MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

begin(end(x0)) → rewrite(end(x0))
begin(q0(x0)) → rotate(cut(Cq0(guess(x0))))
begin(0(x0)) → rotate(cut(C0(guess(x0))))
begin(0'(x0)) → rotate(cut(C0'(guess(x0))))
begin(q1(x0)) → rotate(cut(Cq1(guess(x0))))
begin(1'(x0)) → rotate(cut(C1'(guess(x0))))
begin(1(x0)) → rotate(cut(C1(guess(x0))))
begin(q2(x0)) → rotate(cut(Cq2(guess(x0))))
begin(q3(x0)) → rotate(cut(Cq3(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(q4(x0)) → rotate(cut(Cq4(guess(x0))))
guess(q0(x0)) → Cq0(guess(x0))
guess(0(x0)) → C0(guess(x0))
guess(0'(x0)) → C0'(guess(x0))
guess(q1(x0)) → Cq1(guess(x0))
guess(1'(x0)) → C1'(guess(x0))
guess(1(x0)) → C1(guess(x0))
guess(q2(x0)) → Cq2(guess(x0))
guess(q3(x0)) → Cq3(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(q4(x0)) → Cq4(guess(x0))
guess(q0(x0)) → moveleft(Bq0(wait(x0)))
guess(0(x0)) → moveleft(B0(wait(x0)))
guess(0'(x0)) → moveleft(B0'(wait(x0)))
guess(q1(x0)) → moveleft(Bq1(wait(x0)))
guess(1'(x0)) → moveleft(B1'(wait(x0)))
guess(1(x0)) → moveleft(B1(wait(x0)))
guess(q2(x0)) → moveleft(Bq2(wait(x0)))
guess(q3(x0)) → moveleft(Bq3(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(q4(x0)) → moveleft(Bq4(wait(x0)))
guess(end(x0)) → finish(end(x0))
Cq0(moveleft(Bq0(x0))) → moveleft(Bq0(Aq0(x0)))
C0(moveleft(Bq0(x0))) → moveleft(Bq0(A0(x0)))
C0'(moveleft(Bq0(x0))) → moveleft(Bq0(A0'(x0)))
Cq1(moveleft(Bq0(x0))) → moveleft(Bq0(Aq1(x0)))
C1'(moveleft(Bq0(x0))) → moveleft(Bq0(A1'(x0)))
C1(moveleft(Bq0(x0))) → moveleft(Bq0(A1(x0)))
Cq2(moveleft(Bq0(x0))) → moveleft(Bq0(Aq2(x0)))
Cq3(moveleft(Bq0(x0))) → moveleft(Bq0(Aq3(x0)))
Cb(moveleft(Bq0(x0))) → moveleft(Bq0(Ab(x0)))
Cq4(moveleft(Bq0(x0))) → moveleft(Bq0(Aq4(x0)))
Cq0(moveleft(B0(x0))) → moveleft(B0(Aq0(x0)))
C0(moveleft(B0(x0))) → moveleft(B0(A0(x0)))
C0'(moveleft(B0(x0))) → moveleft(B0(A0'(x0)))
Cq1(moveleft(B0(x0))) → moveleft(B0(Aq1(x0)))
C1'(moveleft(B0(x0))) → moveleft(B0(A1'(x0)))
C1(moveleft(B0(x0))) → moveleft(B0(A1(x0)))
Cq2(moveleft(B0(x0))) → moveleft(B0(Aq2(x0)))
Cq3(moveleft(B0(x0))) → moveleft(B0(Aq3(x0)))
Cb(moveleft(B0(x0))) → moveleft(B0(Ab(x0)))
Cq4(moveleft(B0(x0))) → moveleft(B0(Aq4(x0)))
Cq0(moveleft(B0'(x0))) → moveleft(B0'(Aq0(x0)))
C0(moveleft(B0'(x0))) → moveleft(B0'(A0(x0)))
C0'(moveleft(B0'(x0))) → moveleft(B0'(A0'(x0)))
Cq1(moveleft(B0'(x0))) → moveleft(B0'(Aq1(x0)))
C1'(moveleft(B0'(x0))) → moveleft(B0'(A1'(x0)))
C1(moveleft(B0'(x0))) → moveleft(B0'(A1(x0)))
Cq2(moveleft(B0'(x0))) → moveleft(B0'(Aq2(x0)))
Cq3(moveleft(B0'(x0))) → moveleft(B0'(Aq3(x0)))
