NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(*(x0)) Wait(Right1(x0))
Begin(*(x0)) Wait(Right2(x0))
Begin(0(x0)) Wait(Right3(x0))
Begin(1(x0)) Wait(Right4(x0))
Begin($(x0)) Wait(Right5(x0))
Begin(#(x0)) Wait(Right6(x0))
Begin(*(x0)) Wait(Right7(x0))
Right1(0(End(x0))) Left(*(1(End(x0))))
Right2(1(End(x0))) Left(0(#(End(x0))))
Right3(#(End(x0))) Left(0(#(End(x0))))
Right4(#(End(x0))) Left(1(#(End(x0))))
Right5(#(End(x0))) Left(*($(End(x0))))
Right6(#(End(x0))) Left(#(End(x0)))
Right7(#(End(x0))) Left(*(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))
Right7(0(x0)) A0(Right7(x0))
Right1(*(x0)) A*(Right1(x0))
Right2(*(x0)) A*(Right2(x0))
Right3(*(x0)) A*(Right3(x0))
Right4(*(x0)) A*(Right4(x0))
Right5(*(x0)) A*(Right5(x0))
Right6(*(x0)) A*(Right6(x0))
Right7(*(x0)) A*(Right7(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))
Right1(#(x0)) A#(Right1(x0))
Right2(#(x0)) A#(Right2(x0))
Right3(#(x0)) A#(Right3(x0))
Right4(#(x0)) A#(Right4(x0))
Right5(#(x0)) A#(Right5(x0))
Right6(#(x0)) A#(Right6(x0))
Right7(#(x0)) A#(Right7(x0))
Right1($(x0)) A$(Right1(x0))
Right2($(x0)) A$(Right2(x0))
Right3($(x0)) A$(Right3(x0))
Right4($(x0)) A$(Right4(x0))
Right5($(x0)) A$(Right5(x0))
Right6($(x0)) A$(Right6(x0))
Right7($(x0)) A$(Right7(x0))
A0(Left(x0)) Left(0(x0))
A*(Left(x0)) Left(*(x0))
A1(Left(x0)) Left(1(x0))
A#(Left(x0)) Left(#(x0))
A$(Left(x0)) Left($(x0))
Wait(Left(x0)) Begin(x0)
0(*(x0)) *(1(x0))
1(*(x0)) 0(#(x0))
#(0(x0)) 0(#(x0))
#(1(x0)) 1(#(x0))
#($(x0)) *($(x0))
#(#(x0)) #(x0)
#(*(x0)) *(x0)

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(0(#(End(x11046))))
ε Wait(Right3(#(End(x11046))))
1 Wait(Left(0(#(End(x11046)))))
ε Begin(0(#(End(x11046))))
= t3
where t3 = t0σ and σ = {x11046/x11046}