0.00/0.39 YES 0.00/0.39 0.00/0.39 Problem 1: 0.00/0.39 0.00/0.39 (VAR v_NonEmpty:S x1:S) 0.00/0.39 (RULES 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ) 0.00/0.39 0.00/0.39 Problem 1: 0.00/0.39 0.00/0.39 Dependency Pairs Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A34(a12(a12(x1:S))) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A34(a34(a12(a12(x1:S)))) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A45(a12(a12(x1:S))) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A45(a45(a12(a12(x1:S)))) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A56(a12(a12(x1:S))) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A56(a56(a12(a12(x1:S)))) 0.00/0.39 A13(a13(x1:S)) -> A12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A13(a13(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A13(a13(x1:S)) -> A12(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A13(a13(x1:S)) -> A12(x1:S) 0.00/0.39 A13(a13(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A13(a13(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A14(a14(x1:S)) -> A12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A14(a14(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A14(a14(x1:S)) -> A12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A14(a14(x1:S)) -> A12(x1:S) 0.00/0.39 A14(a14(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A14(a14(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A14(a14(x1:S)) -> A23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A14(a14(x1:S)) -> A23(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A14(a14(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A14(a14(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A15(a15(x1:S)) -> A12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A15(a15(x1:S)) -> A12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A12(x1:S) 0.00/0.39 A15(a15(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A15(a15(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A15(a15(x1:S)) -> A23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A15(a15(x1:S)) -> A45(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A15(a15(x1:S)) -> A45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A16(a16(x1:S)) -> A12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(x1:S) 0.00/0.39 A16(a16(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A16(a16(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A16(a16(x1:S)) -> A23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A16(a16(x1:S)) -> A56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A45(a23(a23(x1:S))) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A45(a45(a23(a23(x1:S)))) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A56(a23(a23(x1:S))) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A56(a56(a23(a23(x1:S)))) 0.00/0.39 A24(a24(x1:S)) -> A23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A24(a24(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A24(a24(x1:S)) -> A23(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A24(a24(x1:S)) -> A23(x1:S) 0.00/0.39 A24(a24(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A24(a24(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A25(a25(x1:S)) -> A23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 A25(a25(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A25(a25(x1:S)) -> A23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S))))))))) 0.00/0.39 A25(a25(x1:S)) -> A23(x1:S) 0.00/0.39 A25(a25(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A25(a25(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A25(a25(x1:S)) -> A34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))) 0.00/0.39 A25(a25(x1:S)) -> A34(a45(a45(a34(a34(a23(a23(x1:S))))))) 0.00/0.39 A25(a25(x1:S)) -> A45(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A25(a25(x1:S)) -> A45(a45(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A26(a26(x1:S)) -> A23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A26(a26(x1:S)) -> A23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A23(x1:S) 0.00/0.39 A26(a26(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A26(a26(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A26(a26(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a45(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))) 0.00/0.39 