0.00/0.03 YES 0.00/0.03 0.00/0.03 Problem 1: 0.00/0.03 0.00/0.03 (VAR v_NonEmpty:S x1:S) 0.00/0.03 (RULES 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ) 0.00/0.03 0.00/0.03 Problem 1: 0.00/0.03 0.00/0.03 Dependency Pairs Processor: 0.00/0.03 -> Pairs: 0.00/0.03 A12(a34(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a34(x1:S)) -> A34(a12(x1:S)) 0.00/0.03 A12(a45(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a45(x1:S)) -> A45(a12(x1:S)) 0.00/0.03 A12(a56(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a56(x1:S)) -> A56(a12(x1:S)) 0.00/0.03 A13(x1:S) -> A12(a23(a12(x1:S))) 0.00/0.03 A13(x1:S) -> A12(x1:S) 0.00/0.03 A13(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A14(x1:S) -> A12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 A14(x1:S) -> A12(x1:S) 0.00/0.03 A14(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A14(x1:S) -> A23(a34(a23(a12(x1:S)))) 0.00/0.03 A14(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A15(x1:S) -> A12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 A15(x1:S) -> A12(x1:S) 0.00/0.03 A15(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A15(x1:S) -> A23(a34(a45(a34(a23(a12(x1:S)))))) 0.00/0.03 A15(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A15(x1:S) -> A34(a45(a34(a23(a12(x1:S))))) 0.00/0.03 A15(x1:S) -> A45(a34(a23(a12(x1:S)))) 0.00/0.03 A16(x1:S) -> A12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 A16(x1:S) -> A12(x1:S) 0.00/0.03 A16(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A16(x1:S) -> A23(a34(a45(a56(a45(a34(a23(a12(x1:S)))))))) 0.00/0.03 A16(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A16(x1:S) -> A34(a45(a56(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 A16(x1:S) -> A45(a34(a23(a12(x1:S)))) 0.00/0.03 A16(x1:S) -> A45(a56(a45(a34(a23(a12(x1:S)))))) 0.00/0.03 A16(x1:S) -> A56(a45(a34(a23(a12(x1:S))))) 0.00/0.03 A23(a45(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a45(x1:S)) -> A45(a23(x1:S)) 0.00/0.03 A23(a56(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a56(x1:S)) -> A56(a23(x1:S)) 0.00/0.03 A24(x1:S) -> A23(a34(a23(x1:S))) 0.00/0.03 A24(x1:S) -> A23(x1:S) 0.00/0.03 A24(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A25(x1:S) -> A23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 A25(x1:S) -> A23(x1:S) 0.00/0.03 A25(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A25(x1:S) -> A34(a45(a34(a23(x1:S)))) 0.00/0.03 A25(x1:S) -> A45(a34(a23(x1:S))) 0.00/0.03 A26(x1:S) -> A23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 A26(x1:S) -> A23(x1:S) 0.00/0.03 A26(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A26(x1:S) -> A34(a45(a56(a45(a34(a23(x1:S)))))) 0.00/0.03 A26(x1:S) -> A45(a34(a23(x1:S))) 0.00/0.03 A26(x1:S) -> A45(a56(a45(a34(a23(x1:S))))) 0.00/0.03 A26(x1:S) -> A56(a45(a34(a23(x1:S)))) 0.00/0.03 A34(a56(x1:S)) -> A34(x1:S) 0.00/0.03 A34(a56(x1:S)) -> A56(a34(x1:S)) 0.00/0.03 A35(x1:S) -> A34(a45(a34(x1:S))) 0.00/0.03 A35(x1:S) -> A34(x1:S) 0.00/0.03 A35(x1:S) -> A45(a34(x1:S)) 0.00/0.03 A36(x1:S) -> A34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 A36(x1:S) -> A34(x1:S) 0.00/0.03 A36(x1:S) -> A45(a34(x1:S)) 0.00/0.03 A36(x1:S) -> A45(a56(a45(a34(x1:S)))) 0.00/0.03 A36(x1:S) -> A56(a45(a34(x1:S))) 0.00/0.03 A46(x1:S) -> A45(a56(a45(x1:S))) 0.00/0.03 A46(x1:S) -> A45(x1:S) 0.00/0.03 A46(x1:S) -> A56(a45(x1:S)) 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 0.00/0.03 Problem 1: 0.00/0.03 0.00/0.03 SCC Processor: 0.00/0.03 -> Pairs: 0.00/0.03 A12(a34(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a34(x1:S)) -> A34(a12(x1:S)) 0.00/0.03 A12(a45(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a45(x1:S)) -> A45(a12(x1:S)) 0.00/0.03 A12(a56(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a56(x1:S)) -> A56(a12(x1:S)) 0.00/0.03 A13(x1:S) -> A12(a23(a12(x1:S))) 0.00/0.03 A13(x1:S) -> A12(x1:S) 0.00/0.03 A13(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A14(x1:S) -> A12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 A14(x1:S) -> A12(x1:S) 0.00/0.03 A14(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A14(x1:S) -> A23(a34(a23(a12(x1:S)))) 0.00/0.03 A14(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A15(x1:S) -> A12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 A15(x1:S) -> A12(x1:S) 0.00/0.03 A15(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A15(x1:S) -> A23(a34(a45(a34(a23(a12(x1:S)))))) 0.00/0.03 A15(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A15(x1:S) -> A34(a45(a34(a23(a12(x1:S))))) 0.00/0.03 A15(x1:S) -> A45(a34(a23(a12(x1:S)))) 0.00/0.03 A16(x1:S) -> A12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 A16(x1:S) -> A12(x1:S) 0.00/0.03 A16(x1:S) -> A23(a12(x1:S)) 0.00/0.03 A16(x1:S) -> A23(a34(a45(a56(a45(a34(a23(a12(x1:S)))))))) 0.00/0.03 A16(x1:S) -> A34(a23(a12(x1:S))) 0.00/0.03 A16(x1:S) -> A34(a45(a56(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 A16(x1:S) -> A45(a34(a23(a12(x1:S)))) 0.00/0.03 A16(x1:S) -> A45(a56(a45(a34(a23(a12(x1:S)))))) 0.00/0.03 A16(x1:S) -> A56(a45(a34(a23(a12(x1:S))))) 0.00/0.03 A23(a45(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a45(x1:S)) -> A45(a23(x1:S)) 0.00/0.03 A23(a56(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a56(x1:S)) -> A56(a23(x1:S)) 0.00/0.03 A24(x1:S) -> A23(a34(a23(x1:S))) 0.00/0.03 A24(x1:S) -> A23(x1:S) 0.00/0.03 A24(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A25(x1:S) -> A23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 A25(x1:S) -> A23(x1:S) 0.00/0.03 A25(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A25(x1:S) -> A34(a45(a34(a23(x1:S)))) 0.00/0.03 A25(x1:S) -> A45(a34(a23(x1:S))) 0.00/0.03 A26(x1:S) -> A23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 A26(x1:S) -> A23(x1:S) 0.00/0.03 A26(x1:S) -> A34(a23(x1:S)) 0.00/0.03 A26(x1:S) -> A34(a45(a56(a45(a34(a23(x1:S)))))) 0.00/0.03 A26(x1:S) -> A45(a34(a23(x1:S))) 0.00/0.03 A26(x1:S) -> A45(a56(a45(a34(a23(x1:S))))) 0.00/0.03 A26(x1:S) -> A56(a45(a34(a23(x1:S)))) 0.00/0.03 A34(a56(x1:S)) -> A34(x1:S) 0.00/0.03 A34(a56(x1:S)) -> A56(a34(x1:S)) 0.00/0.03 A35(x1:S) -> A34(a45(a34(x1:S))) 0.00/0.03 A35(x1:S) -> A34(x1:S) 0.00/0.03 A35(x1:S) -> A45(a34(x1:S)) 0.00/0.03 A36(x1:S) -> A34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 A36(x1:S) -> A34(x1:S) 0.00/0.03 A36(x1:S) -> A45(a34(x1:S)) 0.00/0.03 A36(x1:S) -> A45(a56(a45(a34(x1:S)))) 0.00/0.03 A36(x1:S) -> A56(a45(a34(x1:S))) 0.00/0.03 A46(x1:S) -> A45(a56(a45(x1:S))) 0.00/0.03 A46(x1:S) -> A45(x1:S) 0.00/0.03 A46(x1:S) -> A56(a45(x1:S)) 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Strongly Connected Components: 0.00/0.03 ->->Cycle: 0.00/0.03 ->->-> Pairs: 0.00/0.03 A34(a56(x1:S)) -> A34(x1:S) 0.00/0.03 ->->-> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->->Cycle: 0.00/0.03 ->->-> Pairs: 0.00/0.03 A23(a45(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a56(x1:S)) -> A23(x1:S) 0.00/0.03 ->->-> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->->Cycle: 0.00/0.03 ->->-> Pairs: 0.00/0.03 A12(a34(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a45(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a56(x1:S)) -> A12(x1:S) 0.00/0.03 ->->-> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 0.00/0.03 0.00/0.03 The problem is decomposed in 3 subproblems. 