Cb(moveleft(B0'(x0))) → moveleft(B0'(Ab(x0)))
Cq4(moveleft(B0'(x0))) → moveleft(B0'(Aq4(x0)))
Cq0(moveleft(Bq1(x0))) → moveleft(Bq1(Aq0(x0)))
C0(moveleft(Bq1(x0))) → moveleft(Bq1(A0(x0)))
C0'(moveleft(Bq1(x0))) → moveleft(Bq1(A0'(x0)))
Cq1(moveleft(Bq1(x0))) → moveleft(Bq1(Aq1(x0)))
C1'(moveleft(Bq1(x0))) → moveleft(Bq1(A1'(x0)))
C1(moveleft(Bq1(x0))) → moveleft(Bq1(A1(x0)))
Cq2(moveleft(Bq1(x0))) → moveleft(Bq1(Aq2(x0)))
Cq3(moveleft(Bq1(x0))) → moveleft(Bq1(Aq3(x0)))
Cb(moveleft(Bq1(x0))) → moveleft(Bq1(Ab(x0)))
Cq4(moveleft(Bq1(x0))) → moveleft(Bq1(Aq4(x0)))
Cq0(moveleft(B1'(x0))) → moveleft(B1'(Aq0(x0)))
C0(moveleft(B1'(x0))) → moveleft(B1'(A0(x0)))
C0'(moveleft(B1'(x0))) → moveleft(B1'(A0'(x0)))
Cq1(moveleft(B1'(x0))) → moveleft(B1'(Aq1(x0)))
C1'(moveleft(B1'(x0))) → moveleft(B1'(A1'(x0)))
C1(moveleft(B1'(x0))) → moveleft(B1'(A1(x0)))
Cq2(moveleft(B1'(x0))) → moveleft(B1'(Aq2(x0)))
Cq3(moveleft(B1'(x0))) → moveleft(B1'(Aq3(x0)))
Cb(moveleft(B1'(x0))) → moveleft(B1'(Ab(x0)))
Cq4(moveleft(B1'(x0))) → moveleft(B1'(Aq4(x0)))
Cq0(moveleft(B1(x0))) → moveleft(B1(Aq0(x0)))
C0(moveleft(B1(x0))) → moveleft(B1(A0(x0)))
C0'(moveleft(B1(x0))) → moveleft(B1(A0'(x0)))
Cq1(moveleft(B1(x0))) → moveleft(B1(Aq1(x0)))
C1'(moveleft(B1(x0))) → moveleft(B1(A1'(x0)))
C1(moveleft(B1(x0))) → moveleft(B1(A1(x0)))
Cq2(moveleft(B1(x0))) → moveleft(B1(Aq2(x0)))
Cq3(moveleft(B1(x0))) → moveleft(B1(Aq3(x0)))
Cb(moveleft(B1(x0))) → moveleft(B1(Ab(x0)))
Cq4(moveleft(B1(x0))) → moveleft(B1(Aq4(x0)))
Cq0(moveleft(Bq2(x0))) → moveleft(Bq2(Aq0(x0)))
C0(moveleft(Bq2(x0))) → moveleft(Bq2(A0(x0)))
C0'(moveleft(Bq2(x0))) → moveleft(Bq2(A0'(x0)))
Cq1(moveleft(Bq2(x0))) → moveleft(Bq2(Aq1(x0)))
C1'(moveleft(Bq2(x0))) → moveleft(Bq2(A1'(x0)))
C1(moveleft(Bq2(x0))) → moveleft(Bq2(A1(x0)))
Cq2(moveleft(Bq2(x0))) → moveleft(Bq2(Aq2(x0)))
Cq3(moveleft(Bq2(x0))) → moveleft(Bq2(Aq3(x0)))
Cb(moveleft(Bq2(x0))) → moveleft(Bq2(Ab(x0)))
Cq4(moveleft(Bq2(x0))) → moveleft(Bq2(Aq4(x0)))
Cq0(moveleft(Bq3(x0))) → moveleft(Bq3(Aq0(x0)))
C0(moveleft(Bq3(x0))) → moveleft(Bq3(A0(x0)))
C0'(moveleft(Bq3(x0))) → moveleft(Bq3(A0'(x0)))
Cq1(moveleft(Bq3(x0))) → moveleft(Bq3(Aq1(x0)))
C1'(moveleft(Bq3(x0))) → moveleft(Bq3(A1'(x0)))
C1(moveleft(Bq3(x0))) → moveleft(Bq3(A1(x0)))
Cq2(moveleft(Bq3(x0))) → moveleft(Bq3(Aq2(x0)))
Cq3(moveleft(Bq3(x0))) → moveleft(Bq3(Aq3(x0)))
Cb(moveleft(Bq3(x0))) → moveleft(Bq3(Ab(x0)))
Cq4(moveleft(Bq3(x0))) → moveleft(Bq3(Aq4(x0)))
Cq0(moveleft(Bb(x0))) → moveleft(Bb(Aq0(x0)))
C0(moveleft(Bb(x0))) → moveleft(Bb(A0(x0)))
