 f4 = 0. 0.98/1.03 0.98/1.03 f5 = 1. 0.98/1.03 0.98/1.03 f6 = 2. 0.98/1.03 0.98/1.03 f11(0) = 0. 0.98/1.03 f11(1) = 0. 0.98/1.03 f11(2) = 0. 0.98/1.03 f11(3) = 0. 0.98/1.03 0.98/1.03 f12(0) = 0. 0.98/1.03 f12(1) = 1. 0.98/1.03 f12(2) = 2. 0.98/1.03 f12(3) = 0. 0.98/1.03 0.98/1.03 f2(0) = 0. 0.98/1.03 f2(1) = 1. 0.98/1.03 f2(2) = 2. 0.98/1.03 f2(3) = 0. 0.98/1.03 0.98/1.03 f3(0) = 0. 0.98/1.03 f3(1) = 0. 0.98/1.03 f3(2) = 0. 0.98/1.03 f3(3) = 0. 0.98/1.03 0.98/1.03 f8(0) = 3. 0.98/1.03 f8(1) = 0. 0.98/1.03 f8(2) = 1. 0.98/1.03 f8(3) = 3. 0.98/1.03 0.98/1.03 f13(0,0) = 0. 0.98/1.03 f13(0,1) = 0. 0.98/1.03 f13(0,2) = 0. 0.98/1.03 f13(0,3) = 3. 0.98/1.03 f13(1,0) = 0. 0.98/1.03 f13(1,1) = 0. 0.98/1.03 f13(1,2) = 0. 0.98/1.03 f13(1,3) = 3. 0.98/1.03 f13(2,0) = 0. 0.98/1.03 f13(2,1) = 0. 0.98/1.03 f13(2,2) = 0. 0.98/1.03 f13(2,3) = 3. 0.98/1.03 f13(3,0) = 3. 0.98/1.03 f13(3,1) = 3. 0.98/1.03 f13(3,2) = 3. 0.98/1.03 f13(3,3) = 3. 0.98/1.03 0.98/1.03 arrowN_s0(0,0). 0.98/1.03 arrowN_s0(0,1). 0.98/1.03 arrowN_s0(0,2). 0.98/1.03 - arrowN_s0(0,3). 0.98/1.03 - arrowN_s0(1,0). 0.98/1.03 - arrowN_s0(1,1). 0.98/1.03 - arrowN_s0(1,2). 0.98/1.03 - arrowN_s0(1,3). 0.98/1.03 - arrowN_s0(2,0). 0.98/1.03 - arrowN_s0(2,1). 0.98/1.03 - arrowN_s0(2,2). 0.98/1.03 - arrowN_s0(2,3). 0.98/1.03 arrowN_s0(3,0). 0.98/1.03 arrowN_s0(3,1). 0.98/1.03 arrowN_s0(3,2). 0.98/1.03 arrowN_s0(3,3). 0.98/1.03 0.98/1.03 arrowStar_s0(0,0). 0.98/1.03 arrowStar_s0(0,1). 0.98/1.03 arrowStar_s0(0,2). 0.98/1.03 - arrowStar_s0(0,3). 0.98/1.03 - arrowStar_s0(1,0). 0.98/1.03 arrowStar_s0(1,1). 0.98/1.03 - arrowStar_s0(1,2). 0.98/1.03 - arrowStar_s0(1,3). 0.98/1.03 - arrowStar_s0(2,0). 0.98/1.03 - arrowStar_s0(2,1). 0.98/1.03 arrowStar_s0(2,2). 0.98/1.03 - arrowStar_s0(2,3). 0.98/1.03 arrowStar_s0(3,0). 0.98/1.03 arrowStar_s0(3,1). 0.98/1.03 arrowStar_s0(3,2). 0.98/1.03 arrowStar_s0(3,3). 0.98/1.03 0.98/1.03 arrow_s0(0,0). 0.98/1.03 arrow_s0(0,1). 0.98/1.03 arrow_s0(0,2). 0.98/1.03 - arrow_s0(0,3). 0.98/1.03 - arrow_s0(1,0). 0.98/1.03 arrow_s0(1,1). 0.98/1.03 - arrow_s0(1,2). 0.98/1.03 - arrow_s0(1,3). 0.98/1.03 - arrow_s0(2,0). 0.98/1.03 - arrow_s0(2,1). 0.98/1.03 - arrow_s0(2,2). 0.98/1.03 - arrow_s0(2,3). 0.98/1.03 arrow_s0(3,0). 0.98/1.03 arrow_s0(3,1). 0.98/1.03 arrow_s0(3,2). 0.98/1.03 arrow_s0(3,3). 0.98/1.03 0.98/1.03 gtrsim_s0(0,0). 0.98/1.03 gtrsim_s0(0,1). 