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(V(x0))))))))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
M(V(2(x0))) → V(X2(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X0(2(x0)) → 2(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X1(2(x0)) → 2(X1(x0))
X2(0(x0)) → 0(X2(x0))
X2(1(x0)) → 1(X2(x0))
X2(2(x0)) → 2(X2(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
X2(E(x0)) → 2(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(2(x0)) → Y2(L(x0))
L(0(0(1(1(0(x0)))))) → D(2(1(2(2(1(0(x0)))))))
L(1(2(2(0(2(x0)))))) → D(1(1(2(1(1(2(x0)))))))
L(0(0(0(2(1(2(x0))))))) → D(2(1(2(1(2(2(1(2(1(x0))))))))))
L(2(0(0(1(2(2(x0))))))) → D(1(2(1(2(1(2(1(x0))))))))
L(2(0(0(2(0(2(x0))))))) → D(2(2(2(2(1(1(1(x0))))))))
L(2(2(2(0(0(2(x0))))))) → D(2(0(2(2(0(2(x0)))))))
L(0(0(1(1(0(0(1(x0)))))))) → D(2(2(2(2(1(2(1(0(x0)))))))))
L(2(1(2(0(2(1(2(0(x0))))))))) → D(2(0(1(0(1(2(1(1(1(1(0(x0))))))))))))
L(1(0(0(1(0(1(1(0(1(x0)))))))))) → D(1(1(2(1(2(1(1(1(2(1(x0)))))))))))
L(1(0(2(0(0(0(0(2(1(x0)))))))))) → D(1(1(2(1(2(1(1(2(1(2(x0)))))))))))
L(2(0(0(0(0(0(2(0(2(x0)))))))))) → D(2(1(2(1(1(0(2(2(1(0(1(1(x0)))))))))))))
L(2(1(1(0(0(1(1(2(2(x0)))))))))) → D(2(1(0(0(2(1(0(1(1(1(x0)))))))))))
L(2(2(1(0(2(0(1(1(0(x0)))))))))) → D(2(2(1(2(1(1(0(0(0(x0))))))))))
L(0(1(0(2(0(1(2(2(2(2(x0))))))))))) → D(0(0(2(2(1(1(1(1(0(0(2(2(x0)))))))))))))
L(2(2(1(0(0(0(2(0(1(1(x0))))))))))) → D(2(1(2(2(0(2(2(1(1(2(1(x0))))))))))))
L(1(0(1(0(2(2(0(0(1(2(2(2(1(x0)))))))))))))) → D(1(0(0(1(0(0(1(0(2(1(2(1(1(2(x0)))))))))))))))
L(2(0(2(0(0(1(1(0(2(2(0(0(0(x0)))))))))))))) → D(2(2(2(2(2(1(1(2(2(2(0(0(0(0(x0)))))))))))))))
L(0(0(0(2(0(0(1(2(1(1(2(0(2(2(x0))))))))))))))) → D(1(0(2(1(1(1(1(2(1(1(2(1(1(1(2(1(2(x0))))))))))))))))))
L(0(2(1(0(2(1(0(0(1(2(1(0(1(2(x0))))))))))))))) → D(1(2(1(2(1(0(0(0(2(1(1(0(1(1(2(x0))))))))))))))))
L(0(2(2(2(1(0(1(0(0(1(0(1(1(0(x0))))))))))))))) → D(1(0(2(2(1(1(2(2(1(2(2(2(0(1(0(x0))))))))))))))))
L(1(2(2(0(0(1(1(1(2(2(2(0(0(1(x0))))))))))))))) → D(2(1(1(0(2(1(0(1(0(1(2(2(1(2(1(x0))))))))))))))))
L(0(1(2(0(0(2(0(0(1(2(2(0(2(1(0(x0)))))))))))))))) → D(2(1(1(2(0(0(1(1(2(2(1(1(1(1(1(0(1(x0))))))))))))))))))
L(0(2(0(2(1(1(1(2(1(1(2(0(0(2(1(x0)))))))))))))))) → D(2(1(1(1(2(0(2(1(1(1(1(0(2(2(1(1(1(2(x0)))))))))))))))))))
L(2(0(0(0(1(1(2(2(1(2(0(1(0(2(2(x0)))))))))))))))) → D(2(1(2(0(1(2(0(0(0(2(1(1(2(2(0(x0))))))))))))))))
L(2(2(0(1(2(1(0(2(2(0(1(1(0(0(1(x0)))))))))))))))) → D(1(1(0(0(2(1(2(1(0(1(1(2(1(1(1(2(x0)))))))))))))))))
L(0(0(0(2(2(0(2(1(2(2(1(0(0(1(1(1(x0))))))))))))))))) → D(0(1(1(0(0(2(0(0(2(1(2(1(1(2(1(1(2(1(x0)))))))))))))))))))
L(0(0(1(0(0(2(2(0(0(2(1(2(1(0(2(1(x0))))))))))))))))) → D(2(2(2(0(2(1(2(2(1(1(0(1(1(2(1(2(1(1(1(2(1(2(x0)))))))))))))))))))))))
L(0(1(2(2(2(2(1(2(1(2(1(0(2(0(1(2(x0))))))))))))))))) → D(0(1(2(1(0(1(2(1(2(2(1(2(2(1(0(1(1(x0))))))))))))))))))
L(2(1(2(0(0(2(1(0(0(1(1(0(0(0(1(2(x0))))))))))))))))) → D(1(1(1(2(1(2(1(0(1(1(1(1(1(0(1(2(2(1(2(x0))))))))))))))))))))
L(0(0(0(0(0(2(1(2(0(0(1(0(1(0(1(2(1(x0)))))))))))))))))) → D(2(1(1(1(1(1(0(2(0(1(0(2(2(1(1(1(1(0(0(2(2(1(2(2(x0)))))))))))))))))))))))))
L(0(0(2(0(0(2(1(2(0(2(1(1(1(2(2(0(0(x0)))))))))))))))))) → D(2(2(1(0(1(1(1(2(1(2(0(1(2(1(0(1(2(1(x0)))))))))))))))))))
L(0(0(2(2(2(2(1(1(0(0(0(1(0(2(2(0(0(x0)))))))))))))))))) → D(2(2(1(1(2(1(0(1(1(0(1(2(1(2(1(1(1(1(1(1(x0)))))))))))))))))))))
L(0(1(0(0(0(0(1(1(0(1(0(2(2(0(1(2(1(x0)))))))))))))))))) → D(1(0(2(1(0(0(1(2(1(1(1(0(1(1(0(0(0(2(1(x0))))))))))))))))))))
L(2(1(0(0(1(2(0(0(1(0(2(0(0(1(0(1(1(x0)))))))))))))))))) → D(2(1(2(1(2(2(0(1(1(2(1(1(1(0(0(1(0(2(2(1(1(2(1(1(x0)))))))))))))))))))))))))
L(2(2(2(0(2(0(1(0(1(1(0(2(1(0(1(2(1(x0)))))))))))))))))) → D(1(2(1(2(1(2(0(2(2(1(1(1(0(1(1(1(1(1(0(2(1(1(2(x0))))))))))))))))))))))))
L(0(0(1(0(2(0(2(0(1(2(0(0(2(2(2(0(1(0(x0))))))))))))))))))) → D(1(2(1(1(1(1(0(0(2(0(0(2(1(2(2(1(2(0(1(x0))))))))))))))))))))
