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(b(x0)) → Wait(Right2(x0))
Begin(c(x0)) → Wait(Right3(x0))
Begin(d(x0)) → Wait(Right4(x0))
Begin(f(x0)) → Wait(Right5(x0))
Begin(g(x0)) → Wait(Right6(x0))
Right1(a(End(x0))) → Left(b(c(End(x0))))
Right2(b(End(x0))) → Left(c(d(End(x0))))
Right3(c(End(x0))) → Left(d(f(End(x0))))
Right4(d(End(x0))) → Left(f(f(f(End(x0)))))
Right5(f(End(x0))) → Left(g(a(End(x0))))
Right6(g(End(x0))) → Left(a(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(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))
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))
Right1(f(x0)) → Af(Right1(x0))
Right2(f(x0)) → Af(Right2(x0))
Right3(f(x0)) → Af(Right3(x0))
Right4(f(x0)) → Af(Right4(x0))
Right5(f(x0)) → Af(Right5(x0))
Right6(f(x0)) → Af(Right6(x0))
Right1(g(x0)) → Ag(Right1(x0))
Right2(g(x0)) → Ag(Right2(x0))
Right3(g(x0)) → Ag(Right3(x0))
Right4(g(x0)) → Ag(Right4(x0))
Right5(g(x0)) → Ag(Right5(x0))
Right6(g(x0)) → Ag(Right6(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))
Af(Left(x0)) → Left(f(x0))
Ag(Left(x0)) → Left(g(x0))
Wait(Left(x0)) → Begin(x0)
a(a(x0)) → b(c(x0))
b(b(x0)) → c(d(x0))
b(x0) → a(x0)
c(c(x0)) → d(f(x0))
d(d(x0)) → f(f(f(x0)))
d(x0) → b(x0)
f(f(x0)) → g(a(x0))
g(g(x0)) → a(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(a(x0)) → Wait(Right1(x0))
Begin(b(x0)) → Wait(Right2(x0))
Begin(c(x0)) → Wait(Right3(x0))
Begin(d(x0)) → Wait(Right4(x0))
Begin(f(x0)) → Wait(Right5(x0))
Begin(g(x0)) → Wait(Right6(x0))
Right1(a(End(x0))) → Left(b(c(End(x0))))
Right2(b(End(x0))) → Left(c(d(End(x0))))
Right3(c(End(x0))) → Left(d(f(End(x0))))
Right4(d(End(x0))) → Left(f(f(f(End(x0)))))
Right5(f(End(x0))) → Left(g(a(End(x0))))
Right6(g(End(x0))) → Left(a(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(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))
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))
Right1(f(x0)) → Af(Right1(x0))
Right2(f(x0)) → Af(Right2(x0))
Right3(f(x0)) → Af(Right3(x0))
Right4(f(x0)) → Af(Right4(x0))
Right5(f(x0)) → Af(Right5(x0))
Right6(f(x0)) → Af(Right6(x0))
Right1(g(x0)) → Ag(Right1(x0))
Right2(g(x0)) → Ag(Right2(x0))
Right3(g(x0)) → Ag(Right3(x0))
Right4(g(x0)) → Ag(Right4(x0))
Right5(g(x0)) → Ag(Right5(x0))
Right6(g(x0)) → Ag(Right6(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))
Af(Left(x0)) → Left(f(x0))
Ag(Left(x0)) → Left(g(x0))
Wait(Left(x0)) → Begin(x0)
a(a(x0)) → b(c(x0))
b(b(x0)) → c(d(x0))
b(x0) → a(x0)
c(c(x0)) → d(f(x0))
d(d(x0)) → f(f(f(x0)))
d(x0) → b(x0)
f(f(x0)) → g(a(x0))
g(g(x0)) → a(x0)