MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(s(x0)) Wait(Right1(x0))
Begin(s(x0)) Wait(Right2(x0))
Begin(s(x0)) Wait(Right3(x0))
Begin(p(s(x0))) Wait(Right4(x0))
Begin(s(x0)) Wait(Right5(x0))
Begin(s(x0)) Wait(Right6(x0))
Right1(a(End(x0))) Left(s(s(s(p(s(b(p(p(s(s(End(x0))))))))))))
Right2(b(End(x0))) Left(s(s(s(p(p(s(s(c(p(s(p(s(End(x0))))))))))))))
Right3(c(End(x0))) Left(p(s(p(s(a(p(s(p(s(End(x0)))))))))))
Right4(p(End(x0))) Left(p(End(x0)))
Right5(p(p(End(x0)))) Left(p(End(x0)))
Right6(p(End(x0))) Left(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))
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))
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))
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))
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))
Aa(Left(x0)) Left(a(x0))
As(Left(x0)) Left(s(x0))
Ap(Left(x0)) Left(p(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
a(s(x0)) s(s(s(p(s(b(p(p(s(s(x0))))))))))
b(s(x0)) s(s(s(p(p(s(s(c(p(s(p(s(x0))))))))))))
c(s(x0)) p(s(p(s(a(p(s(p(s(x0)))))))))
p(p(s(x0))) p(x0)
p(s(x0)) x0

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(s(x0)) Wait(Right1(x0))
Begin(s(x0)) Wait(Right2(x0))
Begin(s(x0)) Wait(Right3(x0))
Begin(p(s(x0))) Wait(Right4(x0))
Begin(s(x0)) Wait(Right5(x0))
Begin(s(x0)) Wait(Right6(x0))
Right1(a(End(x0))) Left(s(s(s(p(s(b(p(p(s(s(End(x0))))))))))))
Right2(b(End(x0))) Left(s(s(s(p(p(s(s(c(p(s(p(s(End(x0))))))))))))))
Right3(c(End(x0))) Left(p(s(p(s(a(p(s(p(s(End(x0)))))))))))
Right4(p(End(x0))) Left(p(End(x0)))
Right5(p(p(End(x0)))) Left(p(End(x0)))
Right6(p(End(x0))) Left(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))
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))
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))
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))
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))
Aa(Left(x0)) Left(a(x0))
As(Left(x0)) Left(s(x0))
Ap(Left(x0)) Left(p(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
a(s(x0)) s(s(s(p(s(b(p(p(s(s(x0))))))))))
b(s(x0)) s(s(s(p(p(s(s(c(p(s(p(s(x0))))))))))))
c(s(x0)) p(s(p(s(a(p(s(p(s(x0)))))))))
p(p(s(x0))) p(x0)
p(s(x0)) x0