L(0(1(2(1(0(2(2(2(0(1(2(0(2(0(0(1(0(1(x0))))))))))))))))))) → D(1(2(1(2(2(2(1(0(1(1(2(0(1(1(2(2(0(0(1(2(x0)))))))))))))))))))))
L(0(2(2(1(0(0(0(0(0(1(2(1(1(0(2(2(0(2(x0))))))))))))))))))) → D(2(2(2(1(1(1(1(1(0(0(1(1(0(2(2(0(2(1(2(x0))))))))))))))))))))
L(1(2(0(1(2(1(2(2(0(2(1(2(1(2(2(2(0(1(x0))))))))))))))))))) → D(2(1(2(0(1(2(2(1(0(1(1(2(2(2(0(2(2(1(x0)))))))))))))))))))
L(2(0(0(1(1(2(2(0(1(1(2(1(0(0(2(1(1(1(x0))))))))))))))))))) → D(0(0(0(1(2(2(1(2(1(2(1(0(2(1(1(0(1(1(x0)))))))))))))))))))
L(2(0(2(2(0(0(1(2(1(0(0(0(2(1(0(2(0(0(x0))))))))))))))))))) → D(1(1(2(2(0(0(2(2(2(1(1(1(1(1(1(0(0(0(0(x0))))))))))))))))))))
L(2(2(2(0(0(0(0(0(0(1(2(0(2(2(2(0(1(1(x0))))))))))))))))))) → D(0(1(0(2(2(1(2(0(0(2(2(0(0(2(0(0(2(1(x0)))))))))))))))))))
L(0(1(0(0(1(1(1(1(0(1(0(0(2(1(1(1(2(0(2(x0)))))))))))))))))))) → D(2(2(0(0(0(2(1(1(2(2(1(2(2(1(2(1(1(1(0(1(x0)))))))))))))))))))))
L(0(1(1(2(0(0(2(2(2(1(0(1(1(2(0(0(2(2(0(x0)))))))))))))))))))) → D(2(1(1(1(0(1(1(2(2(1(2(0(1(1(2(0(0(2(0(2(1(1(x0)))))))))))))))))))))))
L(1(0(1(0(1(2(0(1(1(1(2(2(2(1(2(0(2(1(0(x0)))))))))))))))))))) → D(2(1(2(1(0(1(1(1(1(2(1(2(1(1(2(0(2(0(2(2(1(x0))))))))))))))))))))))
L(1(2(0(1(0(0(0(0(0(0(2(2(1(2(2(1(0(2(1(x0)))))))))))))))))))) → D(0(2(0(2(1(2(1(1(1(1(1(1(1(2(2(2(0(1(2(2(2(x0))))))))))))))))))))))
L(1(2(1(1(0(0(0(2(2(2(2(0(1(2(2(0(1(2(0(x0)))))))))))))))))))) → D(2(1(1(1(1(1(0(2(2(2(0(2(0(0(1(2(2(1(2(0(x0)))))))))))))))))))))
L(2(0(2(2(2(0(1(0(2(1(1(0(2(0(0(0(1(2(1(x0)))))))))))))))))))) → D(0(0(0(1(2(0(2(2(2(1(1(1(1(0(1(1(2(1(1(2(1(2(x0)))))))))))))))))))))))
L(0(1(0(1(2(0(2(1(1(0(1(2(2(1(2(2(0(1(1(2(x0))))))))))))))))))))) → D(0(2(1(1(1(1(2(1(2(1(0(1(1(2(2(1(0(0(1(2(0(2(1(x0))))))))))))))))))))))))
L(0(2(0(0(0(2(2(1(2(2(1(0(0(2(0(1(0(1(0(1(x0))))))))))))))))))))) → D(2(1(0(2(1(0(1(1(1(2(1(2(2(1(0(1(0(0(2(1(2(x0))))))))))))))))))))))
L(1(1(0(0(0(1(2(2(0(2(2(0(2(1(2(0(2(1(1(0(x0))))))))))))))))))))) → D(1(1(2(2(1(1(0(0(1(0(1(0(2(1(1(0(0(2(1(1(0(x0))))))))))))))))))))))
L(1(2(2(0(2(0(0(2(1(2(0(0(0(2(0(2(1(0(2(1(x0))))))))))))))))))))) → D(0(2(2(2(2(0(0(0(0(0(0(0(1(2(1(1(1(2(2(2(x0)))))))))))))))))))))
L(2(0(2(0(1(0(0(2(2(0(1(1(1(0(1(1(0(2(0(1(x0))))))))))))))))))))) → D(0(2(1(1(0(1(1(2(2(1(1(0(2(1(1(1(1(1(0(2(2(1(0(0(0(2(x0)))))))))))))))))))))))))))
L(2(2(1(2(0(0(0(0(1(0(0(2(2(0(0(0(2(2(0(1(x0))))))))))))))))))))) → D(1(2(1(1(2(2(2(1(2(1(0(0(2(1(2(1(0(0(1(0(1(1(1(0(x0)))))))))))))))))))))))))
L(0(0(1(0(0(1(1(1(1(0(2(0(1(1(1(1(2(0(1(2(1(x0)))))))))))))))))))))) → D(0(1(1(0(2(2(1(1(2(1(0(2(2(1(1(1(2(1(1(1(1(2(x0)))))))))))))))))))))))
L(0(0(1(2(2(2(2(2(2(0(1(0(1(1(0(2(0(0(0(2(2(x0)))))))))))))))))))))) → D(2(2(2(1(0(1(0(1(1(2(0(0(0(0(2(1(2(1(0(2(1(1(2(x0))))))))))))))))))))))))
L(0(0(2(2(0(1(1(0(1(0(1(2(1(0(0(0(0(1(1(0(2(x0)))))))))))))))))))))) → D(0(2(0(2(1(2(2(0(0(2(1(0(1(1(2(2(2(2(0(2(1(1(x0)))))))))))))))))))))))
L(0(1(0(2(0(0(0(1(1(1(2(1(2(1(0(1(0(2(2(0(1(x0)))))))))))))))))))))) → D(2(1(1(1(1(1(1(1(2(1(0(0(0(1(2(2(2(2(1(1(2(1(x0)))))))))))))))))))))))
L(0(2(0(0(0(0(0(0(2(1(2(2(2(0(1(2(1(0(0(1(2(x0)))))))))))))))))))))) → D(2(1(1(2(2(0(1(0(2(0(1(1(1(1(2(1(0(1(2(1(1(1(1(2(2(1(x0)))))))))))))))))))))))))))
L(0(2(1(1(2(1(0(1(0(0(1(0(0(0(2(2(1(0(1(0(2(x0)))))))))))))))))))))) → D(0(2(1(2(1(1(2(1(2(2(2(1(0(2(1(1(0(0(1(2(1(2(1(2(x0)))))))))))))))))))))))))
L(1(0(2(2(0(1(2(1(0(2(1(2(1(0(1(0(2(0(1(2(2(x0)))))))))))))))))))))) → D(2(2(0(2(0(1(1(1(1(2(2(1(1(2(2(1(1(1(2(2(0(1(0(x0))))))))))))))))))))))))
L(1(1(0(2(1(0(2(2(0(2(0(1(0(1(1(2(0(2(2(2(1(x0)))))))))))))))))))))) → D(2(0(1(1(2(1(1(2(2(1(2(2(1(0(2(2(0(0(1(1(2(1(x0)))))))))))))))))))))))
L(1(2(0(0(0(0(1(1(1(0(0(2(0(0(2(2(0(0(2(2(1(x0)))))))))))))))))))))) → D(2(1(1(0(2(2(0(0(1(1(1(0(0(1(1(1(0(2(0(1(2(1(x0)))))))))))))))))))))))
L(2(2(0(1(0(2(2(0(1(2(2(1(2(0(0(2(2(2(2(2(2(x0)))))))))))))))))))))) → D(2(1(1(1(2(1(2(0(0(0(0(2(0(2(0(0(0(2(1(2(1(0(x0)))))))))))))))))))))))
