0.00/0.05 YES 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 (VAR v_NonEmpty:S X:S) 0.00/0.05 (RULES 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ) 0.00/0.05 (STRATEGY INNERMOST) 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 Dependency Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 ACTIVE(f(f(a))) -> MARK(f(g(f(a)))) 0.00/0.05 F(active(X:S)) -> F(X:S) 0.00/0.05 F(mark(X:S)) -> F(X:S) 0.00/0.05 G(active(X:S)) -> G(X:S) 0.00/0.05 G(mark(X:S)) -> G(X:S) 0.00/0.05 MARK(f(X:S)) -> ACTIVE(f(X:S)) 0.00/0.05 MARK(g(X:S)) -> ACTIVE(g(mark(X:S))) 0.00/0.05 MARK(g(X:S)) -> G(mark(X:S)) 0.00/0.05 MARK(g(X:S)) -> MARK(X:S) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 ACTIVE(f(f(a))) -> MARK(f(g(f(a)))) 0.00/0.05 F(active(X:S)) -> F(X:S) 0.00/0.05 F(mark(X:S)) -> F(X:S) 0.00/0.05 G(active(X:S)) -> G(X:S) 0.00/0.05 G(mark(X:S)) -> G(X:S) 0.00/0.05 MARK(f(X:S)) -> ACTIVE(f(X:S)) 0.00/0.05 MARK(g(X:S)) -> ACTIVE(g(mark(X:S))) 0.00/0.05 MARK(g(X:S)) -> G(mark(X:S)) 0.00/0.05 MARK(g(X:S)) -> MARK(X:S) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 G(active(X:S)) -> G(X:S) 0.00/0.05 G(mark(X:S)) -> G(X:S) 0.00/0.05 ->->-> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 F(active(X:S)) -> F(X:S) 0.00/0.05 F(mark(X:S)) -> F(X:S) 0.00/0.05 ->->-> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 ACTIVE(f(f(a))) -> MARK(f(g(f(a)))) 0.00/0.05 MARK(f(X:S)) -> ACTIVE(f(X:S)) 0.00/0.05 ->->-> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 MARK(g(X:S)) -> MARK(X:S) 0.00/0.05 ->->-> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 0.00/0.05 0.00/0.05 The problem is decomposed in 4 subproblems. 0.00/0.05 0.00/0.05 Problem 1.1: 0.00/0.05 0.00/0.05 Subterm Processor: 0.00/0.05 -> Pairs: 0.00/0.05 G(active(X:S)) -> G(X:S) 0.00/0.05 G(mark(X:S)) -> G(X:S) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Projection: 0.00/0.05 pi(G) = 1 0.00/0.05 0.00/0.05 Problem 1.1: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 0.00/0.05 Problem 1.2: 0.00/0.05 0.00/0.05 Subterm Processor: 0.00/0.05 -> Pairs: 0.00/0.05 F(active(X:S)) -> F(X:S) 0.00/0.05 F(mark(X:S)) -> F(X:S) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Projection: 0.00/0.05 pi(F) = 1 0.00/0.05 0.00/0.05 Problem 1.2: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 0.00/0.05 Problem 1.3: 0.00/0.05 0.00/0.05 Reduction Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 ACTIVE(f(f(a))) -> MARK(f(g(f(a)))) 0.00/0.05 MARK(f(X:S)) -> ACTIVE(f(X:S)) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 -> Usable rules: 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 ->Interpretation type: 0.00/0.05 Linear 0.00/0.05 ->Coefficients: 0.00/0.05 Natural Numbers 0.00/0.05 ->Dimension: 0.00/0.05 1 0.00/0.05 ->Bound: 0.00/0.05 2 0.00/0.05 ->Interpretation: 0.00/0.05 0.00/0.05 [active](X) = 2.X 0.00/0.05 [f](X) = 2.X + 2 0.00/0.05 [g](X) = 2 0.00/0.05 [mark](X) = 2.X 0.00/0.05 [a] = 2 0.00/0.05 [fSNonEmpty] = 0 0.00/0.05 [ACTIVE](X) = 2.X + 2 0.00/0.05 [F](X) = 0 0.00/0.05 [G](X) = 0 0.00/0.05 [MARK](X) = 2.X + 2 0.00/0.05 0.00/0.05 Problem 1.3: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 MARK(f(X:S)) -> ACTIVE(f(X:S)) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 0.00/0.05 Problem 1.4: 0.00/0.05 0.00/0.05 Subterm Processor: 0.00/0.05 -> Pairs: 0.00/0.05 MARK(g(X:S)) -> MARK(X:S) 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Projection: 0.00/0.05 pi(MARK) = 1 0.00/0.05 0.00/0.05 Problem 1.4: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 active(f(f(a))) -> mark(f(g(f(a)))) 0.00/0.05 f(active(X:S)) -> f(X:S) 0.00/0.05 f(mark(X:S)) -> f(X:S) 0.00/0.05 g(active(X:S)) -> g(X:S) 0.00/0.05 g(mark(X:S)) -> g(X:S) 0.00/0.05 mark(f(X:S)) -> active(f(X:S)) 0.00/0.05 mark(g(X:S)) -> active(g(mark(X:S))) 0.00/0.05 mark(a) -> active(a) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 EOF