A26(a26(x1:S)) -> A56(a45(a45(a34(a34(a23(a23(x1:S))))))) 0.00/0.39 A26(a26(x1:S)) -> A56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(a34(x1:S)) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A56(a34(a34(x1:S))) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A56(a56(a34(a34(x1:S)))) 0.00/0.39 A35(a35(x1:S)) -> A34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 A35(a35(x1:S)) -> A34(a34(x1:S)) 0.00/0.39 A35(a35(x1:S)) -> A34(a45(a45(a34(a34(x1:S))))) 0.00/0.39 A35(a35(x1:S)) -> A34(x1:S) 0.00/0.39 A35(a35(x1:S)) -> A45(a34(a34(x1:S))) 0.00/0.39 A35(a35(x1:S)) -> A45(a45(a34(a34(x1:S)))) 0.00/0.39 A36(a36(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 A36(a36(x1:S)) -> A34(a34(x1:S)) 0.00/0.39 A36(a36(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S))))))))) 0.00/0.39 A36(a36(x1:S)) -> A34(x1:S) 0.00/0.39 A36(a36(x1:S)) -> A45(a34(a34(x1:S))) 0.00/0.39 A36(a36(x1:S)) -> A45(a45(a34(a34(x1:S)))) 0.00/0.39 A36(a36(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))) 0.00/0.39 A36(a36(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(x1:S))))))) 0.00/0.39 A36(a36(x1:S)) -> A56(a45(a45(a34(a34(x1:S))))) 0.00/0.39 A36(a36(x1:S)) -> A56(a56(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 A46(a46(x1:S)) -> A45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 A46(a46(x1:S)) -> A45(a45(x1:S)) 0.00/0.39 A46(a46(x1:S)) -> A45(a56(a56(a45(a45(x1:S))))) 0.00/0.39 A46(a46(x1:S)) -> A45(x1:S) 0.00/0.39 A46(a46(x1:S)) -> A56(a45(a45(x1:S))) 0.00/0.39 A46(a46(x1:S)) -> A56(a56(a45(a45(x1:S)))) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A34(a12(a12(x1:S))) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A34(a34(a12(a12(x1:S)))) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A45(a12(a12(x1:S))) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A45(a45(a12(a12(x1:S)))) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A56(a12(a12(x1:S))) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A56(a56(a12(a12(x1:S)))) 0.00/0.39 A13(a13(x1:S)) -> A12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A13(a13(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A13(a13(x1:S)) -> A12(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A13(a13(x1:S)) -> A12(x1:S) 0.00/0.39 A13(a13(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A13(a13(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A14(a14(x1:S)) -> A12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A14(a14(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A14(a14(x1:S)) -> A12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A14(a14(x1:S)) -> A12(x1:S) 0.00/0.39 A14(a14(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A14(a14(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A14(a14(x1:S)) -> A23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A14(a14(x1:S)) -> A23(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A14(a14(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A14(a14(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A15(a15(x1:S)) -> A12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A15(a15(x1:S)) -> A12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A12(x1:S) 0.00/0.39 A15(a15(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A15(a15(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A15(a15(x1:S)) -> A23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A15(a15(x1:S)) -> A34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A15(a15(x1:S)) -> A45(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A15(a15(x1:S)) -> A45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(a12(x1:S)) 0.00/0.39 A16(a16(x1:S)) -> A12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A12(x1:S) 0.00/0.39 A16(a16(x1:S)) -> A23(a12(a12(x1:S))) 0.00/0.39 A16(a16(x1:S)) -> A23(a23(a12(a12(x1:S)))) 0.00/0.39 A16(a16(x1:S)) -> A23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a23(a23(a12(a12(x1:S))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a34(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a34(a34(a23(a23(a12(a12(x1:S))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))))) 0.00/0.39 A16(a16(x1:S)) -> A56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S))))))))) 0.00/0.39 