L(2(2(2(2(0(0(1(1(0(1(1(1(0(0(2(1(2(2(0(1(0(x0)))))))))))))))))))))) → D(1(0(1(0(1(1(2(0(1(2(1(2(2(1(2(2(2(0(1(1(1(1(0(x0))))))))))))))))))))))))
L(0(0(1(1(2(1(1(0(2(0(1(1(0(1(2(1(0(1(2(0(2(0(x0))))))))))))))))))))))) → D(2(1(1(2(2(0(2(0(2(1(0(2(1(1(1(1(1(2(1(0(2(2(2(2(2(x0))))))))))))))))))))))))))
L(1(0(2(0(2(0(2(2(0(0(1(0(0(0(2(1(2(0(2(0(1(0(x0))))))))))))))))))))))) → D(2(2(2(0(2(0(2(0(2(2(0(0(2(2(1(1(0(2(1(1(1(1(1(x0))))))))))))))))))))))))
L(2(0(0(0(1(0(1(2(0(1(1(2(2(0(1(0(0(0(0(2(1(2(x0))))))))))))))))))))))) → D(0(0(0(0(2(0(0(0(0(1(0(1(2(1(2(0(1(2(2(1(1(2(x0)))))))))))))))))))))))
L(2(1(0(0(0(1(2(2(0(2(2(2(1(0(0(0(0(0(2(0(1(0(x0))))))))))))))))))))))) → D(2(1(2(1(2(2(2(0(1(2(1(2(0(1(1(0(1(0(0(0(0(1(1(x0))))))))))))))))))))))))
L(2(2(1(0(0(0(1(2(2(0(0(0(0(1(2(2(0(2(0(2(2(2(x0))))))))))))))))))))))) → D(2(2(0(1(2(1(2(1(2(1(0(2(2(1(0(1(0(1(1(2(1(1(1(2(x0)))))))))))))))))))))))))
L(2(2(2(0(1(2(1(0(2(1(0(1(0(0(2(2(1(2(1(1(2(2(x0))))))))))))))))))))))) → D(1(0(2(1(2(1(2(1(2(1(2(1(1(1(1(0(2(0(1(0(1(2(2(1(1(x0))))))))))))))))))))))))))
L(0(1(2(2(2(0(1(2(0(0(1(1(2(1(0(0(1(0(1(0(0(2(2(x0)))))))))))))))))))))))) → D(1(0(1(0(2(2(1(2(2(1(0(0(0(1(2(1(2(2(2(2(2(1(0(2(x0)))))))))))))))))))))))))
L(0(2(0(2(2(1(0(1(2(0(0(0(2(2(1(0(0(2(2(0(1(2(1(x0)))))))))))))))))))))))) → D(2(1(1(0(2(0(0(1(0(2(0(0(0(0(1(2(1(1(2(1(1(1(0(1(1(1(2(2(x0)))))))))))))))))))))))))))))
L(0(2(2(0(0(0(1(1(2(0(1(2(2(0(0(2(0(2(0(2(0(1(2(x0)))))))))))))))))))))))) → D(0(2(2(1(1(1(0(0(1(1(2(1(2(0(1(2(1(0(2(1(2(2(2(0(x0)))))))))))))))))))))))))
L(1(2(2(0(1(2(2(0(0(1(1(0(0(2(2(0(0(0(2(0(1(0(1(x0)))))))))))))))))))))))) → D(0(0(2(0(0(2(1(1(1(2(0(0(0(0(2(2(0(0(1(2(1(1(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))
L(2(0(1(0(1(0(0(1(1(0(0(1(2(0(2(2(0(2(2(1(0(2(0(x0)))))))))))))))))))))))) → D(0(0(2(2(1(2(1(1(1(2(0(1(1(2(1(1(1(2(0(2(0(2(1(2(0(1(x0)))))))))))))))))))))))))))
L(2(0(2(0(2(2(0(2(2(1(2(1(1(1(1(2(0(0(1(2(2(1(2(x0)))))))))))))))))))))))) → D(0(2(2(0(0(2(1(1(1(2(1(2(1(2(2(1(0(0(0(0(2(2(1(1(1(x0))))))))))))))))))))))))))
L(0(1(1(0(1(0(1(0(0(0(1(0(0(2(1(0(2(0(0(0(1(0(2(1(x0))))))))))))))))))))))))) → D(0(0(2(1(1(2(2(2(1(1(1(1(1(0(2(0(0(0(0(1(0(2(1(0(1(x0))))))))))))))))))))))))))
L(0(1(2(1(2(1(1(2(1(2(0(2(2(0(1(0(0(1(2(2(0(0(0(2(x0))))))))))))))))))))))))) → D(1(1(2(1(2(1(1(1(1(2(0(1(1(0(2(1(2(0(1(2(0(2(2(1(1(2(0(x0))))))))))))))))))))))))))))
L(1(0(2(0(1(1(0(1(1(2(2(2(0(2(0(2(2(1(0(0(2(2(0(1(x0))))))))))))))))))))))))) → D(2(1(1(2(1(1(2(2(1(0(0(1(1(1(0(2(2(2(2(2(2(2(1(2(2(2(x0)))))))))))))))))))))))))))
L(1(1(2(2(1(0(0(2(0(1(1(1(1(1(1(1(1(2(2(2(2(0(1(1(x0))))))))))))))))))))))))) → D(1(0(2(2(2(1(2(1(2(0(1(1(1(1(1(1(1(0(0(1(1(1(2(2(x0)))))))))))))))))))))))))
L(2(1(0(1(1(0(0(2(0(2(0(1(0(1(2(0(1(0(2(2(1(0(1(0(x0))))))))))))))))))))))))) → D(1(0(2(1(1(2(1(1(2(1(2(0(1(0(0(0(0(2(1(1(1(0(0(1(2(2(1(x0))))))))))))))))))))))))))))
L(2(1(2(2(0(2(0(2(0(2(2(0(0(0(0(0(0(2(0(0(2(2(2(2(x0))))))))))))))))))))))))) → D(1(1(1(0(2(1(1(0(0(2(1(0(0(0(2(1(0(2(2(2(0(2(1(1(0(x0))))))))))))))))))))))))))
L(0(0(1(2(1(1(2(2(2(0(1(0(1(0(1(2(0(0(0(0(1(1(0(1(0(x0)))))))))))))))))))))))))) → D(0(1(2(2(1(1(1(1(1(0(1(1(1(2(1(2(1(2(0(0(0(2(0(2(1(2(1(x0))))))))))))))))))))))))))))
L(0(1(0(2(2(0(1(1(1(2(0(1(2(0(0(1(1(1(0(1(2(2(1(0(2(x0)))))))))))))))))))))))))) → D(0(1(1(2(2(2(2(2(0(2(2(1(1(0(2(2(0(1(2(1(2(2(1(1(2(1(x0)))))))))))))))))))))))))))
L(1(2(0(0(1(2(1(0(0(2(2(2(0(0(1(2(0(0(1(0(1(1(1(2(2(x0)))))))))))))))))))))))))) → D(1(1(1(2(2(2(1(0(0(2(1(0(2(1(0(0(0(0(2(0(1(1(0(2(2(x0))))))))))))))))))))))))))
L(1(2(0(0(2(2(0(1(1(2(0(0(2(2(2(1(2(2(1(0(2(0(1(0(2(x0)))))))))))))))))))))))))) → D(1(1(2(2(0(0(2(0(0(0(0(0(0(0(2(2(1(1(1(2(2(1(1(2(2(2(x0)))))))))))))))))))))))))))
L(1(2(1(0(1(1(1(0(1(2(1(2(2(2(1(1(1(1(0(0(1(1(2(0(1(x0)))))))))))))))))))))))))) → D(2(2(2(1(1(0(1(0(0(2(1(2(1(1(1(1(1(1(0(2(1(0(1(1(1(x0))))))))))))))))))))))))))
L(1(2(2(1(1(0(2(0(2(0(0(1(2(0(0(2(1(0(0(0(2(0(1(0(1(x0)))))))))))))))))))))))))) → D(1(2(1(1(0(2(1(1(1(0(2(2(2(1(0(2(2(0(2(1(0(1(2(0(1(1(x0)))))))))))))))))))))))))))
