91.58/92.63 YES 91.58/92.63 91.58/92.63 Problem 1: 91.58/92.63 91.58/92.63 (VAR v_NonEmpty:S X:S) 91.58/92.63 (RULES 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ) 91.58/92.63 (STRATEGY INNERMOST) 91.58/92.63 91.58/92.63 Problem 1: 91.58/92.63 91.58/92.63 Dependency Pairs Processor: 91.58/92.63 -> Pairs: 91.58/92.63 ACTIVE(g(X:S)) -> ACTIVE(X:S) 91.58/92.63 ACTIVE(g(X:S)) -> G(active(X:S)) 91.58/92.63 F(ok(X:S)) -> F(X:S) 91.58/92.63 G(mark(X:S)) -> G(X:S) 91.58/92.63 G(ok(X:S)) -> G(X:S) 91.58/92.63 PROPER(f(X:S)) -> F(proper(X:S)) 91.58/92.63 PROPER(f(X:S)) -> PROPER(X:S) 91.58/92.63 PROPER(g(X:S)) -> G(proper(X:S)) 91.58/92.63 PROPER(g(X:S)) -> PROPER(X:S) 91.58/92.63 TOP(mark(X:S)) -> PROPER(X:S) 91.58/92.63 TOP(mark(X:S)) -> TOP(proper(X:S)) 91.58/92.63 TOP(ok(X:S)) -> ACTIVE(X:S) 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 91.58/92.63 Problem 1: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 ACTIVE(g(X:S)) -> ACTIVE(X:S) 91.58/92.63 ACTIVE(g(X:S)) -> G(active(X:S)) 91.58/92.63 F(ok(X:S)) -> F(X:S) 91.58/92.63 G(mark(X:S)) -> G(X:S) 91.58/92.63 G(ok(X:S)) -> G(X:S) 91.58/92.63 PROPER(f(X:S)) -> F(proper(X:S)) 91.58/92.63 PROPER(f(X:S)) -> PROPER(X:S) 91.58/92.63 PROPER(g(X:S)) -> G(proper(X:S)) 91.58/92.63 PROPER(g(X:S)) -> PROPER(X:S) 91.58/92.63 TOP(mark(X:S)) -> PROPER(X:S) 91.58/92.63 TOP(mark(X:S)) -> TOP(proper(X:S)) 91.58/92.63 TOP(ok(X:S)) -> ACTIVE(X:S) 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 G(mark(X:S)) -> G(X:S) 91.58/92.63 G(ok(X:S)) -> G(X:S) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 F(ok(X:S)) -> F(X:S) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 PROPER(f(X:S)) -> PROPER(X:S) 91.58/92.63 PROPER(g(X:S)) -> PROPER(X:S) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 ACTIVE(g(X:S)) -> ACTIVE(X:S) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 TOP(mark(X:S)) -> TOP(proper(X:S)) 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 91.58/92.63 91.58/92.63 The problem is decomposed in 5 subproblems. 91.58/92.63 91.58/92.63 Problem 1.1: 91.58/92.63 91.58/92.63 Subterm Processor: 91.58/92.63 -> Pairs: 91.58/92.63 G(mark(X:S)) -> G(X:S) 91.58/92.63 G(ok(X:S)) -> G(X:S) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Projection: 91.58/92.63 pi(G) = 1 91.58/92.63 91.58/92.63 Problem 1.1: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 Empty 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 There is no strongly connected component 91.58/92.63 91.58/92.63 The problem is finite. 91.58/92.63 91.58/92.63 Problem 1.2: 91.58/92.63 91.58/92.63 Subterm Processor: 91.58/92.63 -> Pairs: 91.58/92.63 F(ok(X:S)) -> F(X:S) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Projection: 91.58/92.63 pi(F) = 1 91.58/92.63 91.58/92.63 Problem 1.2: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 Empty 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 There is no strongly connected component 91.58/92.63 91.58/92.63 The problem is finite. 91.58/92.63 91.58/92.63 Problem 1.3: 91.58/92.63 91.58/92.63 Subterm Processor: 91.58/92.63 -> Pairs: 91.58/92.63 PROPER(f(X:S)) -> PROPER(X:S) 91.58/92.63 PROPER(g(X:S)) -> PROPER(X:S) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Projection: 91.58/92.63 pi(PROPER) = 1 91.58/92.63 91.58/92.63 Problem 1.3: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 Empty 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 There is no strongly connected component 91.58/92.63 91.58/92.63 The problem is finite. 