0.00/0.19 YES 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 (VAR v_NonEmpty:S x1:S) 0.00/0.19 (RULES 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Dependency Pairs Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> A(x1:S) 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> A(x1:S) 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 A(b(b(x1:S))) -> A(x1:S) 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 ->->-> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Reduction Pair Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> A(x1:S) 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 -> Usable rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ->Interpretation type: 0.00/0.19 Linear 0.00/0.19 ->Coefficients: 0.00/0.19 Natural Numbers 0.00/0.19 ->Dimension: 0.00/0.19 1 0.00/0.19 ->Bound: 0.00/0.19 2 0.00/0.19 ->Interpretation: 0.00/0.19 0.00/0.19 [a](X) = X + 2 0.00/0.19 [b](X) = X + 1 0.00/0.19 [c](X) = X 0.00/0.19 [A](X) = 2.X + 2 0.00/0.19 [B](X) = 2.X 0.00/0.19 [C](X) = 2.X + 2 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 ->->-> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Reduction Pair Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> B(b(c(c(c(a(x1:S)))))) 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 -> Usable rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ->Interpretation type: 0.00/0.19 Linear 0.00/0.19 ->Coefficients: 0.00/0.19 Natural Numbers 0.00/0.19 ->Dimension: 0.00/0.19 1 0.00/0.19 ->Bound: 0.00/0.19 2 0.00/0.19 ->Interpretation: 0.00/0.19 0.00/0.19 [a](X) = X + 2 0.00/0.19 [b](X) = X + 1 0.00/0.19 [c](X) = X 0.00/0.19 [A](X) = X + 2 0.00/0.19 [B](X) = X 0.00/0.19 [C](X) = X 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.19 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.19 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.19 A(x1:S) -> B(b(x1:S)) 0.00/0.19 A(x1:S) -> B(x1:S) 0.00/0.19 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.19 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.19 B(b(x1:S)) -> C(x1:S) 0.00/0.19 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.19 -> Rules: 0.00/0.19 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.19 a(x1:S) -> b(b(x1:S)) 0.00/0.19 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.19 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.19 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> B(c(c(c(a(x1:S))))) 0.00/0.20 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = X + 2 0.00/0.20 [B](X) = X + 1 0.00/0.20 [C](X) = X + 1 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(a(x1:S)) 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = 2.X + 2 0.00/0.20 [B](X) = 2.X 0.00/0.20 [C](X) = 2.X + 1 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(a(x1:S))) 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = 2.X + 2 0.00/0.20 [B](X) = 2.X 0.00/0.20 [C](X) = 2.X + 1 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(b(b(x1:S))) -> C(c(c(a(x1:S)))) 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = X + 2 0.00/0.20 [B](X) = X + 1 0.00/0.20 [C](X) = X + 1 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(x1:S) -> B(b(x1:S)) 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = X + 2 0.00/0.20 [B](X) = X 0.00/0.20 [C](X) = X 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Pair Processor: 0.00/0.20 -> Pairs: 0.00/0.20 A(x1:S) -> B(x1:S) 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 -> Usable rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [a](X) = X + 2 0.00/0.20 [b](X) = X + 1 0.00/0.20 [c](X) = X 0.00/0.20 [A](X) = 2.X + 2 0.00/0.20 [B](X) = 2.X + 1 0.00/0.20 [C](X) = 2.X + 2 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 B(b(x1:S)) -> C(c(c(x1:S))) 0.00/0.20 B(b(x1:S)) -> C(c(x1:S)) 0.00/0.20 B(b(x1:S)) -> C(x1:S) 0.00/0.20 C(c(c(b(b(x1:S))))) -> A(x1:S) 0.00/0.20 -> Rules: 0.00/0.20 a(b(b(x1:S))) -> b(b(c(c(c(a(x1:S)))))) 0.00/0.20 a(x1:S) -> b(b(x1:S)) 0.00/0.20 b(b(x1:S)) -> c(c(c(x1:S))) 0.00/0.20 c(c(c(b(b(x1:S))))) -> a(x1:S) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 EOF