L(2(0(0(0(1(0(0(1(2(2(0(0(2(0(0(0(1(1(2(0(1(1(1(0(1(x0)))))))))))))))))))))))))) → D(2(1(1(2(1(1(0(0(1(1(1(2(2(2(0(2(2(0(1(1(0(2(1(2(1(0(2(0(1(x0))))))))))))))))))))))))))))))
L(2(2(0(1(0(1(1(0(1(2(2(0(1(1(0(2(1(0(2(0(2(1(1(0(2(x0)))))))))))))))))))))))))) → D(1(1(0(1(1(2(1(1(0(2(1(2(1(1(2(2(1(1(2(0(0(2(0(0(2(1(x0)))))))))))))))))))))))))))
L(0(0(1(2(0(2(2(1(2(0(0(2(1(1(0(0(1(2(0(1(2(2(0(0(0(1(x0))))))))))))))))))))))))))) → D(0(0(0(2(1(2(1(1(0(0(1(0(1(0(2(0(2(2(2(1(1(2(1(0(2(0(0(2(x0)))))))))))))))))))))))))))))
L(0(0(2(0(0(1(0(0(0(1(1(1(0(1(0(1(2(0(2(2(0(0(1(0(1(1(x0))))))))))))))))))))))))))) → D(0(1(0(1(0(1(1(1(2(2(2(1(2(1(1(2(0(1(1(2(2(2(1(1(2(1(1(x0))))))))))))))))))))))))))))
L(1(0(0(0(2(1(1(0(1(0(1(0(1(0(2(2(2(2(0(0(0(2(1(1(2(2(x0))))))))))))))))))))))))))) → D(2(0(2(2(2(0(2(2(0(2(2(0(1(2(1(1(1(2(0(1(0(0(2(1(1(1(2(1(x0)))))))))))))))))))))))))))))
L(1(1(2(1(1(2(2(0(1(0(0(0(2(0(2(2(0(0(1(0(2(0(1(2(2(1(x0))))))))))))))))))))))))))) → D(2(1(1(1(0(1(0(1(1(0(1(2(2(1(2(1(0(1(1(2(1(1(0(1(1(1(1(2(x0)))))))))))))))))))))))))))))
L(2(0(2(0(1(1(2(1(2(1(1(1(1(0(0(0(0(1(1(1(1(0(0(2(1(2(x0))))))))))))))))))))))))))) → D(2(2(1(1(0(1(0(2(1(2(2(2(1(2(2(2(1(2(2(1(1(1(2(1(1(2(2(1(0(1(x0)))))))))))))))))))))))))))))))
L(2(2(0(2(1(0(0(0(0(1(1(0(2(0(2(0(1(2(0(1(2(0(1(1(2(2(x0))))))))))))))))))))))))))) → D(1(1(1(1(2(0(1(0(1(0(1(2(1(2(1(0(1(1(1(0(1(1(2(0(0(2(2(x0))))))))))))))))))))))))))))
L(2(2(1(2(2(1(0(2(0(2(2(1(2(0(2(0(1(1(0(1(2(0(0(1(1(2(x0))))))))))))))))))))))))))) → D(2(0(1(1(1(1(0(2(0(1(2(1(1(2(0(2(0(2(2(2(0(2(0(1(2(2(x0)))))))))))))))))))))))))))
L(0(0(1(0(1(2(0(1(1(2(0(1(2(2(2(2(1(0(1(0(0(1(1(0(0(0(1(x0)))))))))))))))))))))))))))) → D(0(1(0(0(2(2(1(1(1(2(1(0(2(2(2(0(1(2(0(2(0(0(1(1(1(0(0(0(0(x0))))))))))))))))))))))))))))))
L(0(0(1(1(2(1(0(1(1(2(0(0(1(0(2(2(0(2(1(0(2(1(2(0(0(2(2(x0)))))))))))))))))))))))))))) → D(1(0(0(1(2(2(0(1(2(2(2(2(1(1(2(1(0(0(1(1(1(0(0(2(2(1(2(2(1(x0))))))))))))))))))))))))))))))
L(0(1(0(0(2(0(2(2(1(2(1(0(2(1(2(0(0(1(0(2(1(0(2(0(2(2(0(x0)))))))))))))))))))))))))))) → D(0(1(2(1(2(1(1(1(0(2(1(0(2(1(2(1(0(2(2(1(1(0(1(2(0(2(1(1(2(1(x0)))))))))))))))))))))))))))))))
L(1(0(2(0(0(2(1(2(1(0(2(2(0(1(1(1(2(1(2(1(0(2(1(0(1(2(1(x0)))))))))))))))))))))))))))) → D(0(0(2(1(2(0(1(0(0(2(2(2(1(2(2(1(1(2(1(2(2(1(1(2(1(2(1(2(x0)))))))))))))))))))))))))))))
L(2(0(0(2(2(1(0(0(0(0(2(2(2(2(2(2(2(2(1(2(1(2(0(0(1(0(1(x0)))))))))))))))))))))))))))) → D(0(1(0(1(1(1(0(0(1(1(1(1(0(2(1(1(2(0(1(1(1(0(1(2(2(1(1(0(0(1(x0)))))))))))))))))))))))))))))))
L(2(1(2(2(2(2(2(0(0(0(0(2(0(0(1(2(1(1(2(2(0(2(1(2(2(2(0(x0)))))))))))))))))))))))))))) → D(0(2(2(0(2(0(0(2(1(1(2(1(1(2(1(0(1(0(2(1(0(1(1(1(1(0(1(0(2(1(x0)))))))))))))))))))))))))))))))
L(0(0(1(0(2(0(2(2(2(1(2(2(0(1(2(1(0(0(0(0(2(0(1(1(2(0(1(1(x0))))))))))))))))))))))))))))) → D(0(0(2(1(1(0(1(1(0(1(1(0(1(1(2(1(0(2(1(0(1(2(2(1(0(0(0(1(2(x0))))))))))))))))))))))))))))))
L(0(1(1(0(2(0(0(2(1(0(0(1(0(2(2(0(1(0(1(2(0(1(1(1(2(0(1(0(x0))))))))))))))))))))))))))))) → D(0(0(1(1(2(0(0(2(1(0(2(1(1(2(1(0(1(1(0(2(0(0(1(1(0(0(0(2(x0)))))))))))))))))))))))))))))
L(2(1(2(2(2(0(1(2(2(0(1(0(0(0(1(2(1(1(0(0(1(0(2(0(0(2(0(0(x0))))))))))))))))))))))))))))) → D(0(0(2(1(1(1(2(2(2(1(0(0(0(0(2(2(1(0(1(1(2(2(2(0(0(0(0(0(x0)))))))))))))))))))))))))))))
L(0(1(1(0(1(0(0(0(0(0(1(2(1(1(0(0(1(0(0(0(1(1(0(2(0(0(0(2(2(x0)))))))))))))))))))))))))))))) → D(0(0(1(1(0(1(1(1(2(2(0(1(0(1(1(2(1(1(0(1(1(2(2(1(1(2(2(0(0(2(x0)))))))))))))))))))))))))))))))
L(2(0(0(1(1(2(1(2(0(1(0(0(1(2(1(2(2(0(0(1(2(1(0(2(0(1(1(1(1(x0)))))))))))))))))))))))))))))) → D(0(2(1(1(2(2(1(0(0(1(1(1(2(1(1(2(2(0(2(1(2(0(2(1(1(1(1(2(1(2(x0)))))))))))))))))))))))))))))))
L(2(1(0(2(0(1(2(0(2(2(0(2(2(1(2(1(2(0(2(1(1(0(1(2(1(2(2(0(2(x0)))))))))))))))))))))))))))))) → D(0(2(1(0(0(1(1(0(1(2(1(2(1(1(2(0(1(1(2(2(1(1(2(1(0(2(1(1(0(1(x0)))))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
