25.54/25.93 YES 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 (VAR v_NonEmpty:S x1:S) 25.54/25.93 (RULES 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 ) 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 Dependency Pairs Processor: 25.54/25.93 -> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> A(x1:S) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 -> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 SCC Processor: 25.54/25.93 -> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> A(x1:S) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 -> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 ->Strongly Connected Components: 25.54/25.93 ->->Cycle: 25.54/25.93 ->->-> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> A(x1:S) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 ->->-> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 Reduction Pair Processor: 25.54/25.93 -> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> A(x1:S) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 -> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 -> Usable rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 ->Interpretation type: 25.54/25.93 Linear 25.54/25.93 ->Coefficients: 25.54/25.93 All rationals 25.54/25.93 ->Dimension: 25.54/25.93 1 25.54/25.93 ->Bound: 25.54/25.93 4 25.54/25.93 ->Interpretation: 25.54/25.93 25.54/25.93 [a](X) = X + 2/3 25.54/25.93 [c](X) = X + 2 25.54/25.93 [b](X) = X + 2/3 25.54/25.93 [A](X) = 1/4.X + 1 25.54/25.93 [C](X) = 1/4.X + 4/3 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 SCC Processor: 25.54/25.93 -> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 -> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 ->Strongly Connected Components: 25.54/25.93 ->->Cycle: 25.54/25.93 ->->-> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 ->->-> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.54/25.93 25.54/25.93 Problem 1: 25.54/25.93 25.54/25.93 Reduction Pair Processor: 25.54/25.93 -> Pairs: 25.54/25.93 A(b(b(x1:S))) -> C(x1:S) 25.54/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.54/25.93 C(c(x1:S)) -> C(a(x1:S)) 25.54/25.93 -> Rules: 25.54/25.93 a(b(b(x1:S))) -> c(x1:S) 25.54/25.93 a(x1:S) -> b(x1:S) 25.54/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 -> Usable rules: 25.65/25.93 a(b(b(x1:S))) -> c(x1:S) 25.65/25.93 a(x1:S) -> b(x1:S) 25.65/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 ->Interpretation type: 25.65/25.93 Linear 25.65/25.93 ->Coefficients: 25.65/25.93 All rationals 25.65/25.93 ->Dimension: 25.65/25.93 1 25.65/25.93 ->Bound: 25.65/25.93 4 25.65/25.93 ->Interpretation: 25.65/25.93 25.65/25.93 [a](X) = X + 2/3 25.65/25.93 [c](X) = X + 2 25.65/25.93 [b](X) = X + 2/3 25.65/25.93 [A](X) = 3/4.X + 1 25.65/25.93 [C](X) = 3/4.X + 2 25.65/25.93 25.65/25.93 Problem 1: 25.65/25.93 25.65/25.93 SCC Processor: 25.65/25.93 -> Pairs: 25.65/25.93 A(b(b(x1:S))) -> C(x1:S) 25.65/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.65/25.93 -> Rules: 25.65/25.93 a(b(b(x1:S))) -> c(x1:S) 25.65/25.93 a(x1:S) -> b(x1:S) 25.65/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 ->Strongly Connected Components: 25.65/25.93 ->->Cycle: 25.65/25.93 ->->-> Pairs: 25.65/25.93 A(b(b(x1:S))) -> C(x1:S) 25.65/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.65/25.93 ->->-> Rules: 25.65/25.93 a(b(b(x1:S))) -> c(x1:S) 25.65/25.93 a(x1:S) -> b(x1:S) 25.65/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 25.65/25.93 Problem 1: 25.65/25.93 25.65/25.93 Reduction Pair Processor: 25.65/25.93 -> Pairs: 25.65/25.93 A(b(b(x1:S))) -> C(x1:S) 25.65/25.93 C(c(x1:S)) -> A(b(c(a(x1:S)))) 25.65/25.93 -> Rules: 25.65/25.93 a(b(b(x1:S))) -> c(x1:S) 25.65/25.93 a(x1:S) -> b(x1:S) 25.65/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 -> Usable rules: 25.65/25.93 a(b(b(x1:S))) -> c(x1:S) 25.65/25.93 a(x1:S) -> b(x1:S) 25.65/25.93 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.93 ->Mace4 Output: 25.65/25.93 ============================== Mace4 ================================= 25.65/25.94 Mace4 (64) version 2009-11A, November 2009. 