0.00/0.03 0.00/0.03 Problem 1.1: 0.00/0.03 0.00/0.03 Subterm Processor: 0.00/0.03 -> Pairs: 0.00/0.03 A34(a56(x1:S)) -> A34(x1:S) 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Projection: 0.00/0.03 pi(A34) = 1 0.00/0.03 0.00/0.03 Problem 1.1: 0.00/0.03 0.00/0.03 SCC Processor: 0.00/0.03 -> Pairs: 0.00/0.03 Empty 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Strongly Connected Components: 0.00/0.03 There is no strongly connected component 0.00/0.03 0.00/0.03 The problem is finite. 0.00/0.03 0.00/0.03 Problem 1.2: 0.00/0.03 0.00/0.03 Subterm Processor: 0.00/0.03 -> Pairs: 0.00/0.03 A23(a45(x1:S)) -> A23(x1:S) 0.00/0.03 A23(a56(x1:S)) -> A23(x1:S) 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Projection: 0.00/0.03 pi(A23) = 1 0.00/0.03 0.00/0.03 Problem 1.2: 0.00/0.03 0.00/0.03 SCC Processor: 0.00/0.03 -> Pairs: 0.00/0.03 Empty 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Strongly Connected Components: 0.00/0.03 There is no strongly connected component 0.00/0.03 0.00/0.03 The problem is finite. 0.00/0.03 0.00/0.03 Problem 1.3: 0.00/0.03 0.00/0.03 Subterm Processor: 0.00/0.03 -> Pairs: 0.00/0.03 A12(a34(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a45(x1:S)) -> A12(x1:S) 0.00/0.03 A12(a56(x1:S)) -> A12(x1:S) 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Projection: 0.00/0.03 pi(A12) = 1 0.00/0.03 0.00/0.03 Problem 1.3: 0.00/0.03 0.00/0.03 SCC Processor: 0.00/0.03 -> Pairs: 0.00/0.03 Empty 0.00/0.03 -> Rules: 0.00/0.03 a12(a12(x1:S)) -> x1:S 0.00/0.03 a12(a23(a12(a23(a12(a23(x1:S)))))) -> x1:S 0.00/0.03 a12(a34(x1:S)) -> a34(a12(x1:S)) 0.00/0.03 a12(a45(x1:S)) -> a45(a12(x1:S)) 0.00/0.03 a12(a56(x1:S)) -> a56(a12(x1:S)) 0.00/0.03 a13(a13(x1:S)) -> x1:S 0.00/0.03 a13(x1:S) -> a12(a23(a12(x1:S))) 0.00/0.03 a14(a14(x1:S)) -> x1:S 0.00/0.03 a14(x1:S) -> a12(a23(a34(a23(a12(x1:S))))) 0.00/0.03 a15(a15(x1:S)) -> x1:S 0.00/0.03 a15(x1:S) -> a12(a23(a34(a45(a34(a23(a12(x1:S))))))) 0.00/0.03 a16(a16(x1:S)) -> x1:S 0.00/0.03 a16(x1:S) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1:S))))))))) 0.00/0.03 a23(a23(x1:S)) -> x1:S 0.00/0.03 a23(a34(a23(a34(a23(a34(x1:S)))))) -> x1:S 0.00/0.03 a23(a45(x1:S)) -> a45(a23(x1:S)) 0.00/0.03 a23(a56(x1:S)) -> a56(a23(x1:S)) 0.00/0.03 a24(a24(x1:S)) -> x1:S 0.00/0.03 a24(x1:S) -> a23(a34(a23(x1:S))) 0.00/0.03 a25(a25(x1:S)) -> x1:S 0.00/0.03 a25(x1:S) -> a23(a34(a45(a34(a23(x1:S))))) 0.00/0.03 a26(a26(x1:S)) -> x1:S 0.00/0.03 a26(x1:S) -> a23(a34(a45(a56(a45(a34(a23(x1:S))))))) 0.00/0.03 a34(a34(x1:S)) -> x1:S 0.00/0.03 a34(a45(a34(a45(a34(a45(x1:S)))))) -> x1:S 0.00/0.03 a34(a56(x1:S)) -> a56(a34(x1:S)) 0.00/0.03 a35(a35(x1:S)) -> x1:S 0.00/0.03 a35(x1:S) -> a34(a45(a34(x1:S))) 0.00/0.03 a36(a36(x1:S)) -> x1:S 0.00/0.03 a36(x1:S) -> a34(a45(a56(a45(a34(x1:S))))) 0.00/0.03 a45(a45(x1:S)) -> x1:S 0.00/0.03 a45(a56(a45(a56(a45(a56(x1:S)))))) -> x1:S 0.00/0.03 a46(a46(x1:S)) -> x1:S 0.00/0.03 a46(x1:S) -> a45(a56(a45(x1:S))) 0.00/0.03 a56(a56(x1:S)) -> x1:S 0.00/0.03 ->Strongly Connected Components: 0.00/0.03 There is no strongly connected component 0.00/0.03 0.00/0.03 The problem is finite. 0.00/0.03 EOF