Y2(D(x0)) → D(2(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(V(x0))))))))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
M(V(2(x0))) → V(X2(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X0(2(x0)) → 2(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X1(2(x0)) → 2(X1(x0))
X2(0(x0)) → 0(X2(x0))
X2(1(x0)) → 1(X2(x0))
X2(2(x0)) → 2(X2(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
X2(E(x0)) → 2(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(2(x0)) → Y2(L(x0))
L(0(0(1(1(0(x0)))))) → D(2(1(2(2(1(0(x0)))))))
L(1(2(2(0(2(x0)))))) → D(1(1(2(1(1(2(x0)))))))
L(0(0(0(2(1(2(x0))))))) → D(2(1(2(1(2(2(1(2(1(x0))))))))))
L(2(0(0(1(2(2(x0))))))) → D(1(2(1(2(1(2(1(x0))))))))
L(2(0(0(2(0(2(x0))))))) → D(2(2(2(2(1(1(1(x0))))))))
L(2(2(2(0(0(2(x0))))))) → D(2(0(2(2(0(2(x0)))))))
L(0(0(1(1(0(0(1(x0)))))))) → D(2(2(2(2(1(2(1(0(x0)))))))))
L(2(1(2(0(2(1(2(0(x0))))))))) → D(2(0(1(0(1(2(1(1(1(1(0(x0))))))))))))
L(1(0(0(1(0(1(1(0(1(x0)))))))))) → D(1(1(2(1(2(1(1(1(2(1(x0)))))))))))
L(1(0(2(0(0(0(0(2(1(x0)))))))))) → D(1(1(2(1(2(1(1(2(1(2(x0)))))))))))
L(2(0(0(0(0(0(2(0(2(x0)))))))))) → D(2(1(2(1(1(0(2(2(1(0(1(1(x0)))))))))))))
L(2(1(1(0(0(1(1(2(2(x0)))))))))) → D(2(1(0(0(2(1(0(1(1(1(x0)))))))))))
L(2(2(1(0(2(0(1(1(0(x0)))))))))) → D(2(2(1(2(1(1(0(0(0(x0))))))))))
L(0(1(0(2(0(1(2(2(2(2(x0))))))))))) → D(0(0(2(2(1(1(1(1(0(0(2(2(x0)))))))))))))
L(2(2(1(0(0(0(2(0(1(1(x0))))))))))) → D(2(1(2(2(0(2(2(1(1(2(1(x0))))))))))))
L(1(0(1(0(2(2(0(0(1(2(2(2(1(x0)))))))))))))) → D(1(0(0(1(0(0(1(0(2(1(2(1(1(2(x0)))))))))))))))
L(2(0(2(0(0(1(1(0(2(2(0(0(0(x0)))))))))))))) → D(2(2(2(2(2(1(1(2(2(2(0(0(0(0(x0)))))))))))))))
L(0(0(0(2(0(0(1(2(1(1(2(0(2(2(x0))))))))))))))) → D(1(0(2(1(1(1(1(2(1(1(2(1(1(1(2(1(2(x0))))))))))))))))))
L(0(2(1(0(2(1(0(0(1(2(1(0(1(2(x0))))))))))))))) → D(1(2(1(2(1(0(0(0(2(1(1(0(1(1(2(x0))))))))))))))))
L(0(2(2(2(1(0(1(0(0(1(0(1(1(0(x0))))))))))))))) → D(1(0(2(2(1(1(2(2(1(2(2(2(0(1(0(x0))))))))))))))))
L(1(2(2(0(0(1(1(1(2(2(2(0(0(1(x0))))))))))))))) → D(2(1(1(0(2(1(0(1(0(1(2(2(1(2(1(x0))))))))))))))))
L(0(1(2(0(0(2(0(0(1(2(2(0(2(1(0(x0)))))))))))))))) → D(2(1(1(2(0(0(1(1(2(2(1(1(1(1(1(0(1(x0))))))))))))))))))
L(0(2(0(2(1(1(1(2(1(1(2(0(0(2(1(x0)))))))))))))))) → D(2(1(1(1(2(0(2(1(1(1(1(0(2(2(1(1(1(2(x0)))))))))))))))))))
L(2(0(0(0(1(1(2(2(1(2(0(1(0(2(2(x0)))))))))))))))) → D(2(1(2(0(1(2(0(0(0(2(1(1(2(2(0(x0))))))))))))))))
L(2(2(0(1(2(1(0(2(2(0(1(1(0(0(1(x0)))))))))))))))) → D(1(1(0(0(2(1(2(1(0(1(1(2(1(1(1(2(x0)))))))))))))))))
L(0(0(0(2(2(0(2(1(2(2(1(0(0(1(1(1(x0))))))))))))))))) → D(0(1(1(0(0(2(0(0(2(1(2(1(1(2(1(1(2(1(x0)))))))))))))))))))
L(0(0(1(0(0(2(2(0(0(2(1(2(1(0(2(1(x0))))))))))))))))) → D(2(2(2(0(2(1(2(2(1(1(0(1(1(2(1(2(1(1(1(2(1(2(x0)))))))))))))))))))))))
L(0(1(2(2(2(2(1(2(1(2(1(0(2(0(1(2(x0))))))))))))))))) → D(0(1(2(1(0(1(2(1(2(2(1(2(2(1(0(1(1(x0))))))))))))))))))
L(2(1(2(0(0(2(1(0(0(1(1(0(0(0(1(2(x0))))))))))))))))) → D(1(1(1(2(1(2(1(0(1(1(1(1(1(0(1(2(2(1(2(x0))))))))))))))))))))
L(0(0(0(0(0(2(1(2(0(0(1(0(1(0(1(2(1(x0)))))))))))))))))) → D(2(1(1(1(1(1(0(2(0(1(0(2(2(1(1(1(1(0(0(2(2(1(2(2(x0)))))))))))))))))))))))))
L(0(0(2(0(0(2(1(2(0(2(1(1(1(2(2(0(0(x0)))))))))))))))))) → D(2(2(1(0(1(1(1(2(1(2(0(1(2(1(0(1(2(1(x0)))))))))))))))))))
L(0(0(2(2(2(2(1(1(0(0(0(1(0(2(2(0(0(x0)))))))))))))))))) → D(2(2(1(1(2(1(0(1(1(0(1(2(1(2(1(1(1(1(1(1(x0)))))))))))))))))))))
L(0(1(0(0(0(0(1(1(0(1(0(2(2(0(1(2(1(x0)))))))))))))))))) → D(1(0(2(1(0(0(1(2(1(1(1(0(1(1(0(0(0(2(1(x0))))))))))))))))))))
L(2(1(0(0(1(2(0(0(1(0(2(0(0(1(0(1(1(x0)))))))))))))))))) → D(2(1(2(1(2(2(0(1(1(2(1(1(1(0(0(1(0(2(2(1(1(2(1(1(x0)))))))))))))))))))))))))
L(2(2(2(0(2(0(1(0(1(1(0(2(1(0(1(2(1(x0)))))))))))))))))) → D(1(2(1(2(1(2(0(2(2(1(1(1(0(1(1(1(1(1(0(2(1(1(2(x0))))))))))))))))))))))))
L(0(0(1(0(2(0(2(0(1(2(0(0(2(2(2(0(1(0(x0))))))))))))))))))) → D(1(2(1(1(1(1(0(0(2(0(0(2(1(2(2(1(2(0(1(x0))))))))))))))))))))
