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(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(0(x0)))) → D(0(1(1(1(0(1(x0)))))))
L(2(0(0(2(1(2(2(2(0(1(2(x0)))))))))))) → D(0(1(1(2(0(0(0(1(0(2(0(1(2(x0))))))))))))))
L(1(0(0(0(0(2(0(1(2(0(1(2(x0))))))))))))) → D(0(1(1(1(1(0(2(1(1(0(1(0(1(0(1(x0))))))))))))))))
L(2(1(0(1(2(1(0(0(2(0(1(0(0(x0)))))))))))))) → D(0(0(2(0(1(2(0(2(0(0(1(1(0(1(x0)))))))))))))))
L(2(1(0(1(2(1(0(2(1(0(1(2(1(x0)))))))))))))) → D(2(0(0(1(0(1(1(0(1(0(1(1(1(1(1(x0))))))))))))))))
L(2(1(2(1(2(1(0(0(2(1(0(0(2(x0)))))))))))))) → D(1(1(1(1(0(1(1(1(1(1(1(1(2(2(0(0(0(1(x0)))))))))))))))))))
L(2(1(0(2(1(1(0(0(2(2(2(1(0(2(x0))))))))))))))) → D(2(1(2(2(0(0(1(1(1(1(1(2(2(1(1(0(1(1(0(x0))))))))))))))))))))
L(2(2(0(2(2(0(0(0(2(1(1(0(0(0(x0))))))))))))))) → D(0(2(0(0(0(2(1(1(2(0(2(2(0(0(x0)))))))))))))))
L(2(2(2(2(0(2(2(1(2(2(1(1(1(1(x0))))))))))))))) → D(2(0(2(1(1(2(2(0(1(1(1(2(2(0(1(x0))))))))))))))))
L(1(2(1(1(1(0(1(0(0(2(0(1(1(2(1(2(x0))))))))))))))))) → D(1(2(0(2(0(1(1(2(2(2(0(2(0(0(1(0(1(x0))))))))))))))))))
L(2(1(2(1(0(0(0(2(2(1(2(1(2(1(1(2(0(0(2(x0)))))))))))))))))))) → D(1(1(1(2(0(1(1(1(1(1(1(0(2(1(1(0(1(1(1(1(2(1(2(0(0(0(x0)))))))))))))))))))))))))))
L(1(0(0(2(2(0(0(0(0(1(0(2(2(0(0(0(0(0(0(1(x0))))))))))))))))))))) → D(0(0(0(1(2(1(0(2(0(0(1(1(2(0(2(0(2(2(0(0(1(x0))))))))))))))))))))))
L(2(2(0(2(2(0(0(0(2(0(0(1(2(0(2(1(0(1(2(1(x0))))))))))))))))))))) → D(1(2(1(0(0(0(1(2(1(0(0(1(1(0(0(1(1(1(2(0(1(0(1(1(0(x0))))))))))))))))))))))))))
L(1(2(0(2(1(0(2(1(2(0(2(2(2(2(2(2(1(1(1(1(2(x0)))))))))))))))))))))) → D(1(2(1(2(1(2(2(1(1(0(1(2(2(2(1(1(1(1(1(0(1(1(x0)))))))))))))))))))))))
L(2(2(0(0(1(2(0(2(0(1(0(0(2(0(1(1(0(0(0(2(1(x0)))))))))))))))))))))) → D(1(0(0(2(2(0(1(1(2(2(1(2(1(0(0(1(1(1(2(1(1(0(0(x0))))))))))))))))))))))))
L(1(2(0(1(2(2(2(1(0(2(2(1(0(1(2(1(1(0(1(2(2(2(x0))))))))))))))))))))))) → D(2(0(0(0(1(2(1(2(2(1(2(1(0(1(1(0(0(1(1(1(2(0(0(1(x0)))))))))))))))))))))))))
L(1(2(1(0(2(0(0(0(0(2(1(2(0(0(1(2(0(2(2(0(0(0(0(x0)))))))))))))))))))))))) → D(2(1(0(0(1(1(2(2(1(2(1(0(1(0(2(0(0(1(1(1(0(1(0(1(0(2(0(1(x0)))))))))))))))))))))))))))))
L(0(1(1(2(2(2(1(1(1(2(2(0(0(0(2(0(2(2(1(2(2(0(0(2(x0))))))))))))))))))))))))) → D(0(1(0(1(0(2(1(0(2(2(0(2(2(1(0(1(1(1(0(1(0(0(0(0(2(0(x0)))))))))))))))))))))))))))
L(1(0(0(2(0(0(1(0(0(2(1(1(1(0(1(1(2(0(2(2(1(1(0(0(x0))))))))))))))))))))))))) → D(2(2(1(1(2(1(1(0(2(2(0(0(1(2(2(1(1(1(0(1(1(1(0(1(1(1(x0)))))))))))))))))))))))))))
L(1(0(0(2(2(0(2(0(1(2(0(0(0(0(0(0(0(1(0(0(0(1(2(1(x0))))))))))))))))))))))))) → D(0(1(2(2(1(0(1(1(2(1(1(2(0(2(0(0(0(2(1(1(0(2(0(0(1(1(x0)))))))))))))))))))))))))))
L(1(0(2(1(2(2(2(0(0(0(0(0(0(2(0(0(0(2(1(1(2(1(2(2(x0))))))))))))))))))))))))) → D(0(1(1(0(2(0(0(2(2(1(0(2(0(0(1(1(2(0(2(2(2(0(2(2(0(x0))))))))))))))))))))))))))
L(1(2(2(0(2(2(0(1(1(2(1(0(2(2(2(2(0(2(2(2(1(2(2(2(x0))))))))))))))))))))))))) → D(0(0(2(0(0(1(0(2(2(2(1(2(2(2(0(1(1(1(2(1(2(0(1(1(2(x0))))))))))))))))))))))))))
L(2(2(2(1(1(1(2(0(0(2(1(1(1(1(2(0(2(2(0(1(2(2(0(2(x0))))))))))))))))))))))))) → D(2(1(0(0(0(1(0(2(0(1(1(1(1(0(0(1(0(1(1(0(2(2(2(1(1(1(2(x0))))))))))))))))))))))))))))
L(0(1(2(1(1(2(1(0(2(0(2(1(0(2(2(1(0(1(0(2(1(0(0(2(1(1(x0))))))))))))))))))))))))))) → D(0(2(1(2(0(0(0(2(1(2(1(1(0(0(1(0(1(2(0(1(1(0(1(1(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))
L(1(2(0(2(0(2(1(1(0(0(2(2(2(1(0(2(0(1(0(1(0(2(2(0(0(1(x0))))))))))))))))))))))))))) → D(0(1(1(0(1(2(2(0(0(1(1(2(1(2(2(0(2(1(2(2(1(0(1(2(2(1(0(0(1(x0))))))))))))))))))))))))))))))
L(2(0(2(0(0(0(0(2(2(2(0(1(1(2(2(1(1(2(2(2(1(1(1(1(2(0(x0))))))))))))))))))))))))))) → D(0(2(1(0(1(0(0(0(1(1(2(0(1(1(0(1(1(0(1(0(1(1(1(1(2(0(0(x0))))))))))))))))))))))))))))
L(2(1(1(2(0(2(2(1(0(0(2(1(0(0(2(1(1(1(1(2(0(0(2(1(0(2(x0))))))))))))))))))))))))))) → D(0(0(0(0(2(2(0(2(2(2(1(2(0(0(1(0(0(0(1(0(1(2(2(2(0(0(0(x0))))))))))))))))))))))))))))
L(0(1(0(0(2(1(2(2(0(0(0(2(2(2(2(2(0(1(2(1(2(0(2(1(0(2(0(x0)))))))))))))))))))))))))))) → D(0(1(1(1(2(1(0(0(2(0(2(2(2(2(1(2(2(0(2(0(2(0(2(0(2(0(0(x0))))))))))))))))))))))))))))