A16(a16(x1:S)) -> A56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A45(a23(a23(x1:S))) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A45(a45(a23(a23(x1:S)))) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A56(a23(a23(x1:S))) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A56(a56(a23(a23(x1:S)))) 0.00/0.39 A24(a24(x1:S)) -> A23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A24(a24(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A24(a24(x1:S)) -> A23(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A24(a24(x1:S)) -> A23(x1:S) 0.00/0.39 A24(a24(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A24(a24(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A25(a25(x1:S)) -> A23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 A25(a25(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A25(a25(x1:S)) -> A23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S))))))))) 0.00/0.39 A25(a25(x1:S)) -> A23(x1:S) 0.00/0.39 A25(a25(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A25(a25(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A25(a25(x1:S)) -> A34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))) 0.00/0.39 A25(a25(x1:S)) -> A34(a45(a45(a34(a34(a23(a23(x1:S))))))) 0.00/0.39 A25(a25(x1:S)) -> A45(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A25(a25(x1:S)) -> A45(a45(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A26(a26(x1:S)) -> A23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A23(a23(x1:S)) 0.00/0.39 A26(a26(x1:S)) -> A23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A23(x1:S) 0.00/0.39 A26(a26(x1:S)) -> A34(a23(a23(x1:S))) 0.00/0.39 A26(a26(x1:S)) -> A34(a34(a23(a23(x1:S)))) 0.00/0.39 A26(a26(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a34(a34(a23(a23(x1:S))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a45(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 A26(a26(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S))))))))) 0.00/0.39 A26(a26(x1:S)) -> A56(a45(a45(a34(a34(a23(a23(x1:S))))))) 0.00/0.39 A26(a26(x1:S)) -> A56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(a34(x1:S)) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A56(a34(a34(x1:S))) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A56(a56(a34(a34(x1:S)))) 0.00/0.39 A35(a35(x1:S)) -> A34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 A35(a35(x1:S)) -> A34(a34(x1:S)) 0.00/0.39 A35(a35(x1:S)) -> A34(a45(a45(a34(a34(x1:S))))) 0.00/0.39 A35(a35(x1:S)) -> A34(x1:S) 0.00/0.39 A35(a35(x1:S)) -> A45(a34(a34(x1:S))) 0.00/0.39 A35(a35(x1:S)) -> A45(a45(a34(a34(x1:S)))) 0.00/0.39 A36(a36(x1:S)) -> A34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 A36(a36(x1:S)) -> A34(a34(x1:S)) 0.00/0.39 A36(a36(x1:S)) -> A34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S))))))))) 0.00/0.39 A36(a36(x1:S)) -> A34(x1:S) 0.00/0.39 A36(a36(x1:S)) -> A45(a34(a34(x1:S))) 0.00/0.39 A36(a36(x1:S)) -> A45(a45(a34(a34(x1:S)))) 0.00/0.39 A36(a36(x1:S)) -> A45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))) 0.00/0.39 A36(a36(x1:S)) -> A45(a56(a56(a45(a45(a34(a34(x1:S))))))) 0.00/0.39 A36(a36(x1:S)) -> A56(a45(a45(a34(a34(x1:S))))) 0.00/0.39 A36(a36(x1:S)) -> A56(a56(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 A46(a46(x1:S)) -> A45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 A46(a46(x1:S)) -> A45(a45(x1:S)) 0.00/0.39 A46(a46(x1:S)) -> A45(a56(a56(a45(a45(x1:S))))) 0.00/0.39 A46(a46(x1:S)) -> A45(x1:S) 0.00/0.39 A46(a46(x1:S)) -> A56(a45(a45(x1:S))) 0.00/0.39 A46(a46(x1:S)) -> A56(a56(a45(a45(x1:S)))) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(a34(x1:S)) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 0.00/0.39 The problem is decomposed in 3 subproblems. 0.00/0.39 0.00/0.39 Problem 1.1: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(a34(x1:S)) 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a34](X) = 2.X 0.00/0.39 [a45](X) = 2.X 0.00/0.39 [a56](X) = 2.X + 2 0.00/0.39 [A34](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.1: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.1: 0.00/0.39 0.00/0.39 Subterm Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A34(a34(a56(a56(x1:S)))) -> A34(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Projection: 0.00/0.39 pi(A34) = 1 0.00/0.39 0.00/0.39 Problem 1.1: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 Empty 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 There is no strongly connected component 0.00/0.39 0.00/0.39 The problem is finite. 