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(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(V(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(1(0(1(0(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(1(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(0(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(0(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(1(0(1(0(0(0(0(0(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(1(0(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(0(1(1(0(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(0(0(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(1(0(1(1(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(1(1(1(1(0(1(1(0(1(0(1(0(0(0(0(0(0(1(0(0(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(1(0(1(1(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(1(1(1(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(0(0(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(0(0(1(1(0(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(1(1(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(0(0(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
R(D(x0)) → B(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
B(x0) → W(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(V(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(1(0(1(0(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(1(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(1(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(1(0(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(0(1(1(0(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(0(0(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(1(0(1(1(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(1(1(1(1(0(1(1(0(1(0(1(0(0(0(0(0(0(1(0(0(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(0(1(1(1(0(0(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(1(0(1(1(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(1(0(1(1(0(0(1(1(1(1(1(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(0(0(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(0(0(1(1(0(1(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(1(1(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(0(0(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
L(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(1(1(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → D(0(0(1(1(0(0(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(1(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
R(D(x0)) → B(x0)