NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(1(x0)) Wait(Right1(x0))
Begin(2(x0)) Wait(Right2(x0))
Begin(2(x0)) Wait(Right3(x0))
Begin(3(x0)) Wait(Right4(x0))
Begin(4(x0)) Wait(Right5(x0))
Begin(4(x0)) Wait(Right6(x0))
Begin(5(x0)) Wait(Right7(x0))
Begin(6(x0)) Wait(Right8(x0))
Begin(6(x0)) Wait(Right9(x0))
Right1(1(End(x0))) Left(4(3(End(x0))))
Right2(1(End(x0))) Left(2(1(End(x0))))
Right3(2(End(x0))) Left(1(1(1(End(x0)))))
Right4(3(End(x0))) Left(5(6(End(x0))))
Right5(3(End(x0))) Left(1(1(End(x0))))
Right6(4(End(x0))) Left(3(End(x0)))
Right7(5(End(x0))) Left(6(2(End(x0))))
Right8(5(End(x0))) Left(1(2(End(x0))))
Right9(6(End(x0))) Left(2(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))
Right9(1(x0)) A1(Right9(x0))
Right1(4(x0)) A4(Right1(x0))
Right2(4(x0)) A4(Right2(x0))
Right3(4(x0)) A4(Right3(x0))
Right4(4(x0)) A4(Right4(x0))
Right5(4(x0)) A4(Right5(x0))
Right6(4(x0)) A4(Right6(x0))
Right7(4(x0)) A4(Right7(x0))
Right8(4(x0)) A4(Right8(x0))
Right9(4(x0)) A4(Right9(x0))
Right1(3(x0)) A3(Right1(x0))
Right2(3(x0)) A3(Right2(x0))
Right3(3(x0)) A3(Right3(x0))
Right4(3(x0)) A3(Right4(x0))
Right5(3(x0)) A3(Right5(x0))
Right6(3(x0)) A3(Right6(x0))
Right7(3(x0)) A3(Right7(x0))
Right8(3(x0)) A3(Right8(x0))
Right9(3(x0)) A3(Right9(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))
Right9(2(x0)) A2(Right9(x0))
Right1(5(x0)) A5(Right1(x0))
Right2(5(x0)) A5(Right2(x0))
Right3(5(x0)) A5(Right3(x0))
Right4(5(x0)) A5(Right4(x0))
Right5(5(x0)) A5(Right5(x0))
Right6(5(x0)) A5(Right6(x0))
Right7(5(x0)) A5(Right7(x0))
Right8(5(x0)) A5(Right8(x0))
Right9(5(x0)) A5(Right9(x0))
Right1(6(x0)) A6(Right1(x0))
Right2(6(x0)) A6(Right2(x0))
Right3(6(x0)) A6(Right3(x0))
Right4(6(x0)) A6(Right4(x0))
Right5(6(x0)) A6(Right5(x0))
Right6(6(x0)) A6(Right6(x0))
Right7(6(x0)) A6(Right7(x0))
Right8(6(x0)) A6(Right8(x0))
Right9(6(x0)) A6(Right9(x0))
A1(Left(x0)) Left(1(x0))
A4(Left(x0)) Left(4(x0))
A3(Left(x0)) Left(3(x0))
A2(Left(x0)) Left(2(x0))
A5(Left(x0)) Left(5(x0))
A6(Left(x0)) Left(6(x0))
Wait(Left(x0)) Begin(x0)
1(1(x0)) 4(3(x0))
1(2(x0)) 2(1(x0))
2(2(x0)) 1(1(1(x0)))
3(3(x0)) 5(6(x0))
3(4(x0)) 1(1(x0))
4(4(x0)) 3(x0)
5(5(x0)) 6(2(x0))
5(6(x0)) 1(2(x0))
6(6(x0)) 2(1(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(2(1(End(x19283))))
ε Wait(Right2(1(End(x19283))))
1 Wait(Left(2(1(End(x19283)))))
ε Begin(2(1(End(x19283))))
= t3
where t3 = t0σ and σ = {x19283/x19283}