MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(x0)) Wait(Right1(x0))
Begin(a(x0)) Wait(Right2(x0))
Begin(a(x0)) Wait(Right3(x0))
Begin(b(x0)) Wait(Right4(x0))
Right1(A(End(x0))) Left(b(a(B(A(End(x0))))))
Right2(B(End(x0))) Left(a(b(A(B(End(x0))))))
Right3(A(End(x0))) Left(End(x0))
Right4(B(End(x0))) Left(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))
Right1(b(x0)) Ab(Right1(x0))
Right2(b(x0)) Ab(Right2(x0))
Right3(b(x0)) Ab(Right3(x0))
Right4(b(x0)) Ab(Right4(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))
Right1(B(x0)) AB(Right1(x0))
Right2(B(x0)) AB(Right2(x0))
Right3(B(x0)) AB(Right3(x0))
Right4(B(x0)) AB(Right4(x0))
AA(Left(x0)) Left(A(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
AB(Left(x0)) Left(B(x0))
Wait(Left(x0)) Begin(x0)
A(b(x0)) b(a(B(A(x0))))
B(a(x0)) a(b(A(B(x0))))
A(a(x0)) x0
B(b(x0)) x0

Proof

1 Termination Assumption

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