NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(2(1(x0))) → Wait(Right1(x0))
Begin(1(x0)) → Wait(Right2(x0))
Begin(2(1(x0))) → Wait(Right3(x0))
Begin(1(x0)) → Wait(Right4(x0))
Begin(2(0(x0))) → Wait(Right5(x0))
Begin(0(x0)) → Wait(Right6(x0))
Begin(2(0(x0))) → Wait(Right7(x0))
Begin(0(x0)) → Wait(Right8(x0))
Right1(1(End(x0))) → Left(2(0(2(End(x0)))))
Right2(1(2(End(x0)))) → Left(2(0(2(End(x0)))))
Right3(0(End(x0))) → Left(1(0(2(End(x0)))))
Right4(0(2(End(x0)))) → Left(1(0(2(End(x0)))))
Right5(1(End(x0))) → Left(2(0(1(End(x0)))))
Right6(1(2(End(x0)))) → Left(2(0(1(End(x0)))))
Right7(0(End(x0))) → Left(1(0(1(End(x0)))))
Right8(0(2(End(x0)))) → Left(1(0(1(End(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))
Right7(1(x0)) → A1(Right7(x0))
Right8(1(x0)) → A1(Right8(x0))
Right1(2(x0)) → A2(Right1(x0))
Right2(2(x0)) → A2(Right2(x0))
Right3(2(x0)) → A2(Right3(x0))
Right4(2(x0)) → A2(Right4(x0))
Right5(2(x0)) → A2(Right5(x0))
Right6(2(x0)) → A2(Right6(x0))
Right7(2(x0)) → A2(Right7(x0))
Right8(2(x0)) → A2(Right8(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))
Right7(0(x0)) → A0(Right7(x0))
Right8(0(x0)) → A0(Right8(x0))
A1(Left(x0)) → Left(1(x0))
A2(Left(x0)) → Left(2(x0))
A0(Left(x0)) → Left(0(x0))
Wait(Left(x0)) → Begin(x0)
1(2(1(x0))) → 2(0(2(x0)))
0(2(1(x0))) → 1(0(2(x0)))
1(2(0(x0))) → 2(0(1(x0)))
0(2(0(x0))) → 1(0(1(x0)))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(1(0(2(End(x8412)))))
→ε Wait(Right4(0(2(End(x8412)))))
→1 Wait(Left(1(0(2(End(x8412))))))
→ε Begin(1(0(2(End(x8412)))))
= t3
where t3 = t0σ and σ = {x8412/x8412}