by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| Begin(0(x0)) | → | Wait(Right1(x0)) |
| Begin(s(x0)) | → | Wait(Right2(x0)) |
| Begin(0(x0)) | → | Wait(Right3(x0)) |
| Begin(s(x0)) | → | Wait(Right4(x0)) |
| Begin(s(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(0(x0)) | → | Wait(Right7(x0)) |
| Begin(s(x0)) | → | Wait(Right8(x0)) |
| Begin(p(s(x0))) | → | Wait(Right9(x0)) |
| Begin(s(x0)) | → | Wait(Right10(x0)) |
| Begin(s(x0)) | → | Wait(Right11(x0)) |
| Begin(0(x0)) | → | Wait(Right12(x0)) |
| Right1(thrice(End(x0))) | → | Left(p(s(p(p(p(s(s(s(0(p(s(p(s(End(x0))))))))))))))) |
| Right2(thrice(End(x0))) | → | Left(p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(End(x0)))))))))))))))))))) |
| Right3(half(End(x0))) | → | Left(p(p(s(s(p(s(0(p(s(s(s(s(End(x0)))))))))))))) |
| Right4(half(End(x0))) | → | Left(p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0))))))))))))))))))) |
| Right5(half(End(x0))) | → | Left(p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0)))))))))))))))))) |
| Right6(half(s(End(x0)))) | → | Left(p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0)))))))))))))))))) |
| Right7(sixtimes(End(x0))) | → | Left(p(s(p(s(0(s(s(s(s(s(p(s(p(s(End(x0)))))))))))))))) |
| Right8(sixtimes(End(x0))) | → | Left(p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(End(x0))))))))))))))))))))))))))) |
| Right9(p(End(x0))) | → | Left(p(End(x0))) |
| Right10(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right11(p(End(x0))) | → | Left(End(x0)) |
| Right12(p(End(x0))) | → | Left(0(s(s(s(s(End(x0))))))) |
| Right1(thrice(x0)) | → | Athrice(Right1(x0)) |
| Right2(thrice(x0)) | → | Athrice(Right2(x0)) |
| Right3(thrice(x0)) | → | Athrice(Right3(x0)) |
| Right4(thrice(x0)) | → | Athrice(Right4(x0)) |
| Right5(thrice(x0)) | → | Athrice(Right5(x0)) |
| Right6(thrice(x0)) | → | Athrice(Right6(x0)) |
| Right7(thrice(x0)) | → | Athrice(Right7(x0)) |
| Right8(thrice(x0)) | → | Athrice(Right8(x0)) |
| Right9(thrice(x0)) | → | Athrice(Right9(x0)) |
| Right10(thrice(x0)) | → | Athrice(Right10(x0)) |
| Right11(thrice(x0)) | → | Athrice(Right11(x0)) |
| Right12(thrice(x0)) | → | Athrice(Right12(x0)) |
| Right1(0(x0)) | → | A0(Right1(x0)) |
| Right2(0(x0)) | → | A0(Right2(x0)) |
| Right3(0(x0)) | → | A0(Right3(x0)) |
| Right4(0(x0)) | → | A0(Right4(x0)) |
| Right5(0(x0)) | → | A0(Right5(x0)) |
| Right6(0(x0)) | → | A0(Right6(x0)) |
| Right7(0(x0)) | → | A0(Right7(x0)) |
| Right8(0(x0)) | → | A0(Right8(x0)) |
| Right9(0(x0)) | → | A0(Right9(x0)) |
| Right10(0(x0)) | → | A0(Right10(x0)) |
| Right11(0(x0)) | → | A0(Right11(x0)) |
| Right12(0(x0)) | → | A0(Right12(x0)) |
| Right1(p(x0)) | → | Ap(Right1(x0)) |
| Right2(p(x0)) | → | Ap(Right2(x0)) |
| Right3(p(x0)) | → | Ap(Right3(x0)) |
| Right4(p(x0)) | → | Ap(Right4(x0)) |
| Right5(p(x0)) | → | Ap(Right5(x0)) |