C0'(moveleft(Bb(x0))) → moveleft(Bb(A0'(x0)))
Cq1(moveleft(Bb(x0))) → moveleft(Bb(Aq1(x0)))
C1'(moveleft(Bb(x0))) → moveleft(Bb(A1'(x0)))
C1(moveleft(Bb(x0))) → moveleft(Bb(A1(x0)))
Cq2(moveleft(Bb(x0))) → moveleft(Bb(Aq2(x0)))
Cq3(moveleft(Bb(x0))) → moveleft(Bb(Aq3(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cq4(moveleft(Bb(x0))) → moveleft(Bb(Aq4(x0)))
Cq0(moveleft(Bq4(x0))) → moveleft(Bq4(Aq0(x0)))
C0(moveleft(Bq4(x0))) → moveleft(Bq4(A0(x0)))
C0'(moveleft(Bq4(x0))) → moveleft(Bq4(A0'(x0)))
Cq1(moveleft(Bq4(x0))) → moveleft(Bq4(Aq1(x0)))
C1'(moveleft(Bq4(x0))) → moveleft(Bq4(A1'(x0)))
C1(moveleft(Bq4(x0))) → moveleft(Bq4(A1(x0)))
Cq2(moveleft(Bq4(x0))) → moveleft(Bq4(Aq2(x0)))
Cq3(moveleft(Bq4(x0))) → moveleft(Bq4(Aq3(x0)))
Cb(moveleft(Bq4(x0))) → moveleft(Bq4(Ab(x0)))
Cq4(moveleft(Bq4(x0))) → moveleft(Bq4(Aq4(x0)))
cut(moveleft(Bq0(x0))) → Dq0(cut(goright(x0)))
cut(moveleft(B0(x0))) → D0(cut(goright(x0)))
cut(moveleft(B0'(x0))) → D0'(cut(goright(x0)))
cut(moveleft(Bq1(x0))) → Dq1(cut(goright(x0)))
cut(moveleft(B1'(x0))) → D1'(cut(goright(x0)))
cut(moveleft(B1(x0))) → D1(cut(goright(x0)))
cut(moveleft(Bq2(x0))) → Dq2(cut(goright(x0)))
cut(moveleft(Bq3(x0))) → Dq3(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bq4(x0))) → Dq4(cut(goright(x0)))
goright(Aq0(x0)) → Cq0(goright(x0))
goright(A0(x0)) → C0(goright(x0))
goright(A0'(x0)) → C0'(goright(x0))
goright(Aq1(x0)) → Cq1(goright(x0))
goright(A1'(x0)) → C1'(goright(x0))
goright(A1(x0)) → C1(goright(x0))
goright(Aq2(x0)) → Cq2(goright(x0))
goright(Aq3(x0)) → Cq3(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Aq4(x0)) → Cq4(goright(x0))
goright(wait(q0(x0))) → moveleft(Bq0(wait(x0)))
goright(wait(0(x0))) → moveleft(B0(wait(x0)))
goright(wait(0'(x0))) → moveleft(B0'(wait(x0)))
goright(wait(q1(x0))) → moveleft(Bq1(wait(x0)))
goright(wait(1'(x0))) → moveleft(B1'(wait(x0)))
goright(wait(1(x0))) → moveleft(B1(wait(x0)))
goright(wait(q2(x0))) → moveleft(Bq2(wait(x0)))
goright(wait(q3(x0))) → moveleft(Bq3(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(q4(x0))) → moveleft(Bq4(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Cq0(finish(x0)) → finish(q0(x0))
C0(finish(x0)) → finish(0(x0))
C0'(finish(x0)) → finish(0'(x0))
Cq1(finish(x0)) → finish(q1(x0))
C1'(finish(x0)) → finish(1'(x0))
C1(finish(x0)) → finish(1(x0))
Cq2(finish(x0)) → finish(q2(x0))
Cq3(finish(x0)) → finish(q3(x0))
Cb(finish(x0)) → finish(b(x0))
Cq4(finish(x0)) → finish(q4(x0))
cut(finish(x0)) → finish2(x0)
Dq0(finish2(x0)) → finish2(q0(x0))
D0(finish2(x0)) → finish2(0(x0))