0.98/1.03 gtrsim_s0(0,2). 0.98/1.03 - gtrsim_s0(0,3). 0.98/1.03 - gtrsim_s0(1,0). 0.98/1.03 - gtrsim_s0(1,1). 0.98/1.03 - gtrsim_s0(1,2). 0.98/1.03 - gtrsim_s0(1,3). 0.98/1.03 - gtrsim_s0(2,0). 0.98/1.03 - gtrsim_s0(2,1). 0.98/1.03 - gtrsim_s0(2,2). 0.98/1.03 - gtrsim_s0(2,3). 0.98/1.03 gtrsim_s0(3,0). 0.98/1.03 gtrsim_s0(3,1). 0.98/1.03 gtrsim_s0(3,2). 0.98/1.03 gtrsim_s0(3,3). 0.98/1.03 0.98/1.03 - sqsupsetStar_s0(0,0). 0.98/1.03 sqsupsetStar_s0(0,1). 0.98/1.03 sqsupsetStar_s0(0,2). 0.98/1.03 - sqsupsetStar_s0(0,3). 0.98/1.03 - sqsupsetStar_s0(1,0). 0.98/1.03 - sqsupsetStar_s0(1,1). 0.98/1.03 sqsupsetStar_s0(1,2). 0.98/1.03 - sqsupsetStar_s0(1,3). 0.98/1.03 - sqsupsetStar_s0(2,0). 0.98/1.03 - sqsupsetStar_s0(2,1). 0.98/1.03 - sqsupsetStar_s0(2,2). 0.98/1.03 - sqsupsetStar_s0(2,3). 0.98/1.03 - sqsupsetStar_s0(3,0). 0.98/1.03 sqsupsetStar_s0(3,1). 0.98/1.03 sqsupsetStar_s0(3,2). 0.98/1.03 - sqsupsetStar_s0(3,3). 0.98/1.03 0.98/1.03 - sqsupset_s0(0,0). 0.98/1.03 sqsupset_s0(0,1). 0.98/1.03 sqsupset_s0(0,2). 0.98/1.03 - sqsupset_s0(0,3). 0.98/1.03 - sqsupset_s0(1,0). 0.98/1.03 - sqsupset_s0(1,1). 0.98/1.03 sqsupset_s0(1,2). 0.98/1.03 - sqsupset_s0(1,3). 0.98/1.03 - sqsupset_s0(2,0). 0.98/1.03 - sqsupset_s0(2,1). 0.98/1.03 - sqsupset_s0(2,2). 0.98/1.03 - sqsupset_s0(2,3). 0.98/1.03 - sqsupset_s0(3,0). 0.98/1.03 sqsupset_s0(3,1). 0.98/1.03 sqsupset_s0(3,2). 0.98/1.03 - sqsupset_s0(3,3). 0.98/1.03 0.98/1.03 - succeq_s0(0,0). 0.98/1.03 - succeq_s0(0,1). 0.98/1.03 - succeq_s0(0,2). 0.98/1.03 - succeq_s0(0,3). 0.98/1.03 - succeq_s0(1,0). 0.98/1.03 - succeq_s0(1,1). 0.98/1.03 - succeq_s0(1,2). 0.98/1.03 - succeq_s0(1,3). 0.98/1.03 - succeq_s0(2,0). 0.98/1.03 - succeq_s0(2,1). 0.98/1.03 - succeq_s0(2,2). 0.98/1.03 - succeq_s0(2,3). 0.98/1.03 - succeq_s0(3,0). 0.98/1.03 - succeq_s0(3,1). 0.98/1.03 - succeq_s0(3,2). 0.98/1.03 - succeq_s0(3,3). 0.98/1.03 0.98/1.03 0.98/1.03 Problem 1.2: 0.98/1.03 0.98/1.03 SCC Processor: 0.98/1.03 -> Pairs: 0.98/1.03 Empty 0.98/1.03 -> QPairs: 0.98/1.03 Empty 0.98/1.03 -> Rules: 0.98/1.03 pin(a) -> pout(b) 0.98/1.03 pin(b) -> pout(c) 0.98/1.03 tc(x:S) -> x:S 0.98/1.03 tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S 0.98/1.03 ->Strongly Connected Components: 0.98/1.03 There is no strongly connected component 0.98/1.03 0.98/1.03 The problem is finite. 0.98/1.03 EOF