L(0(1(1(2(2(0(0(1(2(0(0(0(2(2(1(0(0(2(1(2(1(0(1(2(0(0(2(x0)))))))))))))))))))))))))))) → D(0(0(0(0(0(1(2(2(0(0(0(2(0(2(0(1(1(0(1(1(0(1(1(2(1(1(0(2(x0)))))))))))))))))))))))))))))
L(2(2(2(0(2(0(1(1(0(0(0(0(2(0(1(2(1(0(0(1(2(1(1(1(2(2(1(x0)))))))))))))))))))))))))))) → D(1(1(0(0(0(0(1(1(0(2(1(2(1(1(2(0(2(2(2(2(0(0(1(2(2(0(1(x0))))))))))))))))))))))))))))
L(1(1(1(2(0(2(0(1(0(2(2(0(0(2(1(0(2(1(0(1(0(0(0(2(1(1(1(0(x0))))))))))))))))))))))))))))) → D(0(1(0(1(0(1(0(1(1(1(2(1(2(1(1(1(0(1(2(0(1(1(0(0(1(0(0(1(2(1(1(0(1(1(1(x0))))))))))))))))))))))))))))))))))))
L(1(1(2(2(1(2(1(1(2(0(1(2(2(2(1(2(2(1(1(2(2(0(2(1(2(2(2(1(0(x0)))))))))))))))))))))))))))))) → D(0(2(2(0(1(1(1(1(2(0(0(2(1(0(1(0(0(0(1(2(1(2(1(0(2(0(0(1(0(0(1(x0))))))))))))))))))))))))))))))))
L(2(0(0(2(2(2(0(2(0(0(2(2(2(2(2(0(0(0(0(1(0(2(2(1(1(1(2(1(1(2(x0))))))))))))))))))))))))))))))) → D(0(1(0(1(1(1(1(1(2(2(0(1(1(0(1(2(1(2(2(1(2(0(0(2(1(0(2(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))
L(2(1(0(0(2(2(2(2(1(2(2(1(1(2(0(0(2(0(0(2(2(2(2(2(0(1(0(0(2(2(x0))))))))))))))))))))))))))))))) → D(0(1(2(1(0(2(1(2(2(0(1(1(2(1(0(0(1(1(1(1(0(2(2(0(0(2(2(0(0(1(1(1(1(x0))))))))))))))))))))))))))))))))))
L(0(2(2(2(0(0(2(0(2(1(1(0(2(2(0(2(2(0(1(2(1(2(2(2(0(1(1(2(1(2(2(x0)))))))))))))))))))))))))))))))) → D(0(1(2(0(0(2(0(2(1(2(1(0(1(1(0(2(0(1(0(2(0(0(0(1(1(0(1(2(1(2(0(1(0(x0))))))))))))))))))))))))))))))))))
L(2(0(2(2(1(1(0(0(0(2(2(2(0(0(0(2(0(2(2(0(1(1(2(2(1(1(2(0(0(0(2(x0)))))))))))))))))))))))))))))))) → D(0(1(1(1(0(2(1(1(2(1(1(0(0(2(1(0(0(1(1(1(1(0(2(0(2(0(1(2(1(1(0(0(2(x0))))))))))))))))))))))))))))))))))
L(1(2(1(2(2(0(1(1(2(2(0(0(0(1(0(2(2(1(2(1(1(2(0(2(1(1(2(0(0(2(1(0(x0))))))))))))))))))))))))))))))))) → D(1(1(2(2(1(2(0(1(1(2(2(1(0(1(2(0(2(2(0(1(0(0(0(0(0(0(1(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))
L(2(0(1(0(2(1(0(2(2(0(0(0(0(0(1(1(2(2(0(1(2(1(2(0(0(0(2(0(0(2(2(2(x0))))))))))))))))))))))))))))))))) → D(1(1(2(2(1(1(2(0(0(1(0(0(1(1(0(1(0(1(1(2(0(0(2(2(2(1(2(0(0(1(1(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))
L(0(0(1(0(2(1(1(1(2(1(1(2(0(2(1(1(1(2(1(0(2(1(0(1(2(0(2(2(0(2(1(0(0(x0)))))))))))))))))))))))))))))))))) → D(0(2(2(0(0(0(0(1(0(1(0(2(1(0(2(0(0(0(1(0(0(1(0(0(1(0(2(2(1(0(2(2(1(0(0(1(0(x0))))))))))))))))))))))))))))))))))))))
L(0(1(2(2(2(2(2(0(0(2(2(1(0(0(0(0(1(0(0(1(2(2(2(1(2(0(0(0(1(2(0(1(0(2(x0))))))))))))))))))))))))))))))))))) → D(0(1(1(1(1(1(1(1(1(1(0(1(1(1(2(0(1(2(0(1(0(0(2(2(0(0(1(1(2(2(2(2(0(2(2(2(1(0(1(2(1(1(1(x0))))))))))))))))))))))))))))))))))))))))))))
L(2(1(2(2(2(0(1(2(0(2(0(1(0(0(2(2(1(2(0(1(0(2(1(0(0(2(1(2(1(1(0(2(1(0(x0))))))))))))))))))))))))))))))))))) → D(0(2(0(2(0(1(0(1(1(2(2(1(2(1(0(1(0(0(1(0(1(2(1(1(2(0(1(1(2(1(1(1(0(0(1(0(1(1(2(0(0(x0))))))))))))))))))))))))))))))))))))))))))
L(2(2(0(2(1(2(2(2(2(1(1(1(0(1(2(1(1(2(2(0(2(2(2(2(2(2(2(1(0(2(1(1(1(0(x0))))))))))))))))))))))))))))))))))) → D(2(0(1(2(0(1(0(1(1(2(0(0(1(0(0(2(0(2(0(2(0(1(0(0(2(1(2(2(1(2(1(2(1(1(0(x0))))))))))))))))))))))))))))))))))))
L(0(2(0(2(2(2(0(0(1(0(2(1(0(1(1(2(2(2(2(0(0(2(0(1(0(0(2(2(0(0(2(1(2(2(2(x0)))))))))))))))))))))))))))))))))))) → D(0(1(0(0(2(0(0(0(0(1(1(2(0(1(0(2(2(1(2(0(2(2(1(0(2(0(1(2(0(2(1(0(0(1(1(2(x0)))))))))))))))))))))))))))))))))))))
L(1(2(1(1(1(0(2(2(1(2(0(0(1(2(0(0(1(0(0(2(2(2(1(1(1(2(1(0(2(1(2(2(1(1(0(x0)))))))))))))))))))))))))))))))))))) → D(0(1(0(1(0(0(1(0(2(2(2(0(2(0(1(2(1(0(2(2(2(0(2(1(2(2(0(1(1(2(0(2(2(0(0(1(0(x0))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(2(2(2(0(1(2(2(0(1(2(1(0(1(2(1(0(2(1(0(1(1(2(0(2(2(1(2(2(1(0(0(0(x0))))))))))))))))))))))))))))))))))))) → D(1(0(1(0(0(1(1(2(2(1(2(2(2(0(0(1(0(1(1(2(1(1(0(2(1(1(1(1(2(1(1(2(0(0(1(1(0(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(2(2(1(2(1(2(2(1(2(0(0(2(2(2(2(0(2(2(0(2(1(1(0(0(0(0(1(2(1(1(0(0(0(0(2(2(x0))))))))))))))))))))))))))))))))))))) → D(2(1(2(2(1(2(0(0(2(1(0(1(1(1(0(1(1(2(1(0(1(2(0(2(1(2(0(0(0(2(1(1(2(0(2(0(2(x0))))))))))))))))))))))))))))))))))))))
