MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(d(x0)) Wait(Right1(x0))
Begin(d(b(x0))) Wait(Right2(x0))
Begin(b(x0)) Wait(Right3(x0))
Begin(f(x0)) Wait(Right4(x0))
Right1(a(End(x0))) Left(d(b(c(b(d(End(x0)))))))
Right2(b(End(x0))) Left(a(d(End(x0))))
Right3(b(d(End(x0)))) Left(a(d(End(x0))))
Right4(d(End(x0))) Left(b(d(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))
Right1(d(x0)) Ad(Right1(x0))
Right2(d(x0)) Ad(Right2(x0))
Right3(d(x0)) Ad(Right3(x0))
Right4(d(x0)) Ad(Right4(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))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(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))
Aa(Left(x0)) Left(a(x0))
Ad(Left(x0)) Left(d(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Af(Left(x0)) Left(f(x0))
Wait(Left(x0)) Begin(x0)
a(d(x0)) d(b(c(b(d(x0)))))
a(x0) b(b(f(b(b(x0)))))
b(d(b(x0))) a(d(x0))
d(f(x0)) b(d(x0))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(d(x0)) Wait(Right1(x0))
Begin(d(b(x0))) Wait(Right2(x0))
Begin(b(x0)) Wait(Right3(x0))
Begin(f(x0)) Wait(Right4(x0))
Right1(a(End(x0))) Left(d(b(c(b(d(End(x0)))))))
Right2(b(End(x0))) Left(a(d(End(x0))))
Right3(b(d(End(x0)))) Left(a(d(End(x0))))
Right4(d(End(x0))) Left(b(d(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))
Right1(d(x0)) Ad(Right1(x0))
Right2(d(x0)) Ad(Right2(x0))
Right3(d(x0)) Ad(Right3(x0))
Right4(d(x0)) Ad(Right4(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))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(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))
Aa(Left(x0)) Left(a(x0))
Ad(Left(x0)) Left(d(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Af(Left(x0)) Left(f(x0))
Wait(Left(x0)) Begin(x0)
a(d(x0)) d(b(c(b(d(x0)))))
a(x0) b(b(f(b(b(x0)))))
b(d(b(x0))) a(d(x0))
d(f(x0)) b(d(x0))