25.65/25.94 Process 35491 was started by sandbox on n034.star.cs.uiowa.edu, 25.65/25.94 Fri Mar 29 12:52:09 2019 25.65/25.94 The command was "./mace4 -c -f /tmp/mace43272545861572276965.in". 25.65/25.94 ============================== end of head =========================== 25.65/25.94 25.65/25.94 ============================== INPUT ================================= 25.65/25.94 25.65/25.94 % Reading from file /tmp/mace43272545861572276965.in 25.65/25.94 25.65/25.94 assign(max_seconds,20). 25.65/25.94 25.65/25.94 formulas(assumptions). 25.65/25.94 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 25.65/25.94 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 25.65/25.94 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f7(x1),f7(y)) # label(congruence). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence). 25.65/25.94 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2),f9(y,x2)) # label(congruence). 25.65/25.94 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2),f9(x1,y)) # label(congruence). 25.65/25.94 arrow_s0(f2(f4(f4(x1))),f3(x1)) # label(replacement). 25.65/25.94 arrow_s0(f2(x1),f4(x1)) # label(replacement). 25.65/25.94 arrow_s0(f3(f3(x1)),f2(f4(f3(f2(x1))))) # label(replacement). 25.65/25.94 arrow_s0(f9(x2,x3),x2) # label(replacement). 25.65/25.94 arrow_s0(f9(x2,x3),x3) # label(replacement). 25.65/25.94 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 25.65/25.94 sqsupset_s0(f8(f3(x1)),f7(f4(f3(f2(x1))))) # label(replacement). 25.65/25.94 succeq_s0(f7(f4(f4(x1))),f8(x1)) # label(replacement). 25.65/25.94 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 25.65/25.94 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 25.65/25.94 end_of_list. 25.65/25.94 25.65/25.94 formulas(goals). 25.65/25.94 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 25.65/25.94 end_of_list. 25.65/25.94 25.65/25.94 ============================== end of input ========================== 25.65/25.94 25.65/25.94 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.65/25.94 25.65/25.94 % Formulas that are not ordinary clauses: 25.65/25.94 1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 25.65/25.94 2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 25.65/25.94 3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 25.65/25.94 4 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 5 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 6 arrow_s0(x1,y) -> arrow_s0(f4(x1),f4(y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 7 arrow_s0(x1,y) -> arrow_s0(f7(x1),f7(y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 8 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 9 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2),f9(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 10 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2),f9(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.65/25.94 11 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 25.65/25.94 12 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 25.65/25.94 13 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 25.65/25.94 14 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 25.65/25.94 25.65/25.94 ============================== end of process non-clausal formulas === 25.65/25.94 25.65/25.94 ============================== CLAUSES FOR SEARCH ==================== 25.65/25.94 25.65/25.94 formulas(mace4_clauses). 