NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

B(x0) → W(M(V(x0)))
M(x0) → x0
M(V(a(x0))) → V(Xa(x0))
M(V(b(x0))) → V(Xb(x0))
Xa(a(x0)) → a(Xa(x0))
Xa(b(x0)) → b(Xa(x0))
Xb(a(x0)) → a(Xb(x0))
Xb(b(x0)) → b(Xb(x0))
Xa(E(x0)) → a(E(x0))
Xb(E(x0)) → b(E(x0))
W(V(x0)) → R(L(x0))
L(a(x0)) → Ya(L(x0))
L(b(x0)) → Yb(L(x0))
L(a(b(x0))) → D(b(a(x0)))
Ya(D(x0)) → D(a(x0))
Yb(D(x0)) → D(b(x0))
R(D(x0)) → B(x0)

Proof

1 Loop

The following loop proves nontermination.

t0 = B(b(a(E(x88704))))
→ε W(M(V(b(a(E(x88704))))))
→1 W(V(Xb(a(E(x88704)))))
→ε R(L(Xb(a(E(x88704)))))
→1.1 R(L(a(Xb(E(x88704)))))
→1.1.1 R(L(a(b(E(x88704)))))
→1 R(D(b(a(E(x88704)))))
→ε B(b(a(E(x88704))))
= t7
where t7 = t0σ and σ = {x88704/x88704}