D0'(finish2(x0)) → finish2(0'(x0))
Dq1(finish2(x0)) → finish2(q1(x0))
D1'(finish2(x0)) → finish2(1'(x0))
D1(finish2(x0)) → finish2(1(x0))
Dq2(finish2(x0)) → finish2(q2(x0))
Dq3(finish2(x0)) → finish2(q3(x0))
Db(finish2(x0)) → finish2(b(x0))
Dq4(finish2(x0)) → finish2(q4(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(q0(0(x0))) → begin(0'(q1(x0)))
rewrite(q1(0(x0))) → begin(0(q1(x0)))
rewrite(q1(1'(x0))) → begin(1'(q1(x0)))
rewrite(0(q1(1(x0)))) → begin(q2(0(1'(x0))))
rewrite(0'(q1(1(x0)))) → begin(q2(0'(1'(x0))))
rewrite(1'(q1(1(x0)))) → begin(q2(1'(1'(x0))))
rewrite(0(q2(0(x0)))) → begin(q2(0(0(x0))))
rewrite(0'(q2(0(x0)))) → begin(q2(0'(0(x0))))
rewrite(1'(q2(0(x0)))) → begin(q2(1'(0(x0))))
rewrite(0(q2(1'(x0)))) → begin(q2(0(1'(x0))))
rewrite(0'(q2(1'(x0)))) → begin(q2(0'(1'(x0))))
rewrite(1'(q2(1'(x0)))) → begin(q2(1'(1'(x0))))
rewrite(q2(0'(x0))) → begin(0'(q0(x0)))
rewrite(q0(1'(x0))) → begin(1'(q3(x0)))
rewrite(q3(1'(x0))) → begin(1'(q3(x0)))
rewrite(q3(b(x0))) → begin(b(q4(x0)))

Proof

1 Termination Assumption

We assume termination of the following TRS
begin(end(x0)) → rewrite(end(x0))
begin(q0(x0)) → rotate(cut(Cq0(guess(x0))))
begin(0(x0)) → rotate(cut(C0(guess(x0))))
begin(0'(x0)) → rotate(cut(C0'(guess(x0))))
begin(q1(x0)) → rotate(cut(Cq1(guess(x0))))
begin(1'(x0)) → rotate(cut(C1'(guess(x0))))
begin(1(x0)) → rotate(cut(C1(guess(x0))))
begin(q2(x0)) → rotate(cut(Cq2(guess(x0))))
begin(q3(x0)) → rotate(cut(Cq3(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(q4(x0)) → rotate(cut(Cq4(guess(x0))))
guess(q0(x0)) → Cq0(guess(x0))
guess(0(x0)) → C0(guess(x0))
guess(0'(x0)) → C0'(guess(x0))
guess(q1(x0)) → Cq1(guess(x0))
guess(1'(x0)) → C1'(guess(x0))
guess(1(x0)) → C1(guess(x0))
guess(q2(x0)) → Cq2(guess(x0))
guess(q3(x0)) → Cq3(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(q4(x0)) → Cq4(guess(x0))
guess(q0(x0)) → moveleft(Bq0(wait(x0)))
guess(0(x0)) → moveleft(B0(wait(x0)))
guess(0'(x0)) → moveleft(B0'(wait(x0)))
guess(q1(x0)) → moveleft(Bq1(wait(x0)))
guess(1'(x0)) → moveleft(B1'(wait(x0)))
guess(1(x0)) → moveleft(B1(wait(x0)))
guess(q2(x0)) → moveleft(Bq2(wait(x0)))
guess(q3(x0)) → moveleft(Bq3(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(q4(x0)) → moveleft(Bq4(wait(x0)))
guess(end(x0)) → finish(end(x0))
Cq0(moveleft(Bq0(x0))) → moveleft(Bq0(Aq0(x0)))
C0(moveleft(Bq0(x0))) → moveleft(Bq0(A0(x0)))
C0'(moveleft(Bq0(x0))) → moveleft(Bq0(A0'(x0)))
Cq1(moveleft(Bq0(x0))) → moveleft(Bq0(Aq1(x0)))
C1'(moveleft(Bq0(x0))) → moveleft(Bq0(A1'(x0)))
