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 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> 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 A(s(x1:S)) -> B(p(p(s(s(x1:S))))) 0.00/0.12 A(s(x1:S)) -> P(p(s(s(x1:S)))) 0.00/0.12 A(s(x1:S)) -> P(s(b(p(p(s(s(x1:S))))))) 0.00/0.12 A(s(x1:S)) -> P(s(s(x1:S))) 0.00/0.12 B(s(x1:S)) -> C(p(s(p(s(x1:S))))) 0.00/0.12 B(s(x1:S)) -> P(p(s(s(c(p(s(p(s(x1:S))))))))) 0.00/0.12 B(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.12 B(s(x1:S)) -> P(s(s(c(p(s(p(s(x1:S)))))))) 0.00/0.12 B(s(x1:S)) -> P(s(x1:S)) 0.00/0.12 C(s(x1:S)) -> A(p(s(p(s(x1:S))))) 0.00/0.12 C(s(x1:S)) -> P(s(a(p(s(p(s(x1:S))))))) 0.00/0.12 C(s(x1:S)) -> P(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 C(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.12 C(s(x1:S)) -> P(s(x1:S)) 0.00/0.12 P(p(s(x1:S))) -> P(x1:S) 0.00/0.12 -> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> 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 A(s(x1:S)) -> B(p(p(s(s(x1:S))))) 0.00/0.12 A(s(x1:S)) -> P(p(s(s(x1:S)))) 0.00/0.12 A(s(x1:S)) -> P(s(b(p(p(s(s(x1:S))))))) 0.00/0.12 A(s(x1:S)) -> P(s(s(x1:S))) 0.00/0.12 B(s(x1:S)) -> C(p(s(p(s(x1:S))))) 0.00/0.12 B(s(x1:S)) -> P(p(s(s(c(p(s(p(s(x1:S))))))))) 0.00/0.12 B(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.12 B(s(x1:S)) -> P(s(s(c(p(s(p(s(x1:S)))))))) 0.00/0.12 B(s(x1:S)) -> P(s(x1:S)) 0.00/0.12 C(s(x1:S)) -> A(p(s(p(s(x1:S))))) 0.00/0.12 C(s(x1:S)) -> P(s(a(p(s(p(s(x1:S))))))) 0.00/0.12 C(s(x1:S)) -> P(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 C(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.12 C(s(x1:S)) -> P(s(x1:S)) 0.00/0.12 P(p(s(x1:S))) -> P(x1:S) 0.00/0.12 -> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> x1:S 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 P(p(s(x1:S))) -> P(x1:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> x1:S 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 A(s(x1:S)) -> B(p(p(s(s(x1:S))))) 0.00/0.12 B(s(x1:S)) -> C(p(s(p(s(x1:S))))) 0.00/0.12 C(s(x1:S)) -> A(p(s(p(s(x1:S))))) 0.00/0.12 ->->-> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> x1:S 0.00/0.12 0.00/0.12 0.00/0.12 The problem is decomposed in 2 subproblems. 0.00/0.12 0.00/0.12 Problem 1.1: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 P(p(s(x1:S))) -> P(x1:S) 0.00/0.12 -> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> x1:S 0.00/0.12 ->Projection: 0.00/0.12 pi(P) = 1 0.00/0.12 0.00/0.12 Problem 1.1: 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 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> 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 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 Reduction Pair Processor: 0.00/0.12 -> Pairs: 0.00/0.12 A(s(x1:S)) -> B(p(p(s(s(x1:S))))) 0.00/0.12 B(s(x1:S)) -> C(p(s(p(s(x1:S))))) 0.00/0.12 C(s(x1:S)) -> A(p(s(p(s(x1:S))))) 0.00/0.12 -> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> x1:S 0.00/0.12 -> Usable rules: 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> 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 [p](X) = 1/2.X 0.00/0.12 [s](X) = 2.X + 2 0.00/0.12 [A](X) = 2.X 0.00/0.12 [B](X) = 2.X + 1/2 0.00/0.12 [C](X) = X + 2 0.00/0.12 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 B(s(x1:S)) -> C(p(s(p(s(x1:S))))) 0.00/0.12 C(s(x1:S)) -> A(p(s(p(s(x1:S))))) 0.00/0.12 -> Rules: 0.00/0.12 a(s(x1:S)) -> s(s(s(p(s(b(p(p(s(s(x1:S)))))))))) 0.00/0.12 b(s(x1:S)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1:S)))))))))))) 0.00/0.12 c(s(x1:S)) -> p(s(p(s(a(p(s(p(s(x1:S))))))))) 0.00/0.12 p(p(s(x1:S))) -> p(x1:S) 0.00/0.12 p(s(x1:S)) -> 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