L(0(1(2(1(0(2(2(2(0(1(2(0(2(0(0(1(0(1(x0))))))))))))))))))) → D(1(2(1(2(2(2(1(0(1(1(2(0(1(1(2(2(0(0(1(2(x0)))))))))))))))))))))
L(0(2(2(1(0(0(0(0(0(1(2(1(1(0(2(2(0(2(x0))))))))))))))))))) → D(2(2(2(1(1(1(1(1(0(0(1(1(0(2(2(0(2(1(2(x0))))))))))))))))))))
L(1(2(0(1(2(1(2(2(0(2(1(2(1(2(2(2(0(1(x0))))))))))))))))))) → D(2(1(2(0(1(2(2(1(0(1(1(2(2(2(0(2(2(1(x0)))))))))))))))))))
L(2(0(0(1(1(2(2(0(1(1(2(1(0(0(2(1(1(1(x0))))))))))))))))))) → D(0(0(0(1(2(2(1(2(1(2(1(0(2(1(1(0(1(1(x0)))))))))))))))))))
L(2(0(2(2(0(0(1(2(1(0(0(0(2(1(0(2(0(0(x0))))))))))))))))))) → D(1(1(2(2(0(0(2(2(2(1(1(1(1(1(1(0(0(0(0(x0))))))))))))))))))))
L(2(2(2(0(0(0(0(0(0(1(2(0(2(2(2(0(1(1(x0))))))))))))))))))) → D(0(1(0(2(2(1(2(0(0(2(2(0(0(2(0(0(2(1(x0)))))))))))))))))))
L(0(1(0(0(1(1(1(1(0(1(0(0(2(1(1(1(2(0(2(x0)))))))))))))))))))) → D(2(2(0(0(0(2(1(1(2(2(1(2(2(1(2(1(1(1(0(1(x0)))))))))))))))))))))
L(0(1(1(2(0(0(2(2(2(1(0(1(1(2(0(0(2(2(0(x0)))))))))))))))))))) → D(2(1(1(1(0(1(1(2(2(1(2(0(1(1(2(0(0(2(0(2(1(1(x0)))))))))))))))))))))))
L(1(0(1(0(1(2(0(1(1(1(2(2(2(1(2(0(2(1(0(x0)))))))))))))))))))) → D(2(1(2(1(0(1(1(1(1(2(1(2(1(1(2(0(2(0(2(2(1(x0))))))))))))))))))))))
L(1(2(0(1(0(0(0(0(0(0(2(2(1(2(2(1(0(2(1(x0)))))))))))))))))))) → D(0(2(0(2(1(2(1(1(1(1(1(1(1(2(2(2(0(1(2(2(2(x0))))))))))))))))))))))
L(1(2(1(1(0(0(0(2(2(2(2(0(1(2(2(0(1(2(0(x0)))))))))))))))))))) → D(2(1(1(1(1(1(0(2(2(2(0(2(0(0(1(2(2(1(2(0(x0)))))))))))))))))))))
L(2(0(2(2(2(0(1(0(2(1(1(0(2(0(0(0(1(2(1(x0)))))))))))))))))))) → D(0(0(0(1(2(0(2(2(2(1(1(1(1(0(1(1(2(1(1(2(1(2(x0)))))))))))))))))))))))
L(0(1(0(1(2(0(2(1(1(0(1(2(2(1(2(2(0(1(1(2(x0))))))))))))))))))))) → D(0(2(1(1(1(1(2(1(2(1(0(1(1(2(2(1(0(0(1(2(0(2(1(x0))))))))))))))))))))))))
L(0(2(0(0(0(2(2(1(2(2(1(0(0(2(0(1(0(1(0(1(x0))))))))))))))))))))) → D(2(1(0(2(1(0(1(1(1(2(1(2(2(1(0(1(0(0(2(1(2(x0))))))))))))))))))))))
L(1(1(0(0(0(1(2(2(0(2(2(0(2(1(2(0(2(1(1(0(x0))))))))))))))))))))) → D(1(1(2(2(1(1(0(0(1(0(1(0(2(1(1(0(0(2(1(1(0(x0))))))))))))))))))))))
L(1(2(2(0(2(0(0(2(1(2(0(0(0(2(0(2(1(0(2(1(x0))))))))))))))))))))) → D(0(2(2(2(2(0(0(0(0(0(0(0(1(2(1(1(1(2(2(2(x0)))))))))))))))))))))
L(2(0(2(0(1(0(0(2(2(0(1(1(1(0(1(1(0(2(0(1(x0))))))))))))))))))))) → D(0(2(1(1(0(1(1(2(2(1(1(0(2(1(1(1(1(1(0(2(2(1(0(0(0(2(x0)))))))))))))))))))))))))))
L(2(2(1(2(0(0(0(0(1(0(0(2(2(0(0(0(2(2(0(1(x0))))))))))))))))))))) → D(1(2(1(1(2(2(2(1(2(1(0(0(2(1(2(1(0(0(1(0(1(1(1(0(x0)))))))))))))))))))))))))
L(0(0(1(0(0(1(1(1(1(0(2(0(1(1(1(1(2(0(1(2(1(x0)))))))))))))))))))))) → D(0(1(1(0(2(2(1(1(2(1(0(2(2(1(1(1(2(1(1(1(1(2(x0)))))))))))))))))))))))
L(0(0(1(2(2(2(2(2(2(0(1(0(1(1(0(2(0(0(0(2(2(x0)))))))))))))))))))))) → D(2(2(2(1(0(1(0(1(1(2(0(0(0(0(2(1(2(1(0(2(1(1(2(x0))))))))))))))))))))))))
L(0(0(2(2(0(1(1(0(1(0(1(2(1(0(0(0(0(1(1(0(2(x0)))))))))))))))))))))) → D(0(2(0(2(1(2(2(0(0(2(1(0(1(1(2(2(2(2(0(2(1(1(x0)))))))))))))))))))))))
L(0(1(0(2(0(0(0(1(1(1(2(1(2(1(0(1(0(2(2(0(1(x0)))))))))))))))))))))) → D(2(1(1(1(1(1(1(1(2(1(0(0(0(1(2(2(2(2(1(1(2(1(x0)))))))))))))))))))))))
L(0(2(0(0(0(0(0(0(2(1(2(2(2(0(1(2(1(0(0(1(2(x0)))))))))))))))))))))) → D(2(1(1(2(2(0(1(0(2(0(1(1(1(1(2(1(0(1(2(1(1(1(1(2(2(1(x0)))))))))))))))))))))))))))
L(0(2(1(1(2(1(0(1(0(0(1(0(0(0(2(2(1(0(1(0(2(x0)))))))))))))))))))))) → D(0(2(1(2(1(1(2(1(2(2(2(1(0(2(1(1(0(0(1(2(1(2(1(2(x0)))))))))))))))))))))))))
L(1(0(2(2(0(1(2(1(0(2(1(2(1(0(1(0(2(0(1(2(2(x0)))))))))))))))))))))) → D(2(2(0(2(0(1(1(1(1(2(2(1(1(2(2(1(1(1(2(2(0(1(0(x0))))))))))))))))))))))))
L(1(1(0(2(1(0(2(2(0(2(0(1(0(1(1(2(0(2(2(2(1(x0)))))))))))))))))))))) → D(2(0(1(1(2(1(1(2(2(1(2(2(1(0(2(2(0(0(1(1(2(1(x0)))))))))))))))))))))))
L(1(2(0(0(0(0(1(1(1(0(0(2(0(0(2(2(0(0(2(2(1(x0)))))))))))))))))))))) → D(2(1(1(0(2(2(0(0(1(1(1(0(0(1(1(1(0(2(0(1(2(1(x0)))))))))))))))))))))))
L(2(2(0(1(0(2(2(0(1(2(2(1(2(0(0(2(2(2(2(2(2(x0)))))))))))))))))))))) → D(2(1(1(1(2(1(2(0(0(0(0(2(0(2(0(0(0(2(1(2(1(0(x0)))))))))))))))))))))))
L(2(2(2(2(0(0(1(1(0(1(1(1(0(0(2(1(2(2(0(1(0(x0)))))))))))))))))))))) → D(1(0(1(0(1(1(2(0(1(2(1(2(2(1(2(2(2(0(1(1(1(1(0(x0))))))))))))))))))))))))
