NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(x0)) Wait(Right1(x0))
Begin(c(x0)) Wait(Right2(x0))
Begin(d(x0)) Wait(Right3(x0))
Begin(f(x0)) Wait(Right4(x0))
Begin(d(x0)) Wait(Right5(x0))
Begin(f(x0)) Wait(Right6(x0))
Right1(a(End(x0))) Left(b(d(End(x0))))
Right2(a(End(x0))) Left(d(d(d(End(x0)))))
Right3(b(End(x0))) Left(a(c(b(End(x0)))))
Right4(c(End(x0))) Left(d(d(c(End(x0)))))
Right5(d(End(x0))) Left(f(End(x0)))
Right6(f(End(x0))) Left(a(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))
Right5(a(x0)) Aa(Right5(x0))
Right6(a(x0)) Aa(Right6(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))
Right5(b(x0)) Ab(Right5(x0))
Right6(b(x0)) Ab(Right6(x0))
Right1(d(x0)) Ad(Right1(x0))
Right2(d(x0)) Ad(Right2(x0))
Right3(d(x0)) Ad(Right3(x0))
Right4(d(x0)) Ad(Right4(x0))
Right5(d(x0)) Ad(Right5(x0))
Right6(d(x0)) Ad(Right6(x0))
Right1(c(x0)) Ac(Right1(x0))
Right2(c(x0)) Ac(Right2(x0))
Right3(c(x0)) Ac(Right3(x0))
Right4(c(x0)) Ac(Right4(x0))
Right5(c(x0)) Ac(Right5(x0))
Right6(c(x0)) Ac(Right6(x0))
Right1(f(x0)) Af(Right1(x0))
Right2(f(x0)) Af(Right2(x0))
Right3(f(x0)) Af(Right3(x0))
Right4(f(x0)) Af(Right4(x0))
Right5(f(x0)) Af(Right5(x0))
Right6(f(x0)) Af(Right6(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ad(Left(x0)) Left(d(x0))
Ac(Left(x0)) Left(c(x0))
Af(Left(x0)) Left(f(x0))
Wait(Left(x0)) Begin(x0)
a(b(x0)) b(d(x0))
a(c(x0)) d(d(d(x0)))
b(d(x0)) a(c(b(x0)))
c(f(x0)) d(d(c(x0)))
d(d(x0)) f(x0)
f(f(x0)) a(x0)

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(f(c(End(x84358))))
ε Wait(Right4(c(End(x84358))))
1 Wait(Left(d(d(c(End(x84358))))))
ε Begin(d(d(c(End(x84358)))))
1 Begin(f(c(End(x84358))))
= t4
where t4 = t0σ and σ = {x84358/x84358}