MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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