L(1(2(2(2(1(1(2(0(1(1(0(2(1(1(0(1(1(2(0(1(0(0(1(0(0(0(0(2(1(1(1(2(0(0(0(1(0(2(x0))))))))))))))))))))))))))))))))))))))) → D(1(1(2(0(0(1(2(2(2(1(0(1(1(1(2(2(0(1(1(2(0(0(0(1(2(2(0(1(1(0(2(0(1(1(1(2(1(1(1(x0))))))))))))))))))))))))))))))))))))))))
L(2(0(0(2(2(1(2(2(1(2(1(2(0(2(1(1(0(1(2(2(1(1(2(0(1(0(2(2(0(2(2(1(2(0(2(2(2(1(x0))))))))))))))))))))))))))))))))))))))) → D(2(2(0(1(1(1(0(2(0(2(0(0(0(0(2(1(2(0(0(0(1(0(0(2(2(2(2(2(0(2(0(1(2(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))
L(2(2(0(0(0(2(1(1(1(2(2(1(1(0(1(0(1(0(0(0(2(0(0(2(2(2(0(2(1(0(1(1(0(2(0(2(2(2(x0))))))))))))))))))))))))))))))))))))))) → D(0(2(2(1(2(0(1(0(1(2(2(0(1(1(0(0(2(2(1(0(0(0(2(2(1(0(0(1(1(1(2(0(2(0(0(2(2(2(x0)))))))))))))))))))))))))))))))))))))))
L(0(0(0(2(2(2(0(1(0(0(0(0(2(2(2(1(0(0(2(2(1(0(2(1(2(0(1(1(0(0(0(1(0(2(1(2(0(1(2(x0)))))))))))))))))))))))))))))))))))))))) → D(0(1(1(2(1(2(0(1(1(1(1(0(0(0(1(2(0(1(1(1(2(2(1(1(1(2(1(0(0(1(2(1(2(2(2(0(2(2(2(0(x0)))))))))))))))))))))))))))))))))))))))))
L(0(1(2(1(1(0(0(2(0(2(1(2(0(0(1(1(2(1(2(0(1(2(2(1(2(2(2(2(1(2(1(2(1(0(2(1(1(2(0(x0)))))))))))))))))))))))))))))))))))))))) → D(0(2(2(1(0(2(0(0(2(2(0(1(2(2(1(2(2(0(1(0(2(0(1(0(0(1(2(0(1(2(0(0(2(0(1(0(1(0(1(2(0(x0))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(0(2(2(2(0(1(0(1(0(2(2(0(0(2(2(2(2(1(2(2(2(2(2(2(1(2(1(2(2(2(0(0(0(1(2(0(x0)))))))))))))))))))))))))))))))))))))))) → D(1(2(0(2(1(1(0(1(2(0(1(2(1(0(1(1(1(1(0(1(0(2(2(0(0(1(1(2(1(0(2(1(1(2(0(1(1(1(2(2(0(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))
L(1(1(2(1(1(2(2(1(0(1(1(1(2(1(0(0(1(1(2(1(2(0(2(0(0(1(2(0(0(0(2(0(0(0(2(1(0(1(0(x0)))))))))))))))))))))))))))))))))))))))) → D(1(1(0(1(2(0(2(2(0(1(1(1(2(1(0(0(1(1(2(2(1(0(0(0(1(2(2(0(0(0(2(1(0(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))
L(1(2(1(1(2(1(1(2(2(1(2(0(1(2(0(0(0(0(0(2(2(2(0(2(1(2(1(0(0(2(2(0(0(1(0(0(0(0(2(x0)))))))))))))))))))))))))))))))))))))))) → D(2(2(0(1(1(0(0(2(0(2(2(1(2(1(1(1(2(2(2(0(0(1(0(0(0(0(2(2(0(1(1(1(0(1(2(2(2(2(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(1(2(1(1(2(2(0(1(0(0(0(2(2(2(1(2(1(1(1(2(0(1(1(0(1(2(2(2(0(2(0(2(1(0(2(1(2(0(2(x0)))))))))))))))))))))))))))))))))))))))) → D(2(2(1(2(0(2(1(0(1(0(1(1(0(0(1(1(1(2(2(1(2(0(0(2(1(1(0(2(0(1(1(1(0(1(0(1(0(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(0(2(2(0(1(0(1(1(2(1(0(1(0(2(0(2(1(1(1(2(2(1(1(2(2(1(1(2(2(2(2(1(1(2(0(1(2(1(2(1(x0))))))))))))))))))))))))))))))))))))))))) → D(0(0(2(1(1(0(1(1(1(0(1(2(0(0(2(2(0(2(1(1(1(1(1(0(2(2(1(0(2(1(2(0(0(1(0(1(1(2(0(1(0(0(1(1(1(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))
L(1(2(1(2(2(0(2(1(0(2(0(1(2(2(1(0(0(2(2(1(0(0(2(1(2(2(0(0(1(2(2(1(2(0(2(1(0(2(2(0(x0))))))))))))))))))))))))))))))))))))))))) → D(0(2(2(0(0(0(0(2(1(1(0(0(1(1(1(2(0(1(0(0(0(0(0(2(0(0(1(1(1(1(1(1(2(1(1(1(0(0(2(1(1(0(0(x0))))))))))))))))))))))))))))))))))))))))))))
L(1(2(2(1(2(2(2(0(1(0(0(2(2(2(1(1(2(2(2(1(0(1(2(1(0(2(1(1(1(1(0(2(0(0(1(2(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))) → D(2(2(2(0(1(2(2(0(0(0(0(2(1(2(2(0(1(1(2(2(0(2(1(1(1(2(2(1(0(0(1(1(2(2(0(1(1(0(1(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))
L(0(2(0(2(0(2(0(0(2(1(0(2(1(2(0(2(1(1(0(1(2(1(2(2(1(1(1(0(2(2(1(0(2(0(2(2(1(0(2(1(1(x0)))))))))))))))))))))))))))))))))))))))))) → D(0(2(1(1(0(1(2(2(2(2(2(1(1(1(0(0(2(2(1(2(1(1(1(0(1(0(0(0(1(1(2(1(0(0(0(1(1(1(0(0(0(0(2(0(0(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(0(1(0(1(0(2(1(2(2(0(1(2(1(2(2(1(0(0(2(1(0(0(1(0(2(2(2(1(1(1(1(2(2(1(1(2(1(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(1(0(0(0(1(2(1(0(1(1(1(1(2(2(2(0(0(0(2(2(2(0(0(2(2(0(2(2(1(0(0(1(0(1(1(2(0(1(1(1(1(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(2(0(2(2(0(2(1(1(0(1(0(2(2(0(2(2(2(0(0(0(0(0(2(2(2(0(0(2(0(1(1(2(0(2(2(2(0(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(2(0(0(1(1(2(2(0(0(1(0(1(1(2(1(2(2(0(1(1(1(2(1(1(0(2(1(2(2(1(0(1(1(0(2(1(2(0(2(1(0(x0)))))))))))))))))))))))))))))))))))))))))))