| Right6(p(x0)) | → | Ap(Right6(x0)) |
| Right7(p(x0)) | → | Ap(Right7(x0)) |
| Right8(p(x0)) | → | Ap(Right8(x0)) |
| Right9(p(x0)) | → | Ap(Right9(x0)) |
| Right10(p(x0)) | → | Ap(Right10(x0)) |
| Right11(p(x0)) | → | Ap(Right11(x0)) |
| Right12(p(x0)) | → | Ap(Right12(x0)) |
| Right1(s(x0)) | → | As(Right1(x0)) |
| Right2(s(x0)) | → | As(Right2(x0)) |
| Right3(s(x0)) | → | As(Right3(x0)) |
| Right4(s(x0)) | → | As(Right4(x0)) |
| Right5(s(x0)) | → | As(Right5(x0)) |
| Right6(s(x0)) | → | As(Right6(x0)) |
| Right7(s(x0)) | → | As(Right7(x0)) |
| Right8(s(x0)) | → | As(Right8(x0)) |
| Right9(s(x0)) | → | As(Right9(x0)) |
| Right10(s(x0)) | → | As(Right10(x0)) |
| Right11(s(x0)) | → | As(Right11(x0)) |
| Right12(s(x0)) | → | As(Right12(x0)) |
| Right1(half(x0)) | → | Ahalf(Right1(x0)) |
| Right2(half(x0)) | → | Ahalf(Right2(x0)) |
| Right3(half(x0)) | → | Ahalf(Right3(x0)) |
| Right4(half(x0)) | → | Ahalf(Right4(x0)) |
| Right5(half(x0)) | → | Ahalf(Right5(x0)) |
| Right6(half(x0)) | → | Ahalf(Right6(x0)) |
| Right7(half(x0)) | → | Ahalf(Right7(x0)) |
| Right8(half(x0)) | → | Ahalf(Right8(x0)) |
| Right9(half(x0)) | → | Ahalf(Right9(x0)) |
| Right10(half(x0)) | → | Ahalf(Right10(x0)) |
| Right11(half(x0)) | → | Ahalf(Right11(x0)) |
| Right12(half(x0)) | → | Ahalf(Right12(x0)) |
| Right1(sixtimes(x0)) | → | Asixtimes(Right1(x0)) |
| Right2(sixtimes(x0)) | → | Asixtimes(Right2(x0)) |
| Right3(sixtimes(x0)) | → | Asixtimes(Right3(x0)) |
| Right4(sixtimes(x0)) | → | Asixtimes(Right4(x0)) |
| Right5(sixtimes(x0)) | → | Asixtimes(Right5(x0)) |
| Right6(sixtimes(x0)) | → | Asixtimes(Right6(x0)) |
| Right7(sixtimes(x0)) | → | Asixtimes(Right7(x0)) |
| Right8(sixtimes(x0)) | → | Asixtimes(Right8(x0)) |
| Right9(sixtimes(x0)) | → | Asixtimes(Right9(x0)) |
| Right10(sixtimes(x0)) | → | Asixtimes(Right10(x0)) |
| Right11(sixtimes(x0)) | → | Asixtimes(Right11(x0)) |
| Right12(sixtimes(x0)) | → | Asixtimes(Right12(x0)) |
| Athrice(Left(x0)) | → | Left(thrice(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Ahalf(Left(x0)) | → | Left(half(x0)) |
| Asixtimes(Left(x0)) | → | Left(sixtimes(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| thrice(0(x0)) | → | p(s(p(p(p(s(s(s(0(p(s(p(s(x0))))))))))))) |
| thrice(s(x0)) | → | p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(x0)))))))))))))))))) |
| half(0(x0)) | → | p(p(s(s(p(s(0(p(s(s(s(s(x0)))))))))))) |
| half(s(x0)) | → | p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x0))))))))))))))))) |
| half(s(s(x0))) | → | p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x0)))))))))))))))) |
| sixtimes(0(x0)) | → | p(s(p(s(0(s(s(s(s(s(p(s(p(s(x0)))))))))))))) |
| sixtimes(s(x0)) | → | p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(x0))))))))))))))))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(x0))))) |
