NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(a(a(x0))) Wait(Right1(x0))
Begin(a(x0)) Wait(Right2(x0))
Begin(a(x0)) Wait(Right3(x0))
Begin(c(a(x0))) Wait(Right4(x0))
Begin(a(x0)) Wait(Right5(x0))
Begin(b(x0)) Wait(Right6(x0))
Begin(d(x0)) Wait(Right7(x0))
Begin(a(x0)) Wait(Right8(x0))
Right1(b(End(x0))) Left(a(b(c(End(x0)))))
Right2(b(a(End(x0)))) Left(a(b(c(End(x0)))))
Right3(c(End(x0))) Left(a(c(End(x0))))
Right4(b(End(x0))) Left(a(b(c(End(x0)))))
Right5(b(c(End(x0)))) Left(a(b(c(End(x0)))))
Right6(c(End(x0))) Left(d(End(x0)))
Right7(a(End(x0))) Left(d(a(End(x0))))
Right8(a(End(x0))) Left(a(b(a(End(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(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(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(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))
Right7(d(x0)) Ad(Right7(x0))
Right8(d(x0)) Ad(Right8(x0))
Ab(Left(x0)) Left(b(x0))
Aa(Left(x0)) Left(a(x0))
Ac(Left(x0)) Left(c(x0))
Ad(Left(x0)) Left(d(x0))
Wait(Left(x0)) Begin(x0)
b(a(a(x0))) a(b(c(x0)))
c(a(x0)) a(c(x0))
b(c(a(x0))) a(b(c(x0)))
c(b(x0)) d(x0)
d(x0) b(a(x0))
a(d(x0)) d(a(x0))
a(a(x0)) a(b(a(x0)))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(a(c(End(x10931))))
ε Wait(Right3(c(End(x10931))))
1 Wait(Left(a(c(End(x10931)))))
ε Begin(a(c(End(x10931))))
= t3
where t3 = t0σ and σ = {x10931/x10931}