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(p(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(s(x0)) | → | Wait(Right7(x0)) |
| Begin(0(x0)) | → | Wait(Right8(x0)) |
| Right1(foo(End(x0))) | → | Left(0(s(p(p(p(s(s(s(p(s(End(x0)))))))))))) |
| Right2(foo(End(x0))) | → | Left(p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(End(x0)))))))))))))))))))))))))))) |
| Right3(bar(End(x0))) | → | Left(0(p(s(s(s(End(x0))))))) |
| Right4(bar(End(x0))) | → | Left(p(s(p(p(s(s(foo(s(p(p(s(s(End(x0)))))))))))))) |
| Right5(p(End(x0))) | → | Left(p(End(x0))) |
| Right6(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right7(p(End(x0))) | → | Left(End(x0)) |
| Right8(p(End(x0))) | → | Left(0(s(s(s(s(End(x0))))))) |
| Right1(foo(x0)) | → | Afoo(Right1(x0)) |
| Right2(foo(x0)) | → | Afoo(Right2(x0)) |
| Right3(foo(x0)) | → | Afoo(Right3(x0)) |
| Right4(foo(x0)) | → | Afoo(Right4(x0)) |
| Right5(foo(x0)) | → | Afoo(Right5(x0)) |
| Right6(foo(x0)) | → | Afoo(Right6(x0)) |
| Right7(foo(x0)) | → | Afoo(Right7(x0)) |
| Right8(foo(x0)) | → | Afoo(Right8(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)) |
| 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)) |
| 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)) |
| Right1(bar(x0)) | → | Abar(Right1(x0)) |
| Right2(bar(x0)) | → | Abar(Right2(x0)) |
| Right3(bar(x0)) | → | Abar(Right3(x0)) |
| Right4(bar(x0)) | → | Abar(Right4(x0)) |
| Right5(bar(x0)) | → | Abar(Right5(x0)) |
| Right6(bar(x0)) | → | Abar(Right6(x0)) |
| Right7(bar(x0)) | → | Abar(Right7(x0)) |
| Right8(bar(x0)) | → | Abar(Right8(x0)) |
| Afoo(Left(x0)) | → | Left(foo(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| Abar(Left(x0)) | → | Left(bar(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| foo(0(x0)) | → | 0(s(p(p(p(s(s(s(p(s(x0)))))))))) |
| foo(s(x0)) | → | p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x0)))))))))))))))))))))))))) |
| bar(0(x0)) | → | 0(p(s(s(s(x0))))) |
| bar(s(x0)) | → | p(s(p(p(s(s(foo(s(p(p(s(s(x0)))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(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(p(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(s(x0)) | → | Wait(Right7(x0)) |
| Begin(0(x0)) | → | Wait(Right8(x0)) |
| Right1(foo(End(x0))) | → | Left(0(s(p(p(p(s(s(s(p(s(End(x0)))))))))))) |
| Right2(foo(End(x0))) | → | Left(p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(End(x0)))))))))))))))))))))))))))) |
| Right3(bar(End(x0))) | → | Left(0(p(s(s(s(End(x0))))))) |
| Right4(bar(End(x0))) | → | Left(p(s(p(p(s(s(foo(s(p(p(s(s(End(x0)))))))))))))) |
| Right5(p(End(x0))) | → | Left(p(End(x0))) |
| Right6(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right7(p(End(x0))) | → | Left(End(x0)) |
| Right8(p(End(x0))) | → | Left(0(s(s(s(s(End(x0))))))) |
| Right1(foo(x0)) | → | Afoo(Right1(x0)) |
| Right2(foo(x0)) | → | Afoo(Right2(x0)) |
| Right3(foo(x0)) | → | Afoo(Right3(x0)) |
| Right4(foo(x0)) | → | Afoo(Right4(x0)) |
| Right5(foo(x0)) | → | Afoo(Right5(x0)) |
| Right6(foo(x0)) | → | Afoo(Right6(x0)) |
| Right7(foo(x0)) | → | Afoo(Right7(x0)) |
| Right8(foo(x0)) | → | Afoo(Right8(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)) |
| 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)) |
| 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)) |
| Right1(bar(x0)) | → | Abar(Right1(x0)) |
| Right2(bar(x0)) | → | Abar(Right2(x0)) |
| Right3(bar(x0)) | → | Abar(Right3(x0)) |
| Right4(bar(x0)) | → | Abar(Right4(x0)) |
| Right5(bar(x0)) | → | Abar(Right5(x0)) |
| Right6(bar(x0)) | → | Abar(Right6(x0)) |
| Right7(bar(x0)) | → | Abar(Right7(x0)) |
| Right8(bar(x0)) | → | Abar(Right8(x0)) |
| Afoo(Left(x0)) | → | Left(foo(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| Abar(Left(x0)) | → | Left(bar(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| foo(0(x0)) | → | 0(s(p(p(p(s(s(s(p(s(x0)))))))))) |
| foo(s(x0)) | → | p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x0)))))))))))))))))))))))))) |
| bar(0(x0)) | → | 0(p(s(s(s(x0))))) |
| bar(s(x0)) | → | p(s(p(p(s(s(foo(s(p(p(s(s(x0)))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(x0))))) |