L(2(2(0(1(2(2(2(1(1(0(2(1(1(0(0(1(2(0(2(2(0(2(1(2(0(0(2(0(1(0(0(1(1(2(2(2(1(1(2(0(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(2(0(2(1(2(1(2(0(2(1(2(1(2(2(1(2(2(0(0(0(0(0(1(1(1(1(0(0(2(0(2(2(0(2(1(2(2(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(0(2(0(2(1(1(1(2(0(0(0(0(0(2(1(1(2(1(0(1(0(1(0(0(0(1(0(2(1(1(2(0(0(2(0(2(2(0(1(x0))))))))))))))))))))))))))))))))))))))))))) → D(2(0(1(2(0(0(2(0(0(0(2(2(1(1(2(0(0(0(0(0(0(1(0(1(2(0(0(1(0(0(0(1(1(0(1(1(0(1(1(0(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))
L(2(0(1(2(2(1(1(2(2(2(1(1(2(0(2(1(2(0(2(2(1(0(0(2(2(1(2(2(1(2(2(1(0(0(2(0(1(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))) → D(1(1(1(2(0(2(1(0(1(1(1(1(1(0(2(2(1(0(0(1(1(0(1(1(1(0(1(2(0(2(1(2(0(1(2(2(2(0(2(0(2(0(0(1(0(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(0(0(2(0(2(1(1(2(2(2(1(2(1(0(1(2(0(2(2(1(0(0(2(2(0(2(1(0(0(1(2(0(2(2(1(0(0(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))) → D(2(2(1(1(0(2(0(0(1(1(1(0(2(0(1(2(0(2(0(2(2(1(0(1(0(0(2(2(2(1(1(2(1(1(2(2(2(2(1(1(2(1(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(1(0(1(2(2(0(0(2(2(1(2(2(0(2(1(1(1(1(0(1(2(1(1(0(0(2(1(0(0(0(0(2(2(0(0(1(0(2(1(2(2(0(x0))))))))))))))))))))))))))))))))))))))))))))) → D(1(0(1(2(0(1(0(0(0(1(0(2(1(0(0(0(1(2(2(0(1(2(0(1(0(2(0(1(0(2(0(0(0(2(1(0(2(0(1(2(0(0(2(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(0(1(1(1(2(0(1(0(2(2(2(2(0(2(0(2(2(2(0(0(0(0(2(0(2(1(2(0(1(0(0(1(0(1(2(1(0(0(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))) → D(1(1(1(0(0(1(1(2(1(1(2(2(0(2(1(2(2(2(0(2(2(1(2(0(2(0(1(1(1(2(0(2(2(0(2(0(1(1(1(2(2(2(0(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(0(2(0(1(0(1(1(0(1(2(2(1(0(0(0(0(2(1(2(1(0(1(1(2(1(1(1(1(2(1(0(1(2(2(2(0(1(2(2(1(1(2(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(2(0(2(1(1(1(2(1(0(0(1(0(1(1(1(0(1(0(0(0(2(1(1(2(1(0(0(1(0(0(1(2(1(2(1(2(1(2(1(0(1(1(1(1(2(0(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(0(1(0(2(2(2(2(1(0(1(0(2(1(1(0(2(2(0(1(2(0(2(2(2(2(2(1(0(2(1(1(1(0(1(2(2(0(2(0(0(1(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(0(2(2(0(2(1(2(1(2(0(1(0(1(2(2(0(2(2(0(1(2(0(1(0(1(1(2(0(0(0(0(1(2(2(0(0(2(1(1(1(1(0(2(0(2(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(2(2(0(0(1(2(0(1(2(0(0(1(2(0(0(1(2(2(1(1(0(0(2(1(0(1(0(0(0(2(1(0(1(2(1(1(2(2(1(1(0(1(1(2(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(2(1(2(2(1(0(1(2(2(0(2(0(0(2(0(0(2(1(2(0(1(1(1(0(2(2(1(1(0(0(0(2(1(2(1(1(1(0(1(0(1(0(0(1(1(2(x0)))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(2(1(2(1(2(2(1(2(2(1(1(2(2(0(1(0(0(2(2(2(1(1(2(2(1(1(1(2(2(1(0(2(0(2(1(2(1(2(1(0(2(1(1(2(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(0(1(2(0(2(2(2(0(2(1(1(0(1(1(0(0(0(0(0(1(1(0(1(2(0(0(1(1(1(2(1(1(2(0(1(1(0(1(1(1(2(1(1(0(1(1(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(2(2(0(2(0(2(0(2(2(0(2(0(0(1(1(1(2(1(0(2(0(0(0(0(2(1(2(1(1(2(2(2(2(1(0(0(2(0(0(2(1(0(2(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(0(1(2(1(2(0(1(2(1(1(1(2(2(0(1(2(2(1(1(0(1(1(0(1(2(0(2(1(2(2(2(2(0(1(2(1(0(0(2(0(1(2(0(1(1(2(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(0(0(2(0(2(2(0(1(2(0(1(0(2(2(2(1(1(1(1(1(0(0(0(2(2(1(1(2(2(0(1(0(0(0(1(2(0(0(1(2(0(2(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(1(2(2(0(1(1(2(0(1(1(2(1(1(0(0(0(0(1(1(0(2(1(2(2(2(2(1(1(0(2(2(1(0(2(0(1(0(0(0(1(0(0(0(2(1(2(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(0(2(2(1(2(2(1(1(2(2(1(2(2(1(2(1(0(0(0(0(2(2(0(1(2(1(1(0(2(2(0(0(1(1(0(0(2(2(0(1(2(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(2(1(2(1(1(1(0(0(0(1(1(0(2(2(1(1(2(2(0(1(1(1(1(1(1(1(1(0(0(1(0(2(2(0(2(1(0(0(2(2(1(2(1(0(1(1(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(2(1(2(2(2(2(2(2(2(1(0(1(2(1(1(0(2(0(0(2(1(2(1(2(1(0(0(0(0(0(2(0(0(1(0(1(1(0(0(0(2(0(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))) → D(1(2(1(0(2(0(1(2(1(2(0(1(2(1(2(1(1(0(2(1(0(1(1(0(0(1(2(1(1(1(0(0(1(1(1(2(0(2(0(2(2(2(0(0(1(2(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(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(0(x0)))) → D(0(1(1(1(0(1(x0)))))))
