0.00/0.19 YES 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 (VAR v_NonEmpty:S X:S Y:S) 0.00/0.19 (RULES 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ) 0.00/0.19 (STRATEGY INNERMOST) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Dependency Pairs Processor: 0.00/0.19 -> Pairs: 0.00/0.19 +#(X:S,s(Y:S)) -> +#(X:S,Y:S) 0.00/0.19 DOUBLE(X:S) -> +#(X:S,X:S) 0.00/0.19 F(0,s(0),X:S) -> DOUBLE(X:S) 0.00/0.19 F(0,s(0),X:S) -> F(X:S,double(X:S),X:S) 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 +#(X:S,s(Y:S)) -> +#(X:S,Y:S) 0.00/0.19 DOUBLE(X:S) -> +#(X:S,X:S) 0.00/0.19 F(0,s(0),X:S) -> DOUBLE(X:S) 0.00/0.19 F(0,s(0),X:S) -> F(X:S,double(X:S),X:S) 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 +#(X:S,s(Y:S)) -> +#(X:S,Y:S) 0.00/0.19 ->->-> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 F(0,s(0),X:S) -> F(X:S,double(X:S),X:S) 0.00/0.19 ->->-> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 0.00/0.19 0.00/0.19 The problem is decomposed in 2 subproblems. 0.00/0.19 0.00/0.19 Problem 1.1: 0.00/0.19 0.00/0.19 Subterm Processor: 0.00/0.19 -> Pairs: 0.00/0.19 +#(X:S,s(Y:S)) -> +#(X:S,Y:S) 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ->Projection: 0.00/0.19 pi(+#) = 2 0.00/0.19 0.00/0.19 Problem 1.1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 Empty 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 There is no strongly connected component 0.00/0.19 0.00/0.19 The problem is finite. 0.00/0.19 0.00/0.19 Problem 1.2: 0.00/0.19 0.00/0.19 Reduction Pair Processor: 0.00/0.19 -> Pairs: 0.00/0.19 F(0,s(0),X:S) -> F(X:S,double(X:S),X:S) 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 -> Usable rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 ->Mace4 Output: 0.00/0.19 ============================== Mace4 ================================= 0.00/0.19 Mace4 (64) version 2009-11A, November 2009. 0.00/0.19 Process 23999 was started by sandbox on n171.star.cs.uiowa.edu, 0.00/0.19 Thu Mar 28 22:18:57 2019 0.00/0.19 The command was "./mace4 -c -f /tmp/mace4336465782861021530.in". 0.00/0.19 ============================== end of head =========================== 0.00/0.19 0.00/0.19 ============================== INPUT ================================= 0.00/0.19 0.00/0.19 % Reading from file /tmp/mace4336465782861021530.in 0.00/0.19 0.00/0.19 assign(max_seconds,20). 0.00/0.19 0.00/0.19 formulas(assumptions). 0.00/0.19 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2,x3),f4(y,x2,x3)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2,x3),f4(x1,y,x3)) # label(congruence). 0.00/0.19 arrow_s0(x3,y) -> arrow_s0(f4(x1,x2,x3),f4(x1,x2,y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f5(x1,x2),f5(y,x2)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f5(x1,x2),f5(x1,y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f11(x1),f11(y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f12(x1,x2,x3),f12(y,x2,x3)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f12(x1,x2,x3),f12(x1,y,x3)) # label(congruence). 0.00/0.19 arrow_s0(x3,y) -> arrow_s0(f12(x1,x2,x3),f12(x1,x2,y)) # label(congruence). 0.00/0.19 arrow_s0(f2(x1,f6),x1) # label(replacement). 0.00/0.19 arrow_s0(f2(x1,f8(x2)),f8(f2(x1,x2))) # label(replacement). 0.00/0.19 arrow_s0(f3(x1),f2(x1,x1)) # label(replacement). 0.00/0.19 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(f12(f6,f8(f6),x1),f12(x1,f3(x1),x1)) # label(replacement). 0.00/0.19 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 formulas(goals). 