91.58/92.63 91.58/92.63 Problem 1.4: 91.58/92.63 91.58/92.63 Subterm Processor: 91.58/92.63 -> Pairs: 91.58/92.63 ACTIVE(g(X:S)) -> ACTIVE(X:S) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Projection: 91.58/92.63 pi(ACTIVE) = 1 91.58/92.63 91.58/92.63 Problem 1.4: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 Empty 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 There is no strongly connected component 91.58/92.63 91.58/92.63 The problem is finite. 91.58/92.63 91.58/92.63 Problem 1.5: 91.58/92.63 91.58/92.63 Reduction Pairs Processor: 91.58/92.63 -> Pairs: 91.58/92.63 TOP(mark(X:S)) -> TOP(proper(X:S)) 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 -> Usable rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 ->Interpretation type: 91.58/92.63 Linear 91.58/92.63 ->Coefficients: 91.58/92.63 Natural Numbers 91.58/92.63 ->Dimension: 91.58/92.63 2 91.58/92.63 ->Bound: 91.58/92.63 1 91.58/92.63 ->Interpretation: 91.58/92.63 91.58/92.63 [active](X) = [1 1;0 1].X + [1;0] 91.58/92.63 [f](X) = [0 1;1 1].X + [1;1] 91.58/92.63 [g](X) = [0 0;0 1].X + [1;0] 91.58/92.63 [proper](X) = [1 0;0 1].X 91.58/92.63 [top](X) = 0 91.58/92.63 [a] = [1;1] 91.58/92.63 [fSNonEmpty] = 0 91.58/92.63 [mark](X) = [0 0;0 1].X + [1;1] 91.58/92.63 [ok](X) = [1 0;0 1].X 91.58/92.63 [ACTIVE](X) = 0 91.58/92.63 [F](X) = 0 91.58/92.63 [G](X) = 0 91.58/92.63 [PROPER](X) = 0 91.58/92.63 [TOP](X) = [0 1;0 1].X 91.58/92.63 91.58/92.63 Problem 1.5: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 ->->Cycle: 91.58/92.63 ->->-> Pairs: 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 ->->-> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 91.58/92.63 Problem 1.5: 91.58/92.63 91.58/92.63 Reduction Pairs Processor: 91.58/92.63 -> Pairs: 91.58/92.63 TOP(ok(X:S)) -> TOP(active(X:S)) 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 -> Usable rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 ->Interpretation type: 91.58/92.63 Linear 91.58/92.63 ->Coefficients: 91.58/92.63 Natural Numbers 91.58/92.63 ->Dimension: 91.58/92.63 1 91.58/92.63 ->Bound: 91.58/92.63 2 91.58/92.63 ->Interpretation: 91.58/92.63 91.58/92.63 [active](X) = X 91.58/92.63 [f](X) = X + 1 91.58/92.63 [g](X) = 2.X 91.58/92.63 [proper](X) = 0 91.58/92.63 [top](X) = 0 91.58/92.63 [a] = 2 91.58/92.63 [fSNonEmpty] = 0 91.58/92.63 [mark](X) = 2 91.58/92.63 [ok](X) = X + 2 91.58/92.63 [ACTIVE](X) = 0 91.58/92.63 [F](X) = 0 91.58/92.63 [G](X) = 0 91.58/92.63 [PROPER](X) = 0 91.58/92.63 [TOP](X) = 2.X 91.58/92.63 91.58/92.63 Problem 1.5: 91.58/92.63 91.58/92.63 SCC Processor: 91.58/92.63 -> Pairs: 91.58/92.63 Empty 91.58/92.63 -> Rules: 91.58/92.63 active(f(f(a))) -> mark(f(g(f(a)))) 91.58/92.63 active(g(X:S)) -> g(active(X:S)) 91.58/92.63 f(ok(X:S)) -> ok(f(X:S)) 91.58/92.63 g(mark(X:S)) -> mark(g(X:S)) 91.58/92.63 g(ok(X:S)) -> ok(g(X:S)) 91.58/92.63 proper(f(X:S)) -> f(proper(X:S)) 91.58/92.63 proper(g(X:S)) -> g(proper(X:S)) 91.58/92.63 proper(a) -> ok(a) 91.58/92.63 top(mark(X:S)) -> top(proper(X:S)) 91.58/92.63 top(ok(X:S)) -> top(active(X:S)) 91.58/92.63 ->Strongly Connected Components: 91.58/92.63 There is no strongly connected component 91.58/92.63 91.58/92.63 The problem is finite. 91.58/137.69 EOF