| 0(x0) | → | x0 |
| Begin(0(x0)) | → | Wait(Right1(x0)) |
| Begin(s(x0)) | → | Wait(Right2(x0)) |
| Begin(0(x0)) | → | Wait(Right3(x0)) |
| Begin(s(x0)) | → | Wait(Right4(x0)) |
| Begin(s(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(0(x0)) | → | Wait(Right7(x0)) |
| Begin(s(x0)) | → | Wait(Right8(x0)) |
| Begin(p(s(x0))) | → | Wait(Right9(x0)) |
| Begin(s(x0)) | → | Wait(Right10(x0)) |
| Begin(s(x0)) | → | Wait(Right11(x0)) |
| Begin(0(x0)) | → | Wait(Right12(x0)) |
| Right1(thrice(End(x0))) | → | Left(p(s(p(p(p(s(s(s(0(p(s(p(s(End(x0))))))))))))))) |
| Right2(thrice(End(x0))) | → | Left(p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(End(x0)))))))))))))))))))) |
| Right3(half(End(x0))) | → | Left(p(p(s(s(p(s(0(p(s(s(s(s(End(x0)))))))))))))) |
| Right4(half(End(x0))) | → | Left(p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0))))))))))))))))))) |
| Right5(half(End(x0))) | → | Left(p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0)))))))))))))))))) |
| Right6(half(s(End(x0)))) | → | Left(p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(End(x0)))))))))))))))))) |
| Right7(sixtimes(End(x0))) | → | Left(p(s(p(s(0(s(s(s(s(s(p(s(p(s(End(x0)))))))))))))))) |
| Right8(sixtimes(End(x0))) | → | Left(p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(End(x0))))))))))))))))))))))))))) |
| Right9(p(End(x0))) | → | Left(p(End(x0))) |
| Right10(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right11(p(End(x0))) | → | Left(End(x0)) |
| Right12(p(End(x0))) | → | Left(0(s(s(s(s(End(x0))))))) |
| Right1(thrice(x0)) | → | Athrice(Right1(x0)) |
| Right2(thrice(x0)) | → | Athrice(Right2(x0)) |
| Right3(thrice(x0)) | → | Athrice(Right3(x0)) |
| Right4(thrice(x0)) | → | Athrice(Right4(x0)) |
| Right5(thrice(x0)) | → | Athrice(Right5(x0)) |
| Right6(thrice(x0)) | → | Athrice(Right6(x0)) |
| Right7(thrice(x0)) | → | Athrice(Right7(x0)) |
| Right8(thrice(x0)) | → | Athrice(Right8(x0)) |
| Right9(thrice(x0)) | → | Athrice(Right9(x0)) |
| Right10(thrice(x0)) | → | Athrice(Right10(x0)) |
| Right11(thrice(x0)) | → | Athrice(Right11(x0)) |
| Right12(thrice(x0)) | → | Athrice(Right12(x0)) |
| Right1(0(x0)) | → | A0(Right1(x0)) |
| Right2(0(x0)) | → | A0(Right2(x0)) |
| Right3(0(x0)) | → | A0(Right3(x0)) |
| Right4(0(x0)) | → | A0(Right4(x0)) |
| Right5(0(x0)) | → | A0(Right5(x0)) |
| Right6(0(x0)) | → | A0(Right6(x0)) |
| Right7(0(x0)) | → | A0(Right7(x0)) |
| Right8(0(x0)) | → | A0(Right8(x0)) |
| Right9(0(x0)) | → | A0(Right9(x0)) |
| Right10(0(x0)) | → | A0(Right10(x0)) |
| Right11(0(x0)) | → | A0(Right11(x0)) |
| Right12(0(x0)) | → | A0(Right12(x0)) |
| Right1(p(x0)) | → | Ap(Right1(x0)) |
| Right2(p(x0)) | → | Ap(Right2(x0)) |
| Right3(p(x0)) | → | Ap(Right3(x0)) |
| Right4(p(x0)) | → | Ap(Right4(x0)) |
| Right5(p(x0)) | → | Ap(Right5(x0)) |