L(2(0(0(2(1(2(2(2(0(1(2(x0)))))))))))) → D(0(1(1(2(0(0(0(1(0(2(0(1(2(x0))))))))))))))
L(1(0(0(0(0(2(0(1(2(0(1(2(x0))))))))))))) → D(0(1(1(1(1(0(2(1(1(0(1(0(1(0(1(x0))))))))))))))))
L(2(1(0(1(2(1(0(0(2(0(1(0(0(x0)))))))))))))) → D(0(0(2(0(1(2(0(2(0(0(1(1(0(1(x0)))))))))))))))
L(2(1(0(1(2(1(0(2(1(0(1(2(1(x0)))))))))))))) → D(2(0(0(1(0(1(1(0(1(0(1(1(1(1(1(x0))))))))))))))))
L(2(1(2(1(2(1(0(0(2(1(0(0(2(x0)))))))))))))) → D(1(1(1(1(0(1(1(1(1(1(1(1(2(2(0(0(0(1(x0)))))))))))))))))))
L(2(1(0(2(1(1(0(0(2(2(2(1(0(2(x0))))))))))))))) → D(2(1(2(2(0(0(1(1(1(1(1(2(2(1(1(0(1(1(0(x0))))))))))))))))))))
L(2(2(0(2(2(0(0(0(2(1(1(0(0(0(x0))))))))))))))) → D(0(2(0(0(0(2(1(1(2(0(2(2(0(0(x0)))))))))))))))
L(2(2(2(2(0(2(2(1(2(2(1(1(1(1(x0))))))))))))))) → D(2(0(2(1(1(2(2(0(1(1(1(2(2(0(1(x0))))))))))))))))
L(1(2(1(1(1(0(1(0(0(2(0(1(1(2(1(2(x0))))))))))))))))) → D(1(2(0(2(0(1(1(2(2(2(0(2(0(0(1(0(1(x0))))))))))))))))))
L(2(1(2(1(0(0(0(2(2(1(2(1(2(1(1(2(0(0(2(x0)))))))))))))))))))) → D(1(1(1(2(0(1(1(1(1(1(1(0(2(1(1(0(1(1(1(1(2(1(2(0(0(0(x0)))))))))))))))))))))))))))
L(1(0(0(2(2(0(0(0(0(1(0(2(2(0(0(0(0(0(0(1(x0))))))))))))))))))))) → D(0(0(0(1(2(1(0(2(0(0(1(1(2(0(2(0(2(2(0(0(1(x0))))))))))))))))))))))
L(2(2(0(2(2(0(0(0(2(0(0(1(2(0(2(1(0(1(2(1(x0))))))))))))))))))))) → D(1(2(1(0(0(0(1(2(1(0(0(1(1(0(0(1(1(1(2(0(1(0(1(1(0(x0))))))))))))))))))))))))))
L(1(2(0(2(1(0(2(1(2(0(2(2(2(2(2(2(1(1(1(1(2(x0)))))))))))))))))))))) → D(1(2(1(2(1(2(2(1(1(0(1(2(2(2(1(1(1(1(1(0(1(1(x0)))))))))))))))))))))))
L(2(2(0(0(1(2(0(2(0(1(0(0(2(0(1(1(0(0(0(2(1(x0)))))))))))))))))))))) → D(1(0(0(2(2(0(1(1(2(2(1(2(1(0(0(1(1(1(2(1(1(0(0(x0))))))))))))))))))))))))
L(1(2(0(1(2(2(2(1(0(2(2(1(0(1(2(1(1(0(1(2(2(2(x0))))))))))))))))))))))) → D(2(0(0(0(1(2(1(2(2(1(2(1(0(1(1(0(0(1(1(1(2(0(0(1(x0)))))))))))))))))))))))))
L(1(2(1(0(2(0(0(0(0(2(1(2(0(0(1(2(0(2(2(0(0(0(0(x0)))))))))))))))))))))))) → D(2(1(0(0(1(1(2(2(1(2(1(0(1(0(2(0(0(1(1(1(0(1(0(1(0(2(0(1(x0)))))))))))))))))))))))))))))
L(0(1(1(2(2(2(1(1(1(2(2(0(0(0(2(0(2(2(1(2(2(0(0(2(x0))))))))))))))))))))))))) → D(0(1(0(1(0(2(1(0(2(2(0(2(2(1(0(1(1(1(0(1(0(0(0(0(2(0(x0)))))))))))))))))))))))))))
L(1(0(0(2(0(0(1(0(0(2(1(1(1(0(1(1(2(0(2(2(1(1(0(0(x0))))))))))))))))))))))))) → D(2(2(1(1(2(1(1(0(2(2(0(0(1(2(2(1(1(1(0(1(1(1(0(1(1(1(x0)))))))))))))))))))))))))))
L(1(0(0(2(2(0(2(0(1(2(0(0(0(0(0(0(0(1(0(0(0(1(2(1(x0))))))))))))))))))))))))) → D(0(1(2(2(1(0(1(1(2(1(1(2(0(2(0(0(0(2(1(1(0(2(0(0(1(1(x0)))))))))))))))))))))))))))
L(1(0(2(1(2(2(2(0(0(0(0(0(0(2(0(0(0(2(1(1(2(1(2(2(x0))))))))))))))))))))))))) → D(0(1(1(0(2(0(0(2(2(1(0(2(0(0(1(1(2(0(2(2(2(0(2(2(0(x0))))))))))))))))))))))))))
L(1(2(2(0(2(2(0(1(1(2(1(0(2(2(2(2(0(2(2(2(1(2(2(2(x0))))))))))))))))))))))))) → D(0(0(2(0(0(1(0(2(2(2(1(2(2(2(0(1(1(1(2(1(2(0(1(1(2(x0))))))))))))))))))))))))))
L(2(2(2(1(1(1(2(0(0(2(1(1(1(1(2(0(2(2(0(1(2(2(0(2(x0))))))))))))))))))))))))) → D(2(1(0(0(0(1(0(2(0(1(1(1(1(0(0(1(0(1(1(0(2(2(2(1(1(1(2(x0))))))))))))))))))))))))))))
L(0(1(2(1(1(2(1(0(2(0(2(1(0(2(2(1(0(1(0(2(1(0(0(2(1(1(x0))))))))))))))))))))))))))) → D(0(2(1(2(0(0(0(2(1(2(1(1(0(0(1(0(1(2(0(1(1(0(1(1(0(1(1(1(1(1(x0)))))))))))))))))))))))))))))))
L(1(2(0(2(0(2(1(1(0(0(2(2(2(1(0(2(0(1(0(1(0(2(2(0(0(1(x0))))))))))))))))))))))))))) → D(0(1(1(0(1(2(2(0(0(1(1(2(1(2(2(0(2(1(2(2(1(0(1(2(2(1(0(0(1(x0))))))))))))))))))))))))))))))
L(2(0(2(0(0(0(0(2(2(2(0(1(1(2(2(1(1(2(2(2(1(1(1(1(2(0(x0))))))))))))))))))))))))))) → D(0(2(1(0(1(0(0(0(1(1(2(0(1(1(0(1(1(0(1(0(1(1(1(1(2(0(0(x0))))))))))))))))))))))))))))
L(2(1(1(2(0(2(2(1(0(0(2(1(0(0(2(1(1(1(1(2(0(0(2(1(0(2(x0))))))))))))))))))))))))))) → D(0(0(0(0(2(2(0(2(2(2(1(2(0(0(1(0(0(0(1(0(1(2(2(2(0(0(0(x0))))))))))))))))))))))))))))
L(0(1(0(0(2(1(2(2(0(0(0(2(2(2(2(2(0(1(2(1(2(0(2(1(0(2(0(x0)))))))))))))))))))))))))))) → D(0(1(1(1(2(1(0(0(2(0(2(2(2(2(1(2(2(0(2(0(2(0(2(0(2(0(0(x0))))))))))))))))))))))))))))