25.65/25.94 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 25.65/25.94 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 25.65/25.94 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f4(x),f4(y)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f7(x),f7(y)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f9(x,z),f9(y,z)) # label(congruence). 25.65/25.94 -arrow_s0(x,y) | arrow_s0(f9(z,x),f9(z,y)) # label(congruence). 25.65/25.94 arrow_s0(f2(f4(f4(x))),f3(x)) # label(replacement). 25.65/25.94 arrow_s0(f2(x),f4(x)) # label(replacement). 25.65/25.94 arrow_s0(f3(f3(x)),f2(f4(f3(f2(x))))) # label(replacement). 25.65/25.94 arrow_s0(f9(x,y),x) # label(replacement). 25.65/25.94 arrow_s0(f9(x,y),y) # label(replacement). 25.65/25.94 -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 25.65/25.94 sqsupset_s0(f8(f3(x)),f7(f4(f3(f2(x))))) # label(replacement). 25.65/25.94 succeq_s0(f7(f4(f4(x))),f8(x)) # label(replacement). 25.65/25.94 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 25.65/25.94 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 25.65/25.94 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 25.65/25.94 end_of_list. 25.65/25.94 25.65/25.94 ============================== end of clauses for search ============= 25.65/25.94 25.65/25.94 % There are no natural numbers in the input. 25.65/25.94 25.65/25.94 ============================== DOMAIN SIZE 2 ========================= 25.65/25.94 25.65/25.94 ============================== STATISTICS ============================ 25.65/25.94 25.65/25.94 For domain size 2. 25.65/25.94 25.65/25.94 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.65/25.94 Ground clauses: seen=96, kept=96. 25.65/25.94 Selections=901, assignments=1802, propagations=2331, current_models=0. 25.65/25.94 Rewrite_terms=19927, rewrite_bools=13012, indexes=3428. 25.65/25.94 Rules_from_neg_clauses=703, cross_offs=703. 25.65/25.94 25.65/25.94 ============================== end of statistics ===================== 25.65/25.94 25.65/25.94 ============================== DOMAIN SIZE 3 ========================= 25.65/25.94 25.65/25.94 ============================== MODEL ================================= 25.65/25.94 25.65/25.94 interpretation( 3, [number=1, seconds=0], [ 25.65/25.94 25.65/25.94 function(f2(_), [ 0, 0, 1 ]), 25.65/25.94 25.65/25.94 function(f3(_), [ 1, 1, 1 ]), 25.65/25.94 25.65/25.94 function(f4(_), [ 0, 2, 1 ]), 25.65/25.94 25.65/25.94 function(f7(_), [ 0, 0, 1 ]), 25.65/25.94 25.65/25.94 function(f8(_), [ 0, 0, 1 ]), 25.65/25.94 25.65/25.94 function(f9(_,_), [ 25.65/25.94 0, 0, 0, 25.65/25.94 0, 0, 0, 25.65/25.94 0, 0, 0 ]), 25.65/25.94 25.65/25.94 relation(arrow_s0(_,_), [ 25.65/25.94 1, 1, 1, 25.65/25.94 0, 1, 0, 25.65/25.94 0, 0, 1 ]), 25.65/25.94 25.65/25.94 relation(gtrsim_s0(_,_), [ 25.65/25.94 1, 1, 1, 25.65/25.94 0, 1, 0, 25.65/25.94 0, 0, 1 ]), 25.65/25.94 25.65/25.94 relation(sqsupsetStar_s0(_,_), [ 25.65/25.94 0, 1, 0, 25.65/25.94 0, 0, 0, 25.65/25.94 0, 0, 0 ]), 25.65/25.94 25.65/25.94 relation(sqsupset_s0(_,_), [ 25.65/25.94 0, 1, 0, 25.65/25.94 0, 0, 0, 25.65/25.94 0, 0, 0 ]), 25.65/25.94 25.65/25.94 relation(succeq_s0(_,_), [ 25.65/25.94 1, 0, 0, 25.65/25.94 0, 1, 0, 25.65/25.94 0, 0, 0 ]) 25.65/25.94 ]). 