MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(0(x0)) Wait(Right1(x0))
Begin(0(x0)) Wait(Right2(x0))
Begin(s(x0)) Wait(Right3(x0))
Begin(s(x0)) Wait(Right4(x0))
Right1(f(End(x0))) Left(s(0(End(x0))))
Right2(d(End(x0))) Left(0(End(x0)))
Right3(d(End(x0))) Left(s(s(d(End(x0)))))
Right4(f(End(x0))) Left(d(f(End(x0))))
Right1(f(x0)) Af(Right1(x0))
Right2(f(x0)) Af(Right2(x0))
Right3(f(x0)) Af(Right3(x0))
Right4(f(x0)) Af(Right4(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))
Right1(s(x0)) As(Right1(x0))
Right2(s(x0)) As(Right2(x0))
Right3(s(x0)) As(Right3(x0))
Right4(s(x0)) As(Right4(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))
Af(Left(x0)) Left(f(x0))
A0(Left(x0)) Left(0(x0))
As(Left(x0)) Left(s(x0))
Ad(Left(x0)) Left(d(x0))
Wait(Left(x0)) Begin(x0)
f(0(x0)) s(0(x0))
d(0(x0)) 0(x0)
d(s(x0)) s(s(d(x0)))
f(s(x0)) d(f(x0))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(0(x0)) Wait(Right1(x0))
Begin(0(x0)) Wait(Right2(x0))
Begin(s(x0)) Wait(Right3(x0))
Begin(s(x0)) Wait(Right4(x0))
Right1(f(End(x0))) Left(s(0(End(x0))))
Right2(d(End(x0))) Left(0(End(x0)))
Right3(d(End(x0))) Left(s(s(d(End(x0)))))
Right4(f(End(x0))) Left(d(f(End(x0))))
Right1(f(x0)) Af(Right1(x0))
Right2(f(x0)) Af(Right2(x0))
Right3(f(x0)) Af(Right3(x0))
Right4(f(x0)) Af(Right4(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))
Right1(s(x0)) As(Right1(x0))
Right2(s(x0)) As(Right2(x0))
Right3(s(x0)) As(Right3(x0))
Right4(s(x0)) As(Right4(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))
Af(Left(x0)) Left(f(x0))
A0(Left(x0)) Left(0(x0))
As(Left(x0)) Left(s(x0))
Ad(Left(x0)) Left(d(x0))
Wait(Left(x0)) Begin(x0)
f(0(x0)) s(0(x0))
d(0(x0)) 0(x0)
d(s(x0)) s(s(d(x0)))
f(s(x0)) d(f(x0))