0.00/0.19 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 ============================== end of input ========================== 0.00/0.19 0.00/0.19 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.19 0.00/0.19 % Formulas that are not ordinary clauses: 0.00/0.19 1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 4 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 5 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 7 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2,x3),f4(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 8 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2,x3),f4(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 9 arrow_s0(x3,y) -> arrow_s0(f4(x1,x2,x3),f4(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 10 arrow_s0(x1,y) -> arrow_s0(f5(x1,x2),f5(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 11 arrow_s0(x2,y) -> arrow_s0(f5(x1,x2),f5(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 12 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 13 arrow_s0(x1,y) -> arrow_s0(f10(x1,x2),f10(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 14 arrow_s0(x2,y) -> arrow_s0(f10(x1,x2),f10(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 15 arrow_s0(x1,y) -> arrow_s0(f11(x1),f11(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 16 arrow_s0(x1,y) -> arrow_s0(f12(x1,x2,x3),f12(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 17 arrow_s0(x2,y) -> arrow_s0(f12(x1,x2,x3),f12(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 18 arrow_s0(x3,y) -> arrow_s0(f12(x1,x2,x3),f12(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 19 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.19 20 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.19 21 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 22 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.19 0.00/0.19 ============================== end of process non-clausal formulas === 0.00/0.19 0.00/0.19 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.19 0.00/0.19 formulas(mace4_clauses). 0.00/0.19 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f2(x,z),f2(y,z)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f2(z,x),f2(z,y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f4(x,z,u),f4(y,z,u)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f4(z,x,u),f4(z,y,u)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f4(z,u,x),f4(z,u,y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f5(x,z),f5(y,z)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f5(z,x),f5(z,y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f10(x,z),f10(y,z)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f10(z,x),f10(z,y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f11(x),f11(y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f12(x,z,u),f12(y,z,u)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f12(z,x,u),f12(z,y,u)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f12(z,u,x),f12(z,u,y)) # label(congruence). 0.00/0.19 arrow_s0(f2(x,f6),x) # label(replacement). 0.00/0.19 arrow_s0(f2(x,f8(y)),f8(f2(x,y))) # label(replacement). 0.00/0.19 arrow_s0(f3(x),f2(x,x)) # label(replacement). 0.00/0.19 -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(f12(f6,f8(f6),x),f12(x,f3(x),x)) # label(replacement). 0.00/0.19 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.19 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.19 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 ============================== end of clauses for search ============= 0.00/0.19 0.00/0.19 % There are no natural numbers in the input. 0.00/0.19 0.00/0.19 ============================== DOMAIN SIZE 2 ========================= 0.00/0.19 0.00/0.19 ============================== MODEL ================================= 0.00/0.19 0.00/0.19 interpretation( 2, [number=1, seconds=0], [ 0.00/0.19 0.00/0.19 function(f6, [ 0 ]), 0.00/0.19 0.00/0.19 function(f11(_), [ 0, 0 ]), 0.00/0.19 0.00/0.19 function(f3(_), [ 0, 0 ]), 0.00/0.19 0.00/0.19 function(f8(_), [ 1, 0 ]), 0.00/0.19 0.00/0.19 function(f10(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 function(f2(_,_), [ 0.00/0.19 0, 1, 0.00/0.19 1, 0 ]), 