L(0(1(1(2(2(0(0(1(2(0(0(0(2(2(1(0(0(2(1(2(1(0(1(2(0(0(2(x0)))))))))))))))))))))))))))) → D(0(0(0(0(0(1(2(2(0(0(0(2(0(2(0(1(1(0(1(1(0(1(1(2(1(1(0(2(x0)))))))))))))))))))))))))))))
L(2(2(2(0(2(0(1(1(0(0(0(0(2(0(1(2(1(0(0(1(2(1(1(1(2(2(1(x0)))))))))))))))))))))))))))) → D(1(1(0(0(0(0(1(1(0(2(1(2(1(1(2(0(2(2(2(2(0(0(1(2(2(0(1(x0))))))))))))))))))))))))))))
L(1(1(1(2(0(2(0(1(0(2(2(0(0(2(1(0(2(1(0(1(0(0(0(2(1(1(1(0(x0))))))))))))))))))))))))))))) → D(0(1(0(1(0(1(0(1(1(1(2(1(2(1(1(1(0(1(2(0(1(1(0(0(1(0(0(1(2(1(1(0(1(1(1(x0))))))))))))))))))))))))))))))))))))
L(1(1(2(2(1(2(1(1(2(0(1(2(2(2(1(2(2(1(1(2(2(0(2(1(2(2(2(1(0(x0)))))))))))))))))))))))))))))) → D(0(2(2(0(1(1(1(1(2(0(0(2(1(0(1(0(0(0(1(2(1(2(1(0(2(0(0(1(0(0(1(x0))))))))))))))))))))))))))))))))
L(2(0(0(2(2(2(0(2(0(0(2(2(2(2(2(0(0(0(0(1(0(2(2(1(1(1(2(1(1(2(x0))))))))))))))))))))))))))))))) → D(0(1(0(1(1(1(1(1(2(2(0(1(1(0(1(2(1(2(2(1(2(0(0(2(1(0(2(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))
L(2(1(0(0(2(2(2(2(1(2(2(1(1(2(0(0(2(0(0(2(2(2(2(2(0(1(0(0(2(2(x0))))))))))))))))))))))))))))))) → D(0(1(2(1(0(2(1(2(2(0(1(1(2(1(0(0(1(1(1(1(0(2(2(0(0(2(2(0(0(1(1(1(1(x0))))))))))))))))))))))))))))))))))
L(0(2(2(2(0(0(2(0(2(1(1(0(2(2(0(2(2(0(1(2(1(2(2(2(0(1(1(2(1(2(2(x0)))))))))))))))))))))))))))))))) → D(0(1(2(0(0(2(0(2(1(2(1(0(1(1(0(2(0(1(0(2(0(0(0(1(1(0(1(2(1(2(0(1(0(x0))))))))))))))))))))))))))))))))))
L(2(0(2(2(1(1(0(0(0(2(2(2(0(0(0(2(0(2(2(0(1(1(2(2(1(1(2(0(0(0(2(x0)))))))))))))))))))))))))))))))) → D(0(1(1(1(0(2(1(1(2(1(1(0(0(2(1(0(0(1(1(1(1(0(2(0(2(0(1(2(1(1(0(0(2(x0))))))))))))))))))))))))))))))))))
L(1(2(1(2(2(0(1(1(2(2(0(0(0(1(0(2(2(1(2(1(1(2(0(2(1(1(2(0(0(2(1(0(x0))))))))))))))))))))))))))))))))) → D(1(1(2(2(1(2(0(1(1(2(2(1(0(1(2(0(2(2(0(1(0(0(0(0(0(0(1(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))
L(2(0(1(0(2(1(0(2(2(0(0(0(0(0(1(1(2(2(0(1(2(1(2(0(0(0(2(0(0(2(2(2(x0))))))))))))))))))))))))))))))))) → D(1(1(2(2(1(1(2(0(0(1(0(0(1(1(0(1(0(1(1(2(0(0(2(2(2(1(2(0(0(1(1(1(1(1(0(0(x0)))))))))))))))))))))))))))))))))))))
L(0(0(1(0(2(1(1(1(2(1(1(2(0(2(1(1(1(2(1(0(2(1(0(1(2(0(2(2(0(2(1(0(0(x0)))))))))))))))))))))))))))))))))) → D(0(2(2(0(0(0(0(1(0(1(0(2(1(0(2(0(0(0(1(0(0(1(0(0(1(0(2(2(1(0(2(2(1(0(0(1(0(x0))))))))))))))))))))))))))))))))))))))
L(0(1(2(2(2(2(2(0(0(2(2(1(0(0(0(0(1(0(0(1(2(2(2(1(2(0(0(0(1(2(0(1(0(2(x0))))))))))))))))))))))))))))))))))) → D(0(1(1(1(1(1(1(1(1(1(0(1(1(1(2(0(1(2(0(1(0(0(2(2(0(0(1(1(2(2(2(2(0(2(2(2(1(0(1(2(1(1(1(x0))))))))))))))))))))))))))))))))))))))))))))
L(2(1(2(2(2(0(1(2(0(2(0(1(0(0(2(2(1(2(0(1(0(2(1(0(0(2(1(2(1(1(0(2(1(0(x0))))))))))))))))))))))))))))))))))) → D(0(2(0(2(0(1(0(1(1(2(2(1(2(1(0(1(0(0(1(0(1(2(1(1(2(0(1(1(2(1(1(1(0(0(1(0(1(1(2(0(0(x0))))))))))))))))))))))))))))))))))))))))))
L(2(2(0(2(1(2(2(2(2(1(1(1(0(1(2(1(1(2(2(0(2(2(2(2(2(2(2(1(0(2(1(1(1(0(x0))))))))))))))))))))))))))))))))))) → D(2(0(1(2(0(1(0(1(1(2(0(0(1(0(0(2(0(2(0(2(0(1(0(0(2(1(2(2(1(2(1(2(1(1(0(x0))))))))))))))))))))))))))))))))))))
L(0(2(0(2(2(2(0(0(1(0(2(1(0(1(1(2(2(2(2(0(0(2(0(1(0(0(2(2(0(0(2(1(2(2(2(x0)))))))))))))))))))))))))))))))))))) → D(0(1(0(0(2(0(0(0(0(1(1(2(0(1(0(2(2(1(2(0(2(2(1(0(2(0(1(2(0(2(1(0(0(1(1(2(x0)))))))))))))))))))))))))))))))))))))
L(1(2(1(1(1(0(2(2(1(2(0(0(1(2(0(0(1(0(0(2(2(2(1(1(1(2(1(0(2(1(2(2(1(1(0(x0)))))))))))))))))))))))))))))))))))) → D(0(1(0(1(0(0(1(0(2(2(2(0(2(0(1(2(1(0(2(2(2(0(2(1(2(2(0(1(1(2(0(2(2(0(0(1(0(x0))))))))))))))))))))))))))))))))))))))
L(1(0(0(1(2(2(2(0(1(2(2(0(1(2(1(0(1(2(1(0(2(1(0(1(1(2(0(2(2(1(2(2(1(0(0(0(x0))))))))))))))))))))))))))))))))))))) → D(1(0(1(0(0(1(1(2(2(1(2(2(2(0(0(1(0(1(1(2(1(1(0(2(1(1(1(1(2(1(1(2(0(0(1(1(0(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(2(2(1(2(1(2(2(1(2(0(0(2(2(2(2(0(2(2(0(2(1(1(0(0(0(0(1(2(1(1(0(0(0(0(2(2(x0))))))))))))))))))))))))))))))))))))) → D(2(1(2(2(1(2(0(0(2(1(0(1(1(1(0(1(1(2(1(0(1(2(0(2(1(2(0(0(0(2(1(1(2(0(2(0(2(x0))))))))))))))))))))))))))))))))))))))
