NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(b(c(a(x0)))) Wait(Right1(x0))
Begin(c(a(x0))) Wait(Right2(x0))
Begin(a(x0)) Wait(Right3(x0))
Begin(f(f(x0))) Wait(Right4(x0))
Begin(f(x0)) Wait(Right5(x0))
Begin(g(x0)) Wait(Right6(x0))
Begin(a(c(x0))) Wait(Right7(x0))
Begin(c(x0)) Wait(Right8(x0))
Right1(a(End(x0))) Left(b(a(c(b(a(b(End(x0))))))))
Right2(a(b(End(x0)))) Left(b(a(c(b(a(b(End(x0))))))))
Right3(a(b(c(End(x0))))) Left(b(a(c(b(a(b(End(x0))))))))
Right4(a(End(x0))) Left(g(End(x0)))
Right5(a(f(End(x0)))) Left(g(End(x0)))
Right6(b(End(x0))) Left(g(b(End(x0))))
Right7(c(End(x0))) Left(b(c(a(b(c(End(x0)))))))
Right8(c(a(End(x0)))) Left(b(c(a(b(c(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))
Right7(a(x0)) Aa(Right7(x0))
Right8(a(x0)) Aa(Right8(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))
Right7(b(x0)) Ab(Right7(x0))
Right8(b(x0)) Ab(Right8(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))
Right7(c(x0)) Ac(Right7(x0))
Right8(c(x0)) Ac(Right8(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))
Right7(f(x0)) Af(Right7(x0))
Right8(f(x0)) Af(Right8(x0))
Right1(g(x0)) Ag(Right1(x0))
Right2(g(x0)) Ag(Right2(x0))
Right3(g(x0)) Ag(Right3(x0))
Right4(g(x0)) Ag(Right4(x0))
Right5(g(x0)) Ag(Right5(x0))
Right6(g(x0)) Ag(Right6(x0))
Right7(g(x0)) Ag(Right7(x0))
Right8(g(x0)) Ag(Right8(x0))
Aa(Left(x0)) Left(a(x0))
Ab(Left(x0)) Left(b(x0))
Ac(Left(x0)) Left(c(x0))
Af(Left(x0)) Left(f(x0))
Ag(Left(x0)) Left(g(x0))
Wait(Left(x0)) Begin(x0)
a(b(c(a(x0)))) b(a(c(b(a(b(x0))))))
a(f(f(x0))) g(x0)
b(g(x0)) g(b(x0))
c(x0) f(f(x0))
c(a(c(x0))) b(c(a(b(c(x0)))))
g(x0) c(a(x0))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(g(b(End(x20006))))
ε Wait(Right6(b(End(x20006))))
1 Wait(Left(g(b(End(x20006)))))
ε Begin(g(b(End(x20006))))
= t3
where t3 = t0σ and σ = {x20006/x20006}