0.00/0.19 0.00/0.19 function(f5(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 function(f12(_,_,_), [ 0.00/0.19 0, 0, 0.00/0.19 1, 1, 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 function(f4(_,_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0, 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 relation(arrow_s0(_,_), [ 0.00/0.19 1, 0, 0.00/0.19 0, 1 ]), 0.00/0.19 0.00/0.19 relation(gtrsim_s0(_,_), [ 0.00/0.19 1, 0, 0.00/0.19 0, 1 ]), 0.00/0.19 0.00/0.19 relation(sqsupsetStar_s0(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 1, 0 ]), 0.00/0.19 0.00/0.19 relation(sqsupset_s0(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 1, 0 ]), 0.00/0.19 0.00/0.19 relation(succeq_s0(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]) 0.00/0.19 ]). 0.00/0.19 0.00/0.19 ============================== end of model ========================== 0.00/0.19 0.00/0.19 ============================== STATISTICS ============================ 0.00/0.19 0.00/0.19 For domain size 2. 0.00/0.19 0.00/0.19 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.19 Ground clauses: seen=208, kept=208. 0.00/0.19 Selections=47, assignments=64, propagations=44, current_models=1. 0.00/0.19 Rewrite_terms=531, rewrite_bools=748, indexes=53. 0.00/0.19 Rules_from_neg_clauses=7, cross_offs=7. 0.00/0.19 0.00/0.19 ============================== end of statistics ===================== 0.00/0.19 0.00/0.19 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.00/0.19 0.00/0.19 Exiting with 1 model. 0.00/0.19 0.00/0.19 Process 23999 exit (max_models) Thu Mar 28 22:18:57 2019 0.00/0.19 The process finished Thu Mar 28 22:18:57 2019 0.00/0.19 0.00/0.19 0.00/0.19 Mace4 cooked interpretation: 0.00/0.19 0.00/0.19 % number = 1 0.00/0.19 % seconds = 0 0.00/0.19 0.00/0.19 % Interpretation of size 2 0.00/0.19 0.00/0.19 f6 = 0. 0.00/0.19 0.00/0.19 f11(0) = 0. 0.00/0.19 f11(1) = 0. 0.00/0.19 0.00/0.19 f3(0) = 0. 0.00/0.19 f3(1) = 0. 0.00/0.19 0.00/0.19 f8(0) = 1. 0.00/0.19 f8(1) = 0. 0.00/0.19 0.00/0.19 f10(0,0) = 0. 0.00/0.19 f10(0,1) = 0. 0.00/0.19 f10(1,0) = 0. 0.00/0.19 f10(1,1) = 0. 0.00/0.19 0.00/0.19 f2(0,0) = 0. 0.00/0.19 f2(0,1) = 1. 0.00/0.19 f2(1,0) = 1. 0.00/0.19 f2(1,1) = 0. 0.00/0.19 0.00/0.19 f5(0,0) = 0. 0.00/0.19 f5(0,1) = 0. 0.00/0.19 f5(1,0) = 0. 0.00/0.19 f5(1,1) = 0. 0.00/0.19 0.00/0.19 f12(0,0,0) = 0. 0.00/0.19 f12(0,0,1) = 0. 0.00/0.19 f12(0,1,0) = 1. 0.00/0.19 f12(0,1,1) = 1. 0.00/0.19 f12(1,0,0) = 0. 0.00/0.19 f12(1,0,1) = 0. 0.00/0.19 f12(1,1,0) = 0. 0.00/0.19 f12(1,1,1) = 0. 0.00/0.19 0.00/0.19 f4(0,0,0) = 0. 0.00/0.19 f4(0,0,1) = 0. 0.00/0.19 f4(0,1,0) = 0. 0.00/0.19 f4(0,1,1) = 0. 0.00/0.19 f4(1,0,0) = 0. 0.00/0.19 f4(1,0,1) = 0. 0.00/0.19 f4(1,1,0) = 0. 0.00/0.19 f4(1,1,1) = 0. 0.00/0.19 0.00/0.19 arrow_s0(0,0). 0.00/0.19 - arrow_s0(0,1). 0.00/0.19 - arrow_s0(1,0). 0.00/0.19 arrow_s0(1,1). 0.00/0.19 0.00/0.19 gtrsim_s0(0,0). 0.00/0.19 - gtrsim_s0(0,1). 0.00/0.19 - gtrsim_s0(1,0). 0.00/0.19 gtrsim_s0(1,1). 0.00/0.19 0.00/0.19 - sqsupsetStar_s0(0,0). 0.00/0.19 - sqsupsetStar_s0(0,1). 0.00/0.19 sqsupsetStar_s0(1,0). 0.00/0.19 - sqsupsetStar_s0(1,1). 0.00/0.19 0.00/0.19 - sqsupset_s0(0,0). 0.00/0.19 - sqsupset_s0(0,1). 0.00/0.19 sqsupset_s0(1,0). 0.00/0.19 - sqsupset_s0(1,1). 0.00/0.19 0.00/0.19 - succeq_s0(0,0). 0.00/0.19 - succeq_s0(0,1). 0.00/0.19 - succeq_s0(1,0). 0.00/0.19 - succeq_s0(1,1). 0.00/0.19 0.00/0.19 0.00/0.19 Problem 1.2: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 Empty 0.00/0.19 -> Rules: 0.00/0.19 +(X:S,0) -> X:S 0.00/0.19 +(X:S,s(Y:S)) -> s(+(X:S,Y:S)) 0.00/0.19 double(X:S) -> +(X:S,X:S) 0.00/0.19 f(0,s(0),X:S) -> f(X:S,double(X:S),X:S) 0.00/0.19 g(X:S,Y:S) -> X:S 0.00/0.19 g(X:S,Y:S) -> Y:S 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 There is no strongly connected component 0.00/0.19 0.00/0.19 The problem is finite. 0.00/0.19 EOF