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a23](X) = 2.X + 2 0.00/0.39 [a34](X) = 2.X 0.00/0.39 [a45](X) = 2.X + 2 0.00/0.39 [a56](X) = X 0.00/0.39 [A23](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a45(a45(x1:S)))) -> A23(x1:S) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a23](X) = 2.X + 1 0.00/0.39 [a34](X) = 2.X 0.00/0.39 [a45](X) = 2.X + 2 0.00/0.39 [a56](X) = X + 1 0.00/0.39 [A23](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(a23(x1:S)) 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a23](X) = 2.X 0.00/0.39 [a34](X) = 2.X 0.00/0.39 [a45](X) = 2.X + 2 0.00/0.39 [a56](X) = 2.X + 2 0.00/0.39 [A23](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 Subterm Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A23(a23(a56(a56(x1:S)))) -> A23(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Projection: 0.00/0.39 pi(A23) = 1 0.00/0.39 0.00/0.39 Problem 1.2: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 Empty 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 There is no strongly connected component 0.00/0.39 0.00/0.39 The problem is finite. 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a12](X) = 2.X + 1 0.00/0.39 [a23](X) = X 0.00/0.39 [a34](X) = 2.X + 1 0.00/0.39 [a45](X) = 2.X + 2 0.00/0.39 [a56](X) = 2.X + 1 0.00/0.39 [A12](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a34(a34(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a12](X) = 2.X + 1 0.00/0.39 [a23](X) = X 0.00/0.39 [a34](X) = X 0.00/0.39 [a45](X) = X + 1 0.00/0.39 [a56](X) = X 0.00/0.39 [A12](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a12](X) = 2.X + 1 0.00/0.39 [a23](X) = 2.X 0.00/0.39 [a34](X) = 2.X + 2 0.00/0.39 [a45](X) = 2.X + 2 0.00/0.39 [a56](X) = X + 1 0.00/0.39 [A12](X) = 2.X 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 ->->-> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 Reduction Pair Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a45(a45(x1:S)))) -> A12(x1:S) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 -> Usable rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Interpretation type: 0.00/0.39 Linear 0.00/0.39 ->Coefficients: 0.00/0.39 Natural Numbers 0.00/0.39 ->Dimension: 0.00/0.39 1 0.00/0.39 ->Bound: 0.00/0.39 2 0.00/0.39 ->Interpretation: 0.00/0.39 0.00/0.39 [a12](X) = 2.X + 2 0.00/0.39 [a23](X) = 2.X 0.00/0.39 [a34](X) = 2.X + 2 0.00/0.39 [a45](X) = X + 1 0.00/0.39 [a56](X) = 2.X + 2 0.00/0.39 [A12](X) = X 0.00/0.39 0.00/0.39 Problem 1.3: 0.00/0.39 0.00/0.39 SCC Processor: 0.00/0.39 -> Pairs: 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.39 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.39 -> Rules: 0.00/0.39 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.39 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.39 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.39 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.39 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.39 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.39 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.39 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.39 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.39 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.39 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.39 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.39 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.39 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.39 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.39 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.39 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.39 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.39 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.39 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.39 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.39 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.39 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.39 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.39 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.39 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.39 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.39 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.39 