L(1(2(2(2(1(1(2(0(1(1(0(2(1(1(0(1(1(2(0(1(0(0(1(0(0(0(0(2(1(1(1(2(0(0(0(1(0(2(x0))))))))))))))))))))))))))))))))))))))) → D(1(1(2(0(0(1(2(2(2(1(0(1(1(1(2(2(0(1(1(2(0(0(0(1(2(2(0(1(1(0(2(0(1(1(1(2(1(1(1(x0))))))))))))))))))))))))))))))))))))))))
L(2(0(0(2(2(1(2(2(1(2(1(2(0(2(1(1(0(1(2(2(1(1(2(0(1(0(2(2(0(2(2(1(2(0(2(2(2(1(x0))))))))))))))))))))))))))))))))))))))) → D(2(2(0(1(1(1(0(2(0(2(0(0(0(0(2(1(2(0(0(0(1(0(0(2(2(2(2(2(0(2(0(1(2(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))
L(2(2(0(0(0(2(1(1(1(2(2(1(1(0(1(0(1(0(0(0(2(0(0(2(2(2(0(2(1(0(1(1(0(2(0(2(2(2(x0))))))))))))))))))))))))))))))))))))))) → D(0(2(2(1(2(0(1(0(1(2(2(0(1(1(0(0(2(2(1(0(0(0(2(2(1(0(0(1(1(1(2(0(2(0(0(2(2(2(x0)))))))))))))))))))))))))))))))))))))))
L(0(0(0(2(2(2(0(1(0(0(0(0(2(2(2(1(0(0(2(2(1(0(2(1(2(0(1(1(0(0(0(1(0(2(1(2(0(1(2(x0)))))))))))))))))))))))))))))))))))))))) → D(0(1(1(2(1(2(0(1(1(1(1(0(0(0(1(2(0(1(1(1(2(2(1(1(1(2(1(0(0(1(2(1(2(2(2(0(2(2(2(0(x0)))))))))))))))))))))))))))))))))))))))))
L(0(1(2(1(1(0(0(2(0(2(1(2(0(0(1(1(2(1(2(0(1(2(2(1(2(2(2(2(1(2(1(2(1(0(2(1(1(2(0(x0)))))))))))))))))))))))))))))))))))))))) → D(0(2(2(1(0(2(0(0(2(2(0(1(2(2(1(2(2(0(1(0(2(0(1(0(0(1(2(0(1(2(0(0(2(0(1(0(1(0(1(2(0(x0))))))))))))))))))))))))))))))))))))))))))
L(1(0(0(0(2(2(2(0(1(0(1(0(2(2(0(0(2(2(2(2(1(2(2(2(2(2(2(1(2(1(2(2(2(0(0(0(1(2(0(x0)))))))))))))))))))))))))))))))))))))))) → D(1(2(0(2(1(1(0(1(2(0(1(2(1(0(1(1(1(1(0(1(0(2(2(0(0(1(1(2(1(0(2(1(1(2(0(1(1(1(2(2(0(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))
L(1(1(2(1(1(2(2(1(0(1(1(1(2(1(0(0(1(1(2(1(2(0(2(0(0(1(2(0(0(0(2(0(0(0(2(1(0(1(0(x0)))))))))))))))))))))))))))))))))))))))) → D(1(1(0(1(2(0(2(2(0(1(1(1(2(1(0(0(1(1(2(2(1(0(0(0(1(2(2(0(0(0(2(1(0(2(0(1(1(1(0(x0))))))))))))))))))))))))))))))))))))))))
L(1(2(1(1(2(1(1(2(2(1(2(0(1(2(0(0(0(0(0(2(2(2(0(2(1(2(1(0(0(2(2(0(0(1(0(0(0(0(2(x0)))))))))))))))))))))))))))))))))))))))) → D(2(2(0(1(1(0(0(2(0(2(2(1(2(1(1(1(2(2(2(0(0(1(0(0(0(0(2(2(0(1(1(1(0(1(2(2(2(2(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(1(2(1(1(2(2(0(1(0(0(0(2(2(2(1(2(1(1(1(2(0(1(1(0(1(2(2(2(0(2(0(2(1(0(2(1(2(0(2(x0)))))))))))))))))))))))))))))))))))))))) → D(2(2(1(2(0(2(1(0(1(0(1(1(0(0(1(1(1(2(2(1(2(0(0(2(1(1(0(2(0(1(1(1(0(1(0(1(0(0(1(0(x0)))))))))))))))))))))))))))))))))))))))))
L(0(2(2(0(1(0(1(1(2(1(0(1(0(2(0(2(1(1(1(2(2(1(1(2(2(1(1(2(2(2(2(1(1(2(0(1(2(1(2(1(x0))))))))))))))))))))))))))))))))))))))))) → D(0(0(2(1(1(0(1(1(1(0(1(2(0(0(2(2(0(2(1(1(1(1(1(0(2(2(1(0(2(1(2(0(0(1(0(1(1(2(0(1(0(0(1(1(1(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))
L(1(2(1(2(2(0(2(1(0(2(0(1(2(2(1(0(0(2(2(1(0(0(2(1(2(2(0(0(1(2(2(1(2(0(2(1(0(2(2(0(x0))))))))))))))))))))))))))))))))))))))))) → D(0(2(2(0(0(0(0(2(1(1(0(0(1(1(1(2(0(1(0(0(0(0(0(2(0(0(1(1(1(1(1(1(2(1(1(1(0(0(2(1(1(0(0(x0))))))))))))))))))))))))))))))))))))))))))))
L(1(2(2(1(2(2(2(0(1(0(0(2(2(2(1(1(2(2(2(1(0(1(2(1(0(2(1(1(1(1(0(2(0(0(1(2(0(1(1(0(x0))))))))))))))))))))))))))))))))))))))))) → D(2(2(2(0(1(2(2(0(0(0(0(2(1(2(2(0(1(1(2(2(0(2(1(1(1(2(2(1(0(0(1(1(2(2(0(1(1(0(1(1(0(1(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))
L(0(2(0(2(0(2(0(0(2(1(0(2(1(2(0(2(1(1(0(1(2(1(2(2(1(1(1(0(2(2(1(0(2(0(2(2(1(0(2(1(1(x0)))))))))))))))))))))))))))))))))))))))))) → D(0(2(1(1(0(1(2(2(2(2(2(1(1(1(0(0(2(2(1(2(1(1(1(0(1(0(0(0(1(1(2(1(0(0(0(1(1(1(0(0(0(0(2(0(0(1(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(0(1(0(1(0(2(1(2(2(0(1(2(1(2(2(1(0(0(2(1(0(0(1(0(2(2(2(1(1(1(1(2(2(1(1(2(1(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(1(0(0(0(1(2(1(0(1(1(1(1(2(2(2(0(0(0(2(2(2(0(0(2(2(0(2(2(1(0(0(1(0(1(1(2(0(1(1(1(1(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(2(0(2(2(0(2(1(1(0(1(0(2(2(0(2(2(2(0(0(0(0(0(2(2(2(0(0(2(0(1(1(2(0(2(2(2(0(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(2(0(0(1(1(2(2(0(0(1(0(1(1(2(1(2(2(0(1(1(1(2(1(1(0(2(1(2(2(1(0(1(1(0(2(1(2(0(2(1(0(x0)))))))))))))))))))))))))))))))))))))))))))
