MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(b(x0))) Wait(Right1(x0))
Begin(b(x0)) Wait(Right2(x0))
Begin(b(x0)) Wait(Right3(x0))
Right1(a(End(x0))) Left(b(a(b(c(a(End(x0)))))))
Right2(a(a(End(x0)))) Left(b(a(b(c(a(End(x0)))))))
Right3(c(End(x0))) Left(a(End(x0)))
Right1(a(x0)) Aa(Right1(x0))
Right2(a(x0)) Aa(Right2(x0))
Right3(a(x0)) Aa(Right3(x0))
Right1(b(x0)) Ab(Right1(x0))
Right2(b(x0)) Ab(Right2(x0))
Right3(b(x0)) Ab(Right3(x0))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Wait(Left(x0)) Begin(x0)
a(x0) x0
a(a(b(x0))) b(a(b(c(a(x0)))))
c(b(x0)) a(x0)

Proof

1 Termination Assumption

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