MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(x0)) Wait(Right1(x0))
Begin(a(x0)) Wait(Right2(x0))
Begin(b(b(x0))) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Begin(b(x0)) Wait(Right5(x0))
Begin(b(x0)) Wait(Right6(x0))
Begin(d(x0)) Wait(Right7(x0))
Begin(c(x0)) Wait(Right8(x0))
Begin(a(a(x0))) Wait(Right9(x0))
Begin(a(x0)) Wait(Right10(x0))
Right1(a(End(x0))) Left(a(b(a(b(a(End(x0)))))))
Right2(c(End(x0))) Left(a(b(a(a(c(End(x0)))))))
Right3(b(End(x0))) Left(a(b(End(x0))))
Right4(b(b(End(x0)))) Left(a(b(End(x0))))
Right5(c(End(x0))) Left(a(a(c(End(x0)))))
Right6(c(End(x0))) Left(b(a(d(End(x0)))))
Right7(d(End(x0))) Left(d(b(d(b(d(End(x0)))))))
Right8(c(End(x0))) Left(c(d(c(End(x0)))))
Right9(a(End(x0))) Left(a(b(b(End(x0)))))
Right10(a(a(End(x0)))) Left(a(b(b(End(x0)))))
Right1(a(x0)) Aa(Right1(x0))
Right2(a(x0)) Aa(Right2(x0))
Right3(a(x0)) Aa(Right3(x0))
Right4(a(x0)) Aa(Right4(x0))
Right5(a(x0)) Aa(Right5(x0))
Right6(a(x0)) Aa(Right6(x0))
Right7(a(x0)) Aa(Right7(x0))
Right8(a(x0)) Aa(Right8(x0))
Right9(a(x0)) Aa(Right9(x0))
Right10(a(x0)) Aa(Right10(x0))
Right1(b(x0)) Ab(Right1(x0))
Right2(b(x0)) Ab(Right2(x0))
Right3(b(x0)) Ab(Right3(x0))
Right4(b(x0)) Ab(Right4(x0))
Right5(b(x0)) Ab(Right5(x0))
Right6(b(x0)) Ab(Right6(x0))
Right7(b(x0)) Ab(Right7(x0))
Right8(b(x0)) Ab(Right8(x0))
Right9(b(x0)) Ab(Right9(x0))
Right10(b(x0)) Ab(Right10(x0))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(x0))
Right5(c(x0)) Ac(Right5(x0))
Right6(c(x0)) Ac(Right6(x0))
Right7(c(x0)) Ac(Right7(x0))
Right8(c(x0)) Ac(Right8(x0))
Right9(c(x0)) Ac(Right9(x0))
Right10(c(x0)) Ac(Right10(x0))
Right1(d(x0)) Ad(Right1(x0))
Right2(d(x0)) Ad(Right2(x0))
Right3(d(x0)) Ad(Right3(x0))
Right4(d(x0)) Ad(Right4(x0))
Right5(d(x0)) Ad(Right5(x0))
Right6(d(x0)) Ad(Right6(x0))
Right7(d(x0)) Ad(Right7(x0))
Right8(d(x0)) Ad(Right8(x0))
Right9(d(x0)) Ad(Right9(x0))
Right10(d(x0)) Ad(Right10(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Ad(Left(x0)) Left(d(x0))
Wait(Left(x0)) Begin(x0)
a(a(x0)) a(b(a(b(a(x0)))))
c(a(x0)) a(b(a(a(c(x0)))))
b(b(b(x0))) a(b(x0))
c(b(x0)) a(a(c(x0)))
c(b(x0)) b(a(d(x0)))
d(d(x0)) d(b(d(b(d(x0)))))
c(c(x0)) c(d(c(x0)))
a(a(a(x0))) a(b(b(x0)))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(a(x0)) Wait(Right1(x0))
Begin(a(x0)) Wait(Right2(x0))
Begin(b(b(x0))) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Begin(b(x0)) Wait(Right5(x0))
Begin(b(x0)) Wait(Right6(x0))
Begin(d(x0)) Wait(Right7(x0))
Begin(c(x0)) Wait(Right8(x0))
Begin(a(a(x0))) Wait(Right9(x0))
Begin(a(x0)) Wait(Right10(x0))
Right1(a(End(x0))) Left(a(b(a(b(a(End(x0)))))))
Right2(c(End(x0))) Left(a(b(a(a(c(End(x0)))))))
Right3(b(End(x0))) Left(a(b(End(x0))))
Right4(b(b(End(x0)))) Left(a(b(End(x0))))
Right5(c(End(x0))) Left(a(a(c(End(x0)))))
Right6(c(End(x0))) Left(b(a(d(End(x0)))))
Right7(d(End(x0))) Left(d(b(d(b(d(End(x0)))))))
Right8(c(End(x0))) Left(c(d(c(End(x0)))))
Right9(a(End(x0))) Left(a(b(b(End(x0)))))
Right10(a(a(End(x0)))) Left(a(b(b(End(x0)))))
Right1(a(x0)) Aa(Right1(x0))
Right2(a(x0)) Aa(Right2(x0))
Right3(a(x0)) Aa(Right3(x0))
Right4(a(x0)) Aa(Right4(x0))
Right5(a(x0)) Aa(Right5(x0))
Right6(a(x0)) Aa(Right6(x0))
Right7(a(x0)) Aa(Right7(x0))
Right8(a(x0)) Aa(Right8(x0))
Right9(a(x0)) Aa(Right9(x0))
Right10(a(x0)) Aa(Right10(x0))
Right1(b(x0)) Ab(Right1(x0))
Right2(b(x0)) Ab(Right2(x0))
Right3(b(x0)) Ab(Right3(x0))
Right4(b(x0)) Ab(Right4(x0))
Right5(b(x0)) Ab(Right5(x0))
Right6(b(x0)) Ab(Right6(x0))
Right7(b(x0)) Ab(Right7(x0))
Right8(b(x0)) Ab(Right8(x0))
Right9(b(x0)) Ab(Right9(x0))
Right10(b(x0)) Ab(Right10(x0))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(x0))
Right5(c(x0)) Ac(Right5(x0))
Right6(c(x0)) Ac(Right6(x0))
Right7(c(x0)) Ac(Right7(x0))
Right8(c(x0)) Ac(Right8(x0))
Right9(c(x0)) Ac(Right9(x0))
Right10(c(x0)) Ac(Right10(x0))
Right1(d(x0)) Ad(Right1(x0))
Right2(d(x0)) Ad(Right2(x0))
Right3(d(x0)) Ad(Right3(x0))
Right4(d(x0)) Ad(Right4(x0))
Right5(d(x0)) Ad(Right5(x0))
Right6(d(x0)) Ad(Right6(x0))
Right7(d(x0)) Ad(Right7(x0))
Right8(d(x0)) Ad(Right8(x0))
Right9(d(x0)) Ad(Right9(x0))
Right10(d(x0)) Ad(Right10(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Ad(Left(x0)) Left(d(x0))
Wait(Left(x0)) Begin(x0)
a(a(x0)) a(b(a(b(a(x0)))))
c(a(x0)) a(b(a(a(c(x0)))))
b(b(b(x0))) a(b(x0))
c(b(x0)) a(a(c(x0)))
c(b(x0)) b(a(d(x0)))
d(d(x0)) d(b(d(b(d(x0)))))
c(c(x0)) c(d(c(x0)))
a(a(a(x0))) a(b(b(x0)))