0.00/0.35 YES 0.00/0.35 0.00/0.35 Problem 1: 0.00/0.35 0.00/0.35 (VAR v_NonEmpty:S x1:S) 0.00/0.35 (RULES 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ) 0.00/0.35 0.00/0.35 Problem 1: 0.00/0.35 0.00/0.35 Dependency Pairs Processor: 0.00/0.35 -> Pairs: 0.00/0.35 I(0(x1:S)) -> P(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 I(0(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 I(0(x1:S)) -> P(s(0(p(s(p(s(x1:S))))))) 0.00/0.35 I(0(x1:S)) -> P(s(x1:S)) 0.00/0.35 I(s(x1:S)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1:S))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(p(p(p(s(s(s(s(x1:S)))))))) 0.00/0.35 I(s(x1:S)) -> P(p(p(s(s(s(s(x1:S))))))) 0.00/0.35 I(s(x1:S)) -> P(p(s(s(s(s(x1:S)))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(p(p(p(s(s(s(s(x1:S)))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(s(s(s(x1:S))))) 0.00/0.35 J(0(x1:S)) -> P(p(s(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 J(0(x1:S)) -> P(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 J(0(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 J(0(x1:S)) -> P(s(s(0(p(s(p(s(x1:S)))))))) 0.00/0.35 J(0(x1:S)) -> P(s(x1:S)) 0.00/0.35 J(s(x1:S)) -> I(p(s(p(s(x1:S))))) 0.00/0.35 J(s(x1:S)) -> P(p(s(s(i(p(s(p(s(x1:S))))))))) 0.00/0.35 J(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 J(s(x1:S)) -> P(s(s(i(p(s(p(s(x1:S)))))))) 0.00/0.35 J(s(x1:S)) -> P(s(x1:S)) 0.00/0.35 P(p(s(x1:S))) -> P(x1:S) 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 0.00/0.35 Problem 1: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 I(0(x1:S)) -> P(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 I(0(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 I(0(x1:S)) -> P(s(0(p(s(p(s(x1:S))))))) 0.00/0.35 I(0(x1:S)) -> P(s(x1:S)) 0.00/0.35 I(s(x1:S)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1:S))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(p(p(p(s(s(s(s(x1:S)))))))) 0.00/0.35 I(s(x1:S)) -> P(p(p(s(s(s(s(x1:S))))))) 0.00/0.35 I(s(x1:S)) -> P(p(s(s(s(s(x1:S)))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(p(p(p(s(s(s(s(x1:S)))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))) 0.00/0.35 I(s(x1:S)) -> P(s(s(s(s(x1:S))))) 0.00/0.35 J(0(x1:S)) -> P(p(s(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 J(0(x1:S)) -> P(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 J(0(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 J(0(x1:S)) -> P(s(s(0(p(s(p(s(x1:S)))))))) 0.00/0.35 J(0(x1:S)) -> P(s(x1:S)) 0.00/0.35 J(s(x1:S)) -> I(p(s(p(s(x1:S))))) 0.00/0.35 J(s(x1:S)) -> P(p(s(s(i(p(s(p(s(x1:S))))))))) 0.00/0.35 J(s(x1:S)) -> P(s(p(s(x1:S)))) 0.00/0.35 J(s(x1:S)) -> P(s(s(i(p(s(p(s(x1:S)))))))) 0.00/0.35 J(s(x1:S)) -> P(s(x1:S)) 0.00/0.35 P(p(s(x1:S))) -> P(x1:S) 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 P(p(s(x1:S))) -> P(x1:S) 0.00/0.35 ->->-> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 I(s(x1:S)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1:S))))))))))))) 0.00/0.35 J(s(x1:S)) -> I(p(s(p(s(x1:S))))) 0.00/0.35 ->->-> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 0.00/0.35 0.00/0.35 The problem is decomposed in 2 subproblems. 0.00/0.35 0.00/0.35 Problem 1.1: 0.00/0.35 0.00/0.35 Subterm Processor: 0.00/0.35 -> Pairs: 0.00/0.35 P(p(s(x1:S))) -> P(x1:S) 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->Projection: 0.00/0.35 pi(P) = 1 0.00/0.35 0.00/0.35 Problem 1.1: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 Empty 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 There is no strongly connected component 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 Reduction Pair Processor: 0.00/0.35 -> Pairs: 0.00/0.35 I(s(x1:S)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1:S))))))))))))) 0.00/0.35 J(s(x1:S)) -> I(p(s(p(s(x1:S))))) 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 -> Usable rules: 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->Interpretation type: 0.00/0.35 Linear 0.00/0.35 ->Coefficients: 0.00/0.35 All rationals 0.00/0.35 ->Dimension: 0.00/0.35 1 0.00/0.35 ->Bound: 0.00/0.35 4 0.00/0.35 ->Interpretation: 0.00/0.35 0.00/0.35 [p](X) = 1/4.X 0.00/0.35 [0](X) = 0 0.00/0.35 [s](X) = 4.X + 1/4 0.00/0.35 [I](X) = 3.X + 1 0.00/0.35 [J](X) = 2.X + 4/3 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 J(s(x1:S)) -> I(p(s(p(s(x1:S))))) 0.00/0.35 -> Rules: 0.00/0.35 i(0(x1:S)) -> p(s(p(s(0(p(s(p(s(x1:S))))))))) 0.00/0.35 i(s(x1:S)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1:S)))))))))))))))))) 0.00/0.35 j(0(x1:S)) -> p(s(p(p(s(s(0(p(s(p(s(x1:S))))))))))) 0.00/0.35 j(s(x1:S)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1:S))))))))))))) 0.00/0.35 p(p(s(x1:S))) -> p(x1:S) 0.00/0.35 p(0(x1:S)) -> 0(s(s(s(s(s(s(s(s(x1:S))))))))) 0.00/0.35 p(s(x1:S)) -> x1:S 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 There is no strongly connected component 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 EOF