L(0(0(1(1(2(1(1(0(2(0(1(1(0(1(2(1(0(1(2(0(2(0(x0))))))))))))))))))))))) → D(2(1(1(2(2(0(2(0(2(1(0(2(1(1(1(1(1(2(1(0(2(2(2(2(2(x0))))))))))))))))))))))))))
L(1(0(2(0(2(0(2(2(0(0(1(0(0(0(2(1(2(0(2(0(1(0(x0))))))))))))))))))))))) → D(2(2(2(0(2(0(2(0(2(2(0(0(2(2(1(1(0(2(1(1(1(1(1(x0))))))))))))))))))))))))
L(2(0(0(0(1(0(1(2(0(1(1(2(2(0(1(0(0(0(0(2(1(2(x0))))))))))))))))))))))) → D(0(0(0(0(2(0(0(0(0(1(0(1(2(1(2(0(1(2(2(1(1(2(x0)))))))))))))))))))))))
L(2(1(0(0(0(1(2(2(0(2(2(2(1(0(0(0(0(0(2(0(1(0(x0))))))))))))))))))))))) → D(2(1(2(1(2(2(2(0(1(2(1(2(0(1(1(0(1(0(0(0(0(1(1(x0))))))))))))))))))))))))
L(2(2(1(0(0(0(1(2(2(0(0(0(0(1(2(2(0(2(0(2(2(2(x0))))))))))))))))))))))) → D(2(2(0(1(2(1(2(1(2(1(0(2(2(1(0(1(0(1(1(2(1(1(1(2(x0)))))))))))))))))))))))))
L(2(2(2(0(1(2(1(0(2(1(0(1(0(0(2(2(1(2(1(1(2(2(x0))))))))))))))))))))))) → D(1(0(2(1(2(1(2(1(2(1(2(1(1(1(1(0(2(0(1(0(1(2(2(1(1(x0))))))))))))))))))))))))))
L(0(1(2(2(2(0(1(2(0(0(1(1(2(1(0(0(1(0(1(0(0(2(2(x0)))))))))))))))))))))))) → D(1(0(1(0(2(2(1(2(2(1(0(0(0(1(2(1(2(2(2(2(2(1(0(2(x0)))))))))))))))))))))))))
L(0(2(0(2(2(1(0(1(2(0(0(0(2(2(1(0(0(2(2(0(1(2(1(x0)))))))))))))))))))))))) → D(2(1(1(0(2(0(0(1(0(2(0(0(0(0(1(2(1(1(2(1(1(1(0(1(1(1(2(2(x0)))))))))))))))))))))))))))))
L(0(2(2(0(0(0(1(1(2(0(1(2(2(0(0(2(0(2(0(2(0(1(2(x0)))))))))))))))))))))))) → D(0(2(2(1(1(1(0(0(1(1(2(1(2(0(1(2(1(0(2(1(2(2(2(0(x0)))))))))))))))))))))))))
L(1(2(2(0(1(2(2(0(0(1(1(0(0(2(2(0(0(0(2(0(1(0(1(x0)))))))))))))))))))))))) → D(0(0(2(0(0(2(1(1(1(2(0(0(0(0(2(2(0(0(1(2(1(1(1(1(1(0(1(1(x0)))))))))))))))))))))))))))))
L(2(0(1(0(1(0(0(1(1(0(0(1(2(0(2(2(0(2(2(1(0(2(0(x0)))))))))))))))))))))))) → D(0(0(2(2(1(2(1(1(1(2(0(1(1(2(1(1(1(2(0(2(0(2(1(2(0(1(x0)))))))))))))))))))))))))))
L(2(0(2(0(2(2(0(2(2(1(2(1(1(1(1(2(0(0(1(2(2(1(2(x0)))))))))))))))))))))))) → D(0(2(2(0(0(2(1(1(1(2(1(2(1(2(2(1(0(0(0(0(2(2(1(1(1(x0))))))))))))))))))))))))))
L(0(1(1(0(1(0(1(0(0(0(1(0(0(2(1(0(2(0(0(0(1(0(2(1(x0))))))))))))))))))))))))) → D(0(0(2(1(1(2(2(2(1(1(1(1(1(0(2(0(0(0(0(1(0(2(1(0(1(x0))))))))))))))))))))))))))
L(0(1(2(1(2(1(1(2(1(2(0(2(2(0(1(0(0(1(2(2(0(0(0(2(x0))))))))))))))))))))))))) → D(1(1(2(1(2(1(1(1(1(2(0(1(1(0(2(1(2(0(1(2(0(2(2(1(1(2(0(x0))))))))))))))))))))))))))))
L(1(0(2(0(1(1(0(1(1(2(2(2(0(2(0(2(2(1(0(0(2(2(0(1(x0))))))))))))))))))))))))) → D(2(1(1(2(1(1(2(2(1(0(0(1(1(1(0(2(2(2(2(2(2(2(1(2(2(2(x0)))))))))))))))))))))))))))
L(1(1(2(2(1(0(0(2(0(1(1(1(1(1(1(1(1(2(2(2(2(0(1(1(x0))))))))))))))))))))))))) → D(1(0(2(2(2(1(2(1(2(0(1(1(1(1(1(1(1(0(0(1(1(1(2(2(x0)))))))))))))))))))))))))
L(2(1(0(1(1(0(0(2(0(2(0(1(0(1(2(0(1(0(2(2(1(0(1(0(x0))))))))))))))))))))))))) → D(1(0(2(1(1(2(1(1(2(1(2(0(1(0(0(0(0(2(1(1(1(0(0(1(2(2(1(x0))))))))))))))))))))))))))))
L(2(1(2(2(0(2(0(2(0(2(2(0(0(0(0(0(0(2(0(0(2(2(2(2(x0))))))))))))))))))))))))) → D(1(1(1(0(2(1(1(0(0(2(1(0(0(0(2(1(0(2(2(2(0(2(1(1(0(x0))))))))))))))))))))))))))
L(0(0(1(2(1(1(2(2(2(0(1(0(1(0(1(2(0(0(0(0(1(1(0(1(0(x0)))))))))))))))))))))))))) → D(0(1(2(2(1(1(1(1(1(0(1(1(1(2(1(2(1(2(0(0(0(2(0(2(1(2(1(x0))))))))))))))))))))))))))))
L(0(1(0(2(2(0(1(1(1(2(0(1(2(0(0(1(1(1(0(1(2(2(1(0(2(x0)))))))))))))))))))))))))) → D(0(1(1(2(2(2(2(2(0(2(2(1(1(0(2(2(0(1(2(1(2(2(1(1(2(1(x0)))))))))))))))))))))))))))
L(1(2(0(0(1(2(1(0(0(2(2(2(0(0(1(2(0(0(1(0(1(1(1(2(2(x0)))))))))))))))))))))))))) → D(1(1(1(2(2(2(1(0(0(2(1(0(2(1(0(0(0(0(2(0(1(1(0(2(2(x0))))))))))))))))))))))))))
L(1(2(0(0(2(2(0(1(1(2(0(0(2(2(2(1(2(2(1(0(2(0(1(0(2(x0)))))))))))))))))))))))))) → D(1(1(2(2(0(0(2(0(0(0(0(0(0(0(2(2(1(1(1(2(2(1(1(2(2(2(x0)))))))))))))))))))))))))))
L(1(2(1(0(1(1(1(0(1(2(1(2(2(2(1(1(1(1(0(0(1(1(2(0(1(x0)))))))))))))))))))))))))) → D(2(2(2(1(1(0(1(0(0(2(1(2(1(1(1(1(1(1(0(2(1(0(1(1(1(x0))))))))))))))))))))))))))
L(1(2(2(1(1(0(2(0(2(0(0(1(2(0(0(2(1(0(0(0(2(0(1(0(1(x0)))))))))))))))))))))))))) → D(1(2(1(1(0(2(1(1(1(0(2(2(2(1(0(2(2(0(2(1(0(1(2(0(1(1(x0)))))))))))))))))))))))))))
