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