0.00/0.02 YES 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 (VAR X) 0.00/0.02 (STRATEGY CONTEXTSENSITIVE 0.00/0.02 (c) 0.00/0.02 (g) 0.00/0.02 (h) 0.00/0.02 (d) 0.00/0.02 ) 0.00/0.02 (RULES 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 ) 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Innermost Equivalent Processor: 0.00/0.02 -> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 -> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination. 0.00/0.02 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Dependency Pairs Processor: 0.00/0.02 -> Pairs: 0.00/0.02 G(X) -> H(X) 0.00/0.02 H(d) -> G(c) 0.00/0.02 -> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 -> Unhiding Rules: 0.00/0.02 Empty 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 SCC Processor: 0.00/0.02 -> Pairs: 0.00/0.02 G(X) -> H(X) 0.00/0.02 H(d) -> G(c) 0.00/0.02 -> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 -> Unhiding rules: 0.00/0.02 Empty 0.00/0.02 ->Strongly Connected Components: 0.00/0.02 ->->Cycle: 0.00/0.02 ->->-> Pairs: 0.00/0.02 G(X) -> H(X) 0.00/0.02 H(d) -> G(c) 0.00/0.02 ->->-> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 ->->-> Unhiding rules: 0.00/0.02 Empty 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Reduction Pairs Processor: 0.00/0.02 -> Pairs: 0.00/0.02 G(X) -> H(X) 0.00/0.02 H(d) -> G(c) 0.00/0.02 -> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 -> Unhiding rules: 0.00/0.02 Empty 0.00/0.02 -> Usable rules: 0.00/0.02 Empty 0.00/0.02 ->Interpretation type: 0.00/0.02 Linear 0.00/0.02 ->Coefficients: 0.00/0.02 Natural Numbers 0.00/0.02 ->Dimension: 0.00/0.02 1 0.00/0.02 ->Bound: 0.00/0.02 2 0.00/0.02 ->Interpretation: 0.00/0.02 0.00/0.02 [c] = 0 0.00/0.02 [d] = 2 0.00/0.02 [G](X) = 2.X + 2 0.00/0.02 [H](X) = 2.X + 1 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 SCC Processor: 0.00/0.02 -> Pairs: 0.00/0.02 H(d) -> G(c) 0.00/0.02 -> Rules: 0.00/0.02 c -> d 0.00/0.02 g(X) -> h(X) 0.00/0.02 h(d) -> g(c) 0.00/0.02 -> Unhiding rules: 0.00/0.02 Empty 0.00/0.02 ->Strongly Connected Components: 0.00/0.02 There is no strongly connected component 0.00/0.02 0.00/0.02 The problem is finite. 0.00/0.03 EOF