MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

We assume termination of the following TRS
B(x0) → W(M(M(V(x0))))
M(x0) → x0
M(V(a(x0))) → V(Xa(x0))
M(V(b(x0))) → V(Xb(x0))
M(V(c(x0))) → V(Xc(x0))
Xa(a(x0)) → a(Xa(x0))
Xa(b(x0)) → b(Xa(x0))
Xa(c(x0)) → c(Xa(x0))
Xb(a(x0)) → a(Xb(x0))
Xb(b(x0)) → b(Xb(x0))
Xb(c(x0)) → c(Xb(x0))
Xc(a(x0)) → a(Xc(x0))
Xc(b(x0)) → b(Xc(x0))
Xc(c(x0)) → c(Xc(x0))
Xa(E(x0)) → a(E(x0))
Xb(E(x0)) → b(E(x0))
Xc(E(x0)) → c(E(x0))
W(V(x0)) → R(L(x0))
L(a(x0)) → Ya(L(x0))
L(b(x0)) → Yb(L(x0))
L(c(x0)) → Yc(L(x0))
L(a(x0)) → D(x0)
L(a(a(a(x0)))) → D(b(x0))
L(b(c(x0))) → D(c(c(a(b(x0)))))
L(c(x0)) → D(x0)
Ya(D(x0)) → D(a(x0))
Yb(D(x0)) → D(b(x0))
Yc(D(x0)) → D(c(x0))
R(D(x0)) → B(x0)