0.00/0.04 YES 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 (VAR v_NonEmpty:S X:S) 0.00/0.04 (RULES 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ) 0.00/0.04 (STRATEGY INNERMOST) 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 Dependency Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 ACTIVE(g(X:S)) -> H(X:S) 0.00/0.04 ACTIVE(g(X:S)) -> MARK(h(X:S)) 0.00/0.04 ACTIVE(h(d)) -> MARK(g(c)) 0.00/0.04 ACTIVE(c) -> MARK(d) 0.00/0.04 G(active(X:S)) -> G(X:S) 0.00/0.04 G(mark(X:S)) -> G(X:S) 0.00/0.04 H(active(X:S)) -> H(X:S) 0.00/0.04 H(mark(X:S)) -> H(X:S) 0.00/0.04 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.04 MARK(h(X:S)) -> ACTIVE(h(X:S)) 0.00/0.04 MARK(c) -> ACTIVE(c) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 ACTIVE(g(X:S)) -> H(X:S) 0.00/0.04 ACTIVE(g(X:S)) -> MARK(h(X:S)) 0.00/0.04 ACTIVE(h(d)) -> MARK(g(c)) 0.00/0.04 ACTIVE(c) -> MARK(d) 0.00/0.04 G(active(X:S)) -> G(X:S) 0.00/0.04 G(mark(X:S)) -> G(X:S) 0.00/0.04 H(active(X:S)) -> H(X:S) 0.00/0.04 H(mark(X:S)) -> H(X:S) 0.00/0.04 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.04 MARK(h(X:S)) -> ACTIVE(h(X:S)) 0.00/0.04 MARK(c) -> ACTIVE(c) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 H(active(X:S)) -> H(X:S) 0.00/0.04 H(mark(X:S)) -> H(X:S) 0.00/0.04 ->->-> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 G(active(X:S)) -> G(X:S) 0.00/0.04 G(mark(X:S)) -> G(X:S) 0.00/0.04 ->->-> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 ACTIVE(g(X:S)) -> MARK(h(X:S)) 0.00/0.04 ACTIVE(h(d)) -> MARK(g(c)) 0.00/0.04 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.04 MARK(h(X:S)) -> ACTIVE(h(X:S)) 0.00/0.04 ->->-> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 0.00/0.04 0.00/0.04 The problem is decomposed in 3 subproblems. 0.00/0.04 0.00/0.04 Problem 1.1: 0.00/0.04 0.00/0.04 Subterm Processor: 0.00/0.04 -> Pairs: 0.00/0.04 H(active(X:S)) -> H(X:S) 0.00/0.04 H(mark(X:S)) -> H(X:S) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Projection: 0.00/0.04 pi(H) = 1 0.00/0.04 0.00/0.04 Problem 1.1: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 Empty 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 There is no strongly connected component 0.00/0.04 0.00/0.04 The problem is finite. 0.00/0.04 0.00/0.04 Problem 1.2: 0.00/0.04 0.00/0.04 Subterm Processor: 0.00/0.04 -> Pairs: 0.00/0.04 G(active(X:S)) -> G(X:S) 0.00/0.04 G(mark(X:S)) -> G(X:S) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Projection: 0.00/0.04 pi(G) = 1 0.00/0.04 0.00/0.04 Problem 1.2: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 Empty 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 There is no strongly connected component 0.00/0.04 0.00/0.04 The problem is finite. 0.00/0.04 0.00/0.04 Problem 1.3: 0.00/0.04 0.00/0.04 Reduction Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 ACTIVE(g(X:S)) -> MARK(h(X:S)) 0.00/0.04 ACTIVE(h(d)) -> MARK(g(c)) 0.00/0.04 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.04 MARK(h(X:S)) -> ACTIVE(h(X:S)) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 -> Usable rules: 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 ->Interpretation type: 0.00/0.04 Linear 0.00/0.04 ->Coefficients: 0.00/0.04 Natural Numbers 0.00/0.04 ->Dimension: 0.00/0.04 1 0.00/0.04 ->Bound: 0.00/0.04 2 0.00/0.04 ->Interpretation: 0.00/0.04 0.00/0.04 [active](X) = 2.X 0.00/0.04 [g](X) = 2.X + 2 0.00/0.04 [h](X) = 2.X + 1 0.00/0.04 [mark](X) = 2.X 0.00/0.04 [c] = 1 0.00/0.04 [d] = 2 0.00/0.04 [fSNonEmpty] = 0 0.00/0.04 [ACTIVE](X) = 2.X + 2 0.00/0.04 [G](X) = 0 0.00/0.04 [H](X) = 0 0.00/0.04 [MARK](X) = 2.X + 2 0.00/0.04 0.00/0.04 Problem 1.3: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 ACTIVE(h(d)) -> MARK(g(c)) 0.00/0.04 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.04 MARK(h(X:S)) -> ACTIVE(h(X:S)) 0.00/0.04 -> Rules: 0.00/0.04 active(g(X:S)) -> mark(h(X:S)) 0.00/0.04 active(h(d)) -> mark(g(c)) 0.00/0.04 active(c) -> mark(d) 0.00/0.04 g(active(X:S)) -> g(X:S) 0.00/0.04 g(mark(X:S)) -> g(X:S) 0.00/0.04 h(active(X:S)) -> h(X:S) 0.00/0.04 h(mark(X:S)) -> h(X:S) 0.00/0.04 mark(g(X:S)) -> active(g(X:S)) 0.00/0.04 mark(h(X:S)) -> active(h(X:S)) 0.00/0.04 mark(c) -> active(c) 0.00/0.04 mark(d) -> active(d) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 There is no strongly connected component 0.00/0.04 0.00/0.04 The problem is finite. 0.00/0.04 EOF