L(2(2(0(1(2(2(2(1(1(0(2(1(1(0(0(1(2(0(2(2(0(2(1(2(0(0(2(0(1(0(0(1(1(2(2(2(1(1(2(0(2(x0)))))))))))))))))))))))))))))))))))))))))) → D(2(2(0(2(1(2(1(2(0(2(1(2(1(2(2(1(2(2(0(0(0(0(0(1(1(1(1(0(0(2(0(2(2(0(2(1(2(2(1(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(0(2(0(2(1(1(1(2(0(0(0(0(0(2(1(1(2(1(0(1(0(1(0(0(0(1(0(2(1(1(2(0(0(2(0(2(2(0(1(x0))))))))))))))))))))))))))))))))))))))))))) → D(2(0(1(2(0(0(2(0(0(0(2(2(1(1(2(0(0(0(0(0(0(1(0(1(2(0(0(1(0(0(0(1(1(0(1(1(0(1(1(0(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))
L(2(0(1(2(2(1(1(2(2(2(1(1(2(0(2(1(2(0(2(2(1(0(0(2(2(1(2(2(1(2(2(1(0(0(2(0(1(0(0(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))) → D(1(1(1(2(0(2(1(0(1(1(1(1(1(0(2(2(1(0(0(1(1(0(1(1(1(0(1(2(0(2(1(2(0(1(2(2(2(0(2(0(2(0(0(1(0(0(1(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(1(0(0(2(0(2(1(1(2(2(2(1(2(1(0(1(2(0(2(2(1(0(0(2(2(0(2(1(0(0(1(2(0(2(2(1(0(0(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))) → D(2(2(1(1(0(2(0(0(1(1(1(0(2(0(1(2(0(2(0(2(2(1(0(1(0(0(2(2(2(1(1(2(1(1(2(2(2(2(1(1(2(1(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))
L(1(0(1(0(1(2(2(0(0(2(2(1(2(2(0(2(1(1(1(1(0(1(2(1(1(0(0(2(1(0(0(0(0(2(2(0(0(1(0(2(1(2(2(0(x0))))))))))))))))))))))))))))))))))))))))))))) → D(1(0(1(2(0(1(0(0(0(1(0(2(1(0(0(0(1(2(2(0(1(2(0(1(0(2(0(1(0(2(0(0(0(2(1(0(2(0(1(2(0(0(2(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(0(1(1(1(2(0(1(0(2(2(2(2(0(2(0(2(2(2(0(0(0(0(2(0(2(1(2(0(1(0(0(1(0(1(2(1(0(0(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))) → D(1(1(1(0(0(1(1(2(1(1(2(2(0(2(1(2(2(2(0(2(2(1(2(0(2(0(1(1(1(2(0(2(2(0(2(0(1(1(1(2(2(2(0(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(0(2(0(1(0(1(1(0(1(2(2(1(0(0(0(0(2(1(2(1(0(1(1(2(1(1(1(1(2(1(0(1(2(2(2(0(1(2(2(1(1(2(1(0(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(2(0(2(1(1(1(2(1(0(0(1(0(1(1(1(0(1(0(0(0(2(1(1(2(1(0(0(1(0(0(1(2(1(2(1(2(1(2(1(0(1(1(1(1(2(0(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(0(1(0(2(2(2(2(1(0(1(0(2(1(1(0(2(2(0(1(2(0(2(2(2(2(2(1(0(2(1(1(1(0(1(2(2(0(2(0(0(1(0(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(0(2(2(0(2(1(2(1(2(0(1(0(1(2(2(0(2(2(0(1(2(0(1(0(1(1(2(0(0(0(0(1(2(2(0(0(2(1(1(1(1(0(2(0(2(0(0(x0))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(2(2(0(0(1(2(0(1(2(0(0(1(2(0(0(1(2(2(1(1(0(0(2(1(0(1(0(0(0(2(1(0(1(2(1(1(2(2(1(1(0(1(1(2(x0))))))))))))))))))))))))))))))))))))))))))))))) → D(2(1(2(2(1(0(1(2(2(0(2(0(0(2(0(0(2(1(2(0(1(1(1(0(2(2(1(1(0(0(0(2(1(2(1(1(1(0(1(0(1(0(0(1(1(2(x0)))))))))))))))))))))))))))))))))))))))))))))))
L(0(0(2(1(2(1(2(2(1(2(2(1(1(2(2(0(1(0(0(2(2(2(1(1(2(2(1(1(1(2(2(1(0(2(0(2(1(2(1(2(1(0(2(1(1(2(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(0(1(2(0(2(2(2(0(2(1(1(0(1(1(0(0(0(0(0(1(1(0(1(2(0(0(1(1(1(2(1(1(2(0(1(1(0(1(1(1(2(1(1(0(1(1(1(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))
L(0(2(2(0(2(0(2(0(2(2(0(2(0(0(1(1(1(2(1(0(2(0(0(0(0(2(1(2(1(1(2(2(2(2(1(0(0(2(0(0(2(1(0(2(2(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(0(1(2(1(2(0(1(2(1(1(1(2(2(0(1(2(2(1(1(0(1(1(0(1(2(0(2(1(2(2(2(2(0(1(2(1(0(0(2(0(1(2(0(1(1(2(0(0(0(1(x0)))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(0(0(2(0(2(2(0(1(2(0(1(0(2(2(2(1(1(1(1(1(0(0(0(2(2(1(1(2(2(0(1(0(0(0(1(2(0(0(1(2(0(2(1(0(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(1(2(2(0(1(1(2(0(1(1(2(1(1(0(0(0(0(1(1(0(2(1(2(2(2(2(1(1(0(2(2(1(0(2(0(1(0(0(0(1(0(0(0(2(1(2(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(1(0(2(2(1(2(2(1(1(2(2(1(2(2(1(2(1(0(0(0(0(2(2(0(1(2(1(1(0(2(2(0(0(1(1(0(0(2(2(0(1(2(1(1(1(0(x0)))))))))))))))))))))))))))))))))))))))))))))))) → D(2(1(2(1(1(1(0(0(0(1(1(0(2(2(1(1(2(2(0(1(1(1(1(1(1(1(1(0(0(1(0(2(2(0(2(1(0(0(2(2(1(2(1(0(1(1(0(0(1(x0))))))))))))))))))))))))))))))))))))))))))))))))))
L(2(0(2(2(1(2(2(2(2(2(2(2(1(0(1(2(1(1(0(2(0(0(2(1(2(1(2(1(0(0(0(0(0(2(0(0(1(0(1(1(0(0(0(2(0(0(1(1(x0))))))))))))))))))))))))))))))))))))))))))))))))) → D(1(2(1(0(2(0(1(2(1(2(0(1(2(1(2(1(1(0(2(1(0(1(1(0(0(1(2(1(1(1(0(0(1(1(1(2(0(2(0(2(2(2(0(0(1(2(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)