MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(b(b(x0)))) Wait(Right1(x0))
Begin(b(b(x0))) Wait(Right2(x0))
Begin(b(x0)) Wait(Right3(x0))
Begin(a(b(b(a(b(x0)))))) Wait(Right4(x0))
Begin(b(b(a(b(x0))))) Wait(Right5(x0))
Begin(b(a(b(x0)))) Wait(Right6(x0))
Begin(a(b(x0))) Wait(Right7(x0))
Begin(b(x0)) Wait(Right8(x0))
Right1(b(End(x0))) Left(b(b(b(a(b(End(x0)))))))
Right2(b(b(End(x0)))) Left(b(b(b(a(b(End(x0)))))))
Right3(b(b(b(End(x0))))) Left(b(b(b(a(b(End(x0)))))))
Right4(b(End(x0))) Left(b(b(a(b(b(End(x0)))))))
Right5(b(a(End(x0)))) Left(b(b(a(b(b(End(x0)))))))
Right6(b(a(b(End(x0))))) Left(b(b(a(b(b(End(x0)))))))
Right7(b(a(b(b(End(x0)))))) Left(b(b(a(b(b(End(x0)))))))
Right8(b(a(b(b(a(End(x0))))))) Left(b(b(a(b(b(End(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))
Right7(b(x0)) Ab(Right7(x0))
Right8(b(x0)) Ab(Right8(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))
Right7(a(x0)) Aa(Right7(x0))
Right8(a(x0)) Aa(Right8(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Wait(Left(x0)) Begin(x0)
b(b(b(b(x0)))) b(b(b(a(b(x0)))))
b(a(b(b(a(b(x0)))))) b(b(a(b(b(x0)))))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(b(b(b(x0)))) Wait(Right1(x0))
Begin(b(b(x0))) Wait(Right2(x0))
Begin(b(x0)) Wait(Right3(x0))
Begin(a(b(b(a(b(x0)))))) Wait(Right4(x0))
Begin(b(b(a(b(x0))))) Wait(Right5(x0))
Begin(b(a(b(x0)))) Wait(Right6(x0))
Begin(a(b(x0))) Wait(Right7(x0))
Begin(b(x0)) Wait(Right8(x0))
Right1(b(End(x0))) Left(b(b(b(a(b(End(x0)))))))
Right2(b(b(End(x0)))) Left(b(b(b(a(b(End(x0)))))))
Right3(b(b(b(End(x0))))) Left(b(b(b(a(b(End(x0)))))))
Right4(b(End(x0))) Left(b(b(a(b(b(End(x0)))))))
Right5(b(a(End(x0)))) Left(b(b(a(b(b(End(x0)))))))
Right6(b(a(b(End(x0))))) Left(b(b(a(b(b(End(x0)))))))
Right7(b(a(b(b(End(x0)))))) Left(b(b(a(b(b(End(x0)))))))
Right8(b(a(b(b(a(End(x0))))))) Left(b(b(a(b(b(End(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))
Right7(b(x0)) Ab(Right7(x0))
Right8(b(x0)) Ab(Right8(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))
Right7(a(x0)) Aa(Right7(x0))
Right8(a(x0)) Aa(Right8(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Wait(Left(x0)) Begin(x0)
b(b(b(b(x0)))) b(b(b(a(b(x0)))))
b(a(b(b(a(b(x0)))))) b(b(a(b(b(x0)))))