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.39 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.39 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.39 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.39 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.39 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.39 ->Strongly Connected Components: 0.00/0.39 ->->Cycle: 0.00/0.39 ->->-> Pairs: 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.40 ->->-> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 0.00/0.40 Problem 1.3: 0.00/0.40 0.00/0.40 Reduction Pair Processor: 0.00/0.40 -> Pairs: 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(a12(x1:S)) 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.40 -> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 -> Usable rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 ->Interpretation type: 0.00/0.40 Linear 0.00/0.40 ->Coefficients: 0.00/0.40 Natural Numbers 0.00/0.40 ->Dimension: 0.00/0.40 1 0.00/0.40 ->Bound: 0.00/0.40 2 0.00/0.40 ->Interpretation: 0.00/0.40 0.00/0.40 [a12](X) = X 0.00/0.40 [a23](X) = X 0.00/0.40 [a34](X) = 2.X 0.00/0.40 [a45](X) = 2.X 0.00/0.40 [a56](X) = 2.X + 1 0.00/0.40 [A12](X) = 2.X 0.00/0.40 0.00/0.40 Problem 1.3: 0.00/0.40 0.00/0.40 SCC Processor: 0.00/0.40 -> Pairs: 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.40 -> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 ->Strongly Connected Components: 0.00/0.40 ->->Cycle: 0.00/0.40 ->->-> Pairs: 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.40 ->->-> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 0.00/0.40 Problem 1.3: 0.00/0.40 0.00/0.40 Subterm Processor: 0.00/0.40 -> Pairs: 0.00/0.40 A12(a12(a56(a56(x1:S)))) -> A12(x1:S) 0.00/0.40 -> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 ->Projection: 0.00/0.40 pi(A12) = 1 0.00/0.40 0.00/0.40 Problem 1.3: 0.00/0.40 0.00/0.40 SCC Processor: 0.00/0.40 -> Pairs: 0.00/0.40 Empty 0.00/0.40 -> Rules: 0.00/0.40 a12(a12(a12(a12(x1:S)))) -> x1:S 0.00/0.40 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1:S)))))))))))) -> x1:S 0.00/0.40 a12(a12(a34(a34(x1:S)))) -> a34(a34(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a45(a45(x1:S)))) -> a45(a45(a12(a12(x1:S)))) 0.00/0.40 a12(a12(a56(a56(x1:S)))) -> a56(a56(a12(a12(x1:S)))) 0.00/0.40 a13(a13(a13(a13(x1:S)))) -> x1:S 0.00/0.40 a13(a13(x1:S)) -> a12(a12(a23(a23(a12(a12(x1:S)))))) 0.00/0.40 a14(a14(a14(a14(x1:S)))) -> x1:S 0.00/0.40 a14(a14(x1:S)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1:S)))))))))) 0.00/0.40 a15(a15(a15(a15(x1:S)))) -> x1:S 0.00/0.40 a15(a15(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))) 0.00/0.40 a16(a16(a16(a16(x1:S)))) -> x1:S 0.00/0.40 a16(a16(x1:S)) -> a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1:S)))))))))))))))))) 0.00/0.40 a23(a23(a23(a23(x1:S)))) -> x1:S 0.00/0.40 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1:S)))))))))))) -> x1:S 0.00/0.40 a23(a23(a45(a45(x1:S)))) -> a45(a45(a23(a23(x1:S)))) 0.00/0.40 a23(a23(a56(a56(x1:S)))) -> a56(a56(a23(a23(x1:S)))) 0.00/0.40 a24(a24(a24(a24(x1:S)))) -> x1:S 0.00/0.40 a24(a24(x1:S)) -> a23(a23(a34(a34(a23(a23(x1:S)))))) 0.00/0.40 a25(a25(a25(a25(x1:S)))) -> x1:S 0.00/0.40 a25(a25(x1:S)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1:S)))))))))) 0.00/0.40 a26(a26(a26(a26(x1:S)))) -> x1:S 0.00/0.40 a26(a26(x1:S)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1:S)))))))))))))) 0.00/0.40 a34(a34(a34(a34(x1:S)))) -> x1:S 0.00/0.40 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1:S)))))))))))) -> x1:S 0.00/0.40 a34(a34(a56(a56(x1:S)))) -> a56(a56(a34(a34(x1:S)))) 0.00/0.40 a35(a35(a35(a35(x1:S)))) -> x1:S 0.00/0.40 a35(a35(x1:S)) -> a34(a34(a45(a45(a34(a34(x1:S)))))) 0.00/0.40 a36(a36(a36(a36(x1:S)))) -> x1:S 0.00/0.40 a36(a36(x1:S)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1:S)))))))))) 0.00/0.40 a45(a45(a45(a45(x1:S)))) -> x1:S 0.00/0.40 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1:S)))))))))))) -> x1:S 0.00/0.40 a46(a46(a46(a46(x1:S)))) -> x1:S 0.00/0.40 a46(a46(x1:S)) -> a45(a45(a56(a56(a45(a45(x1:S)))))) 0.00/0.40 a56(a56(a56(a56(x1:S)))) -> x1:S 0.00/0.40 ->Strongly Connected Components: 0.00/0.40 There is no strongly connected component 0.00/0.40 0.00/0.40 The problem is finite. 0.00/0.40 EOF