| Right6(p(x0)) | → | Ap(Right6(x0)) |
| Right7(p(x0)) | → | Ap(Right7(x0)) |
| Right8(p(x0)) | → | Ap(Right8(x0)) |
| Right9(p(x0)) | → | Ap(Right9(x0)) |
| Right10(p(x0)) | → | Ap(Right10(x0)) |
| Right11(p(x0)) | → | Ap(Right11(x0)) |
| Right12(p(x0)) | → | Ap(Right12(x0)) |
| Right1(s(x0)) | → | As(Right1(x0)) |
| Right2(s(x0)) | → | As(Right2(x0)) |
| Right3(s(x0)) | → | As(Right3(x0)) |
| Right4(s(x0)) | → | As(Right4(x0)) |
| Right5(s(x0)) | → | As(Right5(x0)) |
| Right6(s(x0)) | → | As(Right6(x0)) |
| Right7(s(x0)) | → | As(Right7(x0)) |
| Right8(s(x0)) | → | As(Right8(x0)) |
| Right9(s(x0)) | → | As(Right9(x0)) |
| Right10(s(x0)) | → | As(Right10(x0)) |
| Right11(s(x0)) | → | As(Right11(x0)) |
| Right12(s(x0)) | → | As(Right12(x0)) |
| Right1(half(x0)) | → | Ahalf(Right1(x0)) |
| Right2(half(x0)) | → | Ahalf(Right2(x0)) |
| Right3(half(x0)) | → | Ahalf(Right3(x0)) |
| Right4(half(x0)) | → | Ahalf(Right4(x0)) |
| Right5(half(x0)) | → | Ahalf(Right5(x0)) |
| Right6(half(x0)) | → | Ahalf(Right6(x0)) |
| Right7(half(x0)) | → | Ahalf(Right7(x0)) |
| Right8(half(x0)) | → | Ahalf(Right8(x0)) |
| Right9(half(x0)) | → | Ahalf(Right9(x0)) |
| Right10(half(x0)) | → | Ahalf(Right10(x0)) |
| Right11(half(x0)) | → | Ahalf(Right11(x0)) |
| Right12(half(x0)) | → | Ahalf(Right12(x0)) |
| Right1(sixtimes(x0)) | → | Asixtimes(Right1(x0)) |
| Right2(sixtimes(x0)) | → | Asixtimes(Right2(x0)) |
| Right3(sixtimes(x0)) | → | Asixtimes(Right3(x0)) |
| Right4(sixtimes(x0)) | → | Asixtimes(Right4(x0)) |
| Right5(sixtimes(x0)) | → | Asixtimes(Right5(x0)) |
| Right6(sixtimes(x0)) | → | Asixtimes(Right6(x0)) |
| Right7(sixtimes(x0)) | → | Asixtimes(Right7(x0)) |
| Right8(sixtimes(x0)) | → | Asixtimes(Right8(x0)) |
| Right9(sixtimes(x0)) | → | Asixtimes(Right9(x0)) |
| Right10(sixtimes(x0)) | → | Asixtimes(Right10(x0)) |
| Right11(sixtimes(x0)) | → | Asixtimes(Right11(x0)) |
| Right12(sixtimes(x0)) | → | Asixtimes(Right12(x0)) |
| Athrice(Left(x0)) | → | Left(thrice(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Ahalf(Left(x0)) | → | Left(half(x0)) |
| Asixtimes(Left(x0)) | → | Left(sixtimes(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| thrice(0(x0)) | → | p(s(p(p(p(s(s(s(0(p(s(p(s(x0))))))))))))) |
| thrice(s(x0)) | → | p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(x0)))))))))))))))))) |
| half(0(x0)) | → | p(p(s(s(p(s(0(p(s(s(s(s(x0)))))))))))) |
| half(s(x0)) | → | p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x0))))))))))))))))) |
| half(s(s(x0))) | → | p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x0)))))))))))))))) |
| sixtimes(0(x0)) | → | p(s(p(s(0(s(s(s(s(s(p(s(p(s(x0)))))))))))))) |
| sixtimes(s(x0)) | → | p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(x0))))))))))))))))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(x0))))) |
| 0(x0) | → | x0 |