L(2(0(0(0(1(0(0(1(2(2(0(0(2(0(0(0(1(1(2(0(1(1(1(0(1(x0)))))))))))))))))))))))))) → D(2(1(1(2(1(1(0(0(1(1(1(2(2(2(0(2(2(0(1(1(0(2(1(2(1(0(2(0(1(x0))))))))))))))))))))))))))))))
L(2(2(0(1(0(1(1(0(1(2(2(0(1(1(0(2(1(0(2(0(2(1(1(0(2(x0)))))))))))))))))))))))))) → D(1(1(0(1(1(2(1(1(0(2(1(2(1(1(2(2(1(1(2(0(0(2(0(0(2(1(x0)))))))))))))))))))))))))))
L(0(0(1(2(0(2(2(1(2(0(0(2(1(1(0(0(1(2(0(1(2(2(0(0(0(1(x0))))))))))))))))))))))))))) → D(0(0(0(2(1(2(1(1(0(0(1(0(1(0(2(0(2(2(2(1(1(2(1(0(2(0(0(2(x0)))))))))))))))))))))))))))))
L(0(0(2(0(0(1(0(0(0(1(1(1(0(1(0(1(2(0(2(2(0(0(1(0(1(1(x0))))))))))))))))))))))))))) → D(0(1(0(1(0(1(1(1(2(2(2(1(2(1(1(2(0(1(1(2(2(2(1(1(2(1(1(x0))))))))))))))))))))))))))))
L(1(0(0(0(2(1(1(0(1(0(1(0(1(0(2(2(2(2(0(0(0(2(1(1(2(2(x0))))))))))))))))))))))))))) → D(2(0(2(2(2(0(2(2(0(2(2(0(1(2(1(1(1(2(0(1(0(0(2(1(1(1(2(1(x0)))))))))))))))))))))))))))))
L(1(1(2(1(1(2(2(0(1(0(0(0(2(0(2(2(0(0(1(0(2(0(1(2(2(1(x0))))))))))))))))))))))))))) → D(2(1(1(1(0(1(0(1(1(0(1(2(2(1(2(1(0(1(1(2(1(1(0(1(1(1(1(2(x0)))))))))))))))))))))))))))))
L(2(0(2(0(1(1(2(1(2(1(1(1(1(0(0(0(0(1(1(1(1(0(0(2(1(2(x0))))))))))))))))))))))))))) → D(2(2(1(1(0(1(0(2(1(2(2(2(1(2(2(2(1(2(2(1(1(1(2(1(1(2(2(1(0(1(x0)))))))))))))))))))))))))))))))
L(2(2(0(2(1(0(0(0(0(1(1(0(2(0(2(0(1(2(0(1(2(0(1(1(2(2(x0))))))))))))))))))))))))))) → D(1(1(1(1(2(0(1(0(1(0(1(2(1(2(1(0(1(1(1(0(1(1(2(0(0(2(2(x0))))))))))))))))))))))))))))
L(2(2(1(2(2(1(0(2(0(2(2(1(2(0(2(0(1(1(0(1(2(0(0(1(1(2(x0))))))))))))))))))))))))))) → D(2(0(1(1(1(1(0(2(0(1(2(1(1(2(0(2(0(2(2(2(0(2(0(1(2(2(x0)))))))))))))))))))))))))))
L(0(0(1(0(1(2(0(1(1(2(0(1(2(2(2(2(1(0(1(0(0(1(1(0(0(0(1(x0)))))))))))))))))))))))))))) → D(0(1(0(0(2(2(1(1(1(2(1(0(2(2(2(0(1(2(0(2(0(0(1(1(1(0(0(0(0(x0))))))))))))))))))))))))))))))
L(0(0(1(1(2(1(0(1(1(2(0(0(1(0(2(2(0(2(1(0(2(1(2(0(0(2(2(x0)))))))))))))))))))))))))))) → D(1(0(0(1(2(2(0(1(2(2(2(2(1(1(2(1(0(0(1(1(1(0(0(2(2(1(2(2(1(x0))))))))))))))))))))))))))))))
L(0(1(0(0(2(0(2(2(1(2(1(0(2(1(2(0(0(1(0(2(1(0(2(0(2(2(0(x0)))))))))))))))))))))))))))) → D(0(1(2(1(2(1(1(1(0(2(1(0(2(1(2(1(0(2(2(1(1(0(1(2(0(2(1(1(2(1(x0)))))))))))))))))))))))))))))))
L(1(0(2(0(0(2(1(2(1(0(2(2(0(1(1(1(2(1(2(1(0(2(1(0(1(2(1(x0)))))))))))))))))))))))))))) → D(0(0(2(1(2(0(1(0(0(2(2(2(1(2(2(1(1(2(1(2(2(1(1(2(1(2(1(2(x0)))))))))))))))))))))))))))))
L(2(0(0(2(2(1(0(0(0(0(2(2(2(2(2(2(2(2(1(2(1(2(0(0(1(0(1(x0)))))))))))))))))))))))))))) → D(0(1(0(1(1(1(0(0(1(1(1(1(0(2(1(1(2(0(1(1(1(0(1(2(2(1(1(0(0(1(x0)))))))))))))))))))))))))))))))
L(2(1(2(2(2(2(2(0(0(0(0(2(0(0(1(2(1(1(2(2(0(2(1(2(2(2(0(x0)))))))))))))))))))))))))))) → D(0(2(2(0(2(0(0(2(1(1(2(1(1(2(1(0(1(0(2(1(0(1(1(1(1(0(1(0(2(1(x0)))))))))))))))))))))))))))))))
L(0(0(1(0(2(0(2(2(2(1(2(2(0(1(2(1(0(0(0(0(2(0(1(1(2(0(1(1(x0))))))))))))))))))))))))))))) → D(0(0(2(1(1(0(1(1(0(1(1(0(1(1(2(1(0(2(1(0(1(2(2(1(0(0(0(1(2(x0))))))))))))))))))))))))))))))
L(0(1(1(0(2(0(0(2(1(0(0(1(0(2(2(0(1(0(1(2(0(1(1(1(2(0(1(0(x0))))))))))))))))))))))))))))) → D(0(0(1(1(2(0(0(2(1(0(2(1(1(2(1(0(1(1(0(2(0(0(1(1(0(0(0(2(x0)))))))))))))))))))))))))))))
L(2(1(2(2(2(0(1(2(2(0(1(0(0(0(1(2(1(1(0(0(1(0(2(0(0(2(0(0(x0))))))))))))))))))))))))))))) → D(0(0(2(1(1(1(2(2(2(1(0(0(0(0(2(2(1(0(1(1(2(2(2(0(0(0(0(0(x0)))))))))))))))))))))))))))))
L(0(1(1(0(1(0(0(0(0(0(1(2(1(1(0(0(1(0(0(0(1(1(0(2(0(0(0(2(2(x0)))))))))))))))))))))))))))))) → D(0(0(1(1(0(1(1(1(2(2(0(1(0(1(1(2(1(1(0(1(1(2(2(1(1(2(2(0(0(2(x0)))))))))))))))))))))))))))))))
L(2(0(0(1(1(2(1(2(0(1(0(0(1(2(1(2(2(0(0(1(2(1(0(2(0(1(1(1(1(x0)))))))))))))))))))))))))))))) → D(0(2(1(1(2(2(1(0(0(1(1(1(2(1(1(2(2(0(2(1(2(0(2(1(1(1(1(2(1(2(x0)))))))))))))))))))))))))))))))
L(2(1(0(2(0(1(2(0(2(2(0(2(2(1(2(1(2(0(2(1(1(0(1(2(1(2(2(0(2(x0)))))))))))))))))))))))))))))) → D(0(2(1(0(0(1(1(0(1(2(1(2(1(1(2(0(1(1(2(2(1(1(2(1(0(2(1(1(0(1(x0)))))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
Y2(D(x0)) → D(2(x0))
R(D(x0)) → B(x0)