MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(0(0(0(x0)))) Wait(Right1(x0))
Begin(0(0(x0))) Wait(Right2(x0))
Begin(0(x0)) Wait(Right3(x0))
Begin(0(0(1(x0)))) Wait(Right4(x0))
Begin(0(1(x0))) Wait(Right5(x0))
Begin(1(x0)) Wait(Right6(x0))
Right1(0(End(x0))) Left(0(0(0(1(End(x0))))))
Right2(0(0(End(x0)))) Left(0(0(0(1(End(x0))))))
Right3(0(0(0(End(x0))))) Left(0(0(0(1(End(x0))))))
Right4(1(End(x0))) Left(0(1(0(0(End(x0))))))
Right5(1(0(End(x0)))) Left(0(1(0(0(End(x0))))))
Right6(1(0(0(End(x0))))) Left(0(1(0(0(End(x0))))))
Right1(0(x0)) A0(Right1(x0))
Right2(0(x0)) A0(Right2(x0))
Right3(0(x0)) A0(Right3(x0))
Right4(0(x0)) A0(Right4(x0))
Right5(0(x0)) A0(Right5(x0))
Right6(0(x0)) A0(Right6(x0))
Right1(1(x0)) A1(Right1(x0))
Right2(1(x0)) A1(Right2(x0))
Right3(1(x0)) A1(Right3(x0))
Right4(1(x0)) A1(Right4(x0))
Right5(1(x0)) A1(Right5(x0))
Right6(1(x0)) A1(Right6(x0))
A0(Left(x0)) Left(0(x0))
A1(Left(x0)) Left(1(x0))
Wait(Left(x0)) Begin(x0)
0(0(0(0(x0)))) 0(0(0(1(x0))))
1(0(0(1(x0)))) 0(1(0(0(x0))))

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(0(0(0(x0)))) Wait(Right1(x0))
Begin(0(0(x0))) Wait(Right2(x0))
Begin(0(x0)) Wait(Right3(x0))
Begin(0(0(1(x0)))) Wait(Right4(x0))
Begin(0(1(x0))) Wait(Right5(x0))
Begin(1(x0)) Wait(Right6(x0))
Right1(0(End(x0))) Left(0(0(0(1(End(x0))))))
Right2(0(0(End(x0)))) Left(0(0(0(1(End(x0))))))
Right3(0(0(0(End(x0))))) Left(0(0(0(1(End(x0))))))
Right4(1(End(x0))) Left(0(1(0(0(End(x0))))))
Right5(1(0(End(x0)))) Left(0(1(0(0(End(x0))))))
Right6(1(0(0(End(x0))))) Left(0(1(0(0(End(x0))))))
Right1(0(x0)) A0(Right1(x0))
Right2(0(x0)) A0(Right2(x0))
Right3(0(x0)) A0(Right3(x0))
Right4(0(x0)) A0(Right4(x0))
Right5(0(x0)) A0(Right5(x0))
Right6(0(x0)) A0(Right6(x0))
Right1(1(x0)) A1(Right1(x0))
Right2(1(x0)) A1(Right2(x0))
Right3(1(x0)) A1(Right3(x0))
Right4(1(x0)) A1(Right4(x0))
Right5(1(x0)) A1(Right5(x0))
Right6(1(x0)) A1(Right6(x0))
A0(Left(x0)) Left(0(x0))
A1(Left(x0)) Left(1(x0))
Wait(Left(x0)) Begin(x0)
0(0(0(0(x0)))) 0(0(0(1(x0))))
1(0(0(1(x0)))) 0(1(0(0(x0))))