25.65/25.94 25.65/25.94 ============================== end of model ========================== 25.65/25.94 25.65/25.94 ============================== STATISTICS ============================ 25.65/25.94 25.65/25.94 For domain size 3. 25.65/25.94 25.65/25.94 Current CPU time: 0.00 seconds (total CPU time: 0.02 seconds). 25.65/25.94 Ground clauses: seen=261, kept=261. 25.65/25.94 Selections=2805, assignments=8229, propagations=4087, current_models=1. 25.65/25.94 Rewrite_terms=68933, rewrite_bools=42500, indexes=5190. 25.65/25.94 Rules_from_neg_clauses=1345, cross_offs=3430. 25.65/25.94 25.65/25.94 ============================== end of statistics ===================== 25.65/25.94 25.65/25.94 User_CPU=0.02, System_CPU=0.01, Wall_clock=0. 25.65/25.94 25.65/25.94 Exiting with 1 model. 25.65/25.94 25.65/25.94 Process 35491 exit (max_models) Fri Mar 29 12:52:09 2019 25.65/25.94 The process finished Fri Mar 29 12:52:09 2019 25.65/25.94 25.65/25.94 25.65/25.94 Mace4 cooked interpretation: 25.65/25.94 25.65/25.94 % number = 1 25.65/25.94 % seconds = 0 25.65/25.94 25.65/25.94 % Interpretation of size 3 25.65/25.94 25.65/25.94 f2(0) = 0. 25.65/25.94 f2(1) = 0. 25.65/25.94 f2(2) = 1. 25.65/25.94 25.65/25.94 f3(0) = 1. 25.65/25.94 f3(1) = 1. 25.65/25.94 f3(2) = 1. 25.65/25.94 25.65/25.94 f4(0) = 0. 25.65/25.94 f4(1) = 2. 25.65/25.94 f4(2) = 1. 25.65/25.94 25.65/25.94 f7(0) = 0. 25.65/25.94 f7(1) = 0. 25.65/25.94 f7(2) = 1. 25.65/25.94 25.65/25.94 f8(0) = 0. 25.65/25.94 f8(1) = 0. 25.65/25.94 f8(2) = 1. 25.65/25.94 25.65/25.94 f9(0,0) = 0. 25.65/25.94 f9(0,1) = 0. 25.65/25.94 f9(0,2) = 0. 25.65/25.94 f9(1,0) = 0. 25.65/25.94 f9(1,1) = 0. 25.65/25.94 f9(1,2) = 0. 25.65/25.94 f9(2,0) = 0. 25.65/25.94 f9(2,1) = 0. 25.65/25.94 f9(2,2) = 0. 25.65/25.94 25.65/25.94 arrow_s0(0,0). 25.65/25.94 arrow_s0(0,1). 25.65/25.94 arrow_s0(0,2). 25.65/25.94 - arrow_s0(1,0). 25.65/25.94 arrow_s0(1,1). 25.65/25.94 - arrow_s0(1,2). 25.65/25.94 - arrow_s0(2,0). 25.65/25.94 - arrow_s0(2,1). 25.65/25.94 arrow_s0(2,2). 25.65/25.94 25.65/25.94 gtrsim_s0(0,0). 25.65/25.94 gtrsim_s0(0,1). 25.65/25.94 gtrsim_s0(0,2). 25.65/25.94 - gtrsim_s0(1,0). 25.65/25.94 gtrsim_s0(1,1). 25.65/25.94 - gtrsim_s0(1,2). 25.65/25.94 - gtrsim_s0(2,0). 25.65/25.94 - gtrsim_s0(2,1). 25.65/25.94 gtrsim_s0(2,2). 25.65/25.94 25.65/25.94 - sqsupsetStar_s0(0,0). 25.65/25.94 sqsupsetStar_s0(0,1). 25.65/25.94 - sqsupsetStar_s0(0,2). 25.65/25.94 - sqsupsetStar_s0(1,0). 25.65/25.94 - sqsupsetStar_s0(1,1). 25.65/25.94 - sqsupsetStar_s0(1,2). 25.65/25.94 - sqsupsetStar_s0(2,0). 25.65/25.94 - sqsupsetStar_s0(2,1). 25.65/25.94 - sqsupsetStar_s0(2,2). 25.65/25.94 25.65/25.94 - sqsupset_s0(0,0). 25.65/25.94 sqsupset_s0(0,1). 25.65/25.94 - sqsupset_s0(0,2). 25.65/25.94 - sqsupset_s0(1,0). 25.65/25.94 - sqsupset_s0(1,1). 25.65/25.94 - sqsupset_s0(1,2). 25.65/25.94 - sqsupset_s0(2,0). 25.65/25.94 - sqsupset_s0(2,1). 25.65/25.94 - sqsupset_s0(2,2). 25.65/25.94 25.65/25.94 succeq_s0(0,0). 25.65/25.94 - succeq_s0(0,1). 25.65/25.94 - succeq_s0(0,2). 25.65/25.94 - succeq_s0(1,0). 25.65/25.94 succeq_s0(1,1). 25.65/25.94 - succeq_s0(1,2). 25.65/25.94 - succeq_s0(2,0). 25.65/25.94 - succeq_s0(2,1). 25.65/25.94 - succeq_s0(2,2). 25.65/25.94 25.65/25.94 25.65/25.94 Problem 1: 25.65/25.94 25.65/25.94 SCC Processor: 25.65/25.94 -> Pairs: 25.65/25.94 A(b(b(x1:S))) -> C(x1:S) 25.65/25.94 -> Rules: 25.65/25.94 a(b(b(x1:S))) -> c(x1:S) 25.65/25.94 a(x1:S) -> b(x1:S) 25.65/25.94 c(c(x1:S)) -> a(b(c(a(x1:S)))) 25.65/25.94 ->Strongly Connected Components: 25.65/25.94 There is no strongly connected component 25.65/25.94 25.65/25.94 The problem is finite. 25.65/25.94 EOF