0.00/0.12 YES 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 (VAR v_NonEmpty:S x1:S) 0.00/0.12 (RULES 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 Dependency Pairs Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(b(c(a(x1:S)))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(b(c(a(x1:S)))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(b(c(a(x1:S)))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 ->->-> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 Reduction Pair Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(b(c(a(x1:S)))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 -> Usable rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Interpretation type: 0.00/0.12 Linear 0.00/0.12 ->Coefficients: 0.00/0.12 Natural Numbers 0.00/0.12 ->Dimension: 0.00/0.12 1 0.00/0.12 ->Bound: 0.00/0.12 2 0.00/0.12 ->Interpretation: 0.00/0.12 0.00/0.12 [b](X) = 2.X + 2 0.00/0.12 [a](X) = X 0.00/0.12 [c](X) = 2.X + 2 0.00/0.12 [B](X) = 2.X 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 ->->-> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 Reduction Pair Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(a(x1:S))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 -> Usable rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Interpretation type: 0.00/0.12 Linear 0.00/0.12 ->Coefficients: 0.00/0.12 Natural Numbers 0.00/0.12 ->Dimension: 0.00/0.12 1 0.00/0.12 ->Bound: 0.00/0.12 2 0.00/0.12 ->Interpretation: 0.00/0.12 0.00/0.12 [b](X) = 2.X 0.00/0.12 [a](X) = X 0.00/0.12 [c](X) = X + 2 0.00/0.12 [B](X) = 2.X 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 ->->-> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 Reduction Pair Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(c(a(b(b(c(x1:S)))))) -> B(c(b(b(c(a(x1:S)))))) 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 -> Usable rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Interpretation type: 0.00/0.12 Linear 0.00/0.12 ->Coefficients: 0.00/0.12 All rationals 0.00/0.12 ->Dimension: 0.00/0.12 1 0.00/0.12 ->Bound: 0.00/0.12 2 0.00/0.12 ->Interpretation: 0.00/0.12 0.00/0.12 [b](X) = 1/2.X 0.00/0.12 [a](X) = 1/2.X + 1/2 0.00/0.12 [c](X) = X + 2 0.00/0.12 [B](X) = 2.X 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 b(c(a(b(b(c(x1:S)))))) -> a(b(c(b(b(c(a(x1:S))))))) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 EOF