C1(moveleft(Bq0(x0))) → moveleft(Bq0(A1(x0)))
Cq2(moveleft(Bq0(x0))) → moveleft(Bq0(Aq2(x0)))
Cq3(moveleft(Bq0(x0))) → moveleft(Bq0(Aq3(x0)))
Cb(moveleft(Bq0(x0))) → moveleft(Bq0(Ab(x0)))
Cq4(moveleft(Bq0(x0))) → moveleft(Bq0(Aq4(x0)))
Cq0(moveleft(B0(x0))) → moveleft(B0(Aq0(x0)))
C0(moveleft(B0(x0))) → moveleft(B0(A0(x0)))
C0'(moveleft(B0(x0))) → moveleft(B0(A0'(x0)))
Cq1(moveleft(B0(x0))) → moveleft(B0(Aq1(x0)))
C1'(moveleft(B0(x0))) → moveleft(B0(A1'(x0)))
C1(moveleft(B0(x0))) → moveleft(B0(A1(x0)))
Cq2(moveleft(B0(x0))) → moveleft(B0(Aq2(x0)))
Cq3(moveleft(B0(x0))) → moveleft(B0(Aq3(x0)))
Cb(moveleft(B0(x0))) → moveleft(B0(Ab(x0)))
Cq4(moveleft(B0(x0))) → moveleft(B0(Aq4(x0)))
Cq0(moveleft(B0'(x0))) → moveleft(B0'(Aq0(x0)))
C0(moveleft(B0'(x0))) → moveleft(B0'(A0(x0)))
C0'(moveleft(B0'(x0))) → moveleft(B0'(A0'(x0)))
Cq1(moveleft(B0'(x0))) → moveleft(B0'(Aq1(x0)))
C1'(moveleft(B0'(x0))) → moveleft(B0'(A1'(x0)))
C1(moveleft(B0'(x0))) → moveleft(B0'(A1(x0)))
Cq2(moveleft(B0'(x0))) → moveleft(B0'(Aq2(x0)))
Cq3(moveleft(B0'(x0))) → moveleft(B0'(Aq3(x0)))
Cb(moveleft(B0'(x0))) → moveleft(B0'(Ab(x0)))
Cq4(moveleft(B0'(x0))) → moveleft(B0'(Aq4(x0)))
Cq0(moveleft(Bq1(x0))) → moveleft(Bq1(Aq0(x0)))
C0(moveleft(Bq1(x0))) → moveleft(Bq1(A0(x0)))
C0'(moveleft(Bq1(x0))) → moveleft(Bq1(A0'(x0)))
Cq1(moveleft(Bq1(x0))) → moveleft(Bq1(Aq1(x0)))
C1'(moveleft(Bq1(x0))) → moveleft(Bq1(A1'(x0)))
C1(moveleft(Bq1(x0))) → moveleft(Bq1(A1(x0)))
Cq2(moveleft(Bq1(x0))) → moveleft(Bq1(Aq2(x0)))
Cq3(moveleft(Bq1(x0))) → moveleft(Bq1(Aq3(x0)))
Cb(moveleft(Bq1(x0))) → moveleft(Bq1(Ab(x0)))
Cq4(moveleft(Bq1(x0))) → moveleft(Bq1(Aq4(x0)))
Cq0(moveleft(B1'(x0))) → moveleft(B1'(Aq0(x0)))
C0(moveleft(B1'(x0))) → moveleft(B1'(A0(x0)))
C0'(moveleft(B1'(x0))) → moveleft(B1'(A0'(x0)))
Cq1(moveleft(B1'(x0))) → moveleft(B1'(Aq1(x0)))
C1'(moveleft(B1'(x0))) → moveleft(B1'(A1'(x0)))
C1(moveleft(B1'(x0))) → moveleft(B1'(A1(x0)))
Cq2(moveleft(B1'(x0))) → moveleft(B1'(Aq2(x0)))
Cq3(moveleft(B1'(x0))) → moveleft(B1'(Aq3(x0)))
Cb(moveleft(B1'(x0))) → moveleft(B1'(Ab(x0)))
Cq4(moveleft(B1'(x0))) → moveleft(B1'(Aq4(x0)))
Cq0(moveleft(B1(x0))) → moveleft(B1(Aq0(x0)))
C0(moveleft(B1(x0))) → moveleft(B1(A0(x0)))
C0'(moveleft(B1(x0))) → moveleft(B1(A0'(x0)))
Cq1(moveleft(B1(x0))) → moveleft(B1(Aq1(x0)))
C1'(moveleft(B1(x0))) → moveleft(B1(A1'(x0)))
C1(moveleft(B1(x0))) → moveleft(B1(A1(x0)))
Cq2(moveleft(B1(x0))) → moveleft(B1(Aq2(x0)))
Cq3(moveleft(B1(x0))) → moveleft(B1(Aq3(x0)))
Cb(moveleft(B1(x0))) → moveleft(B1(Ab(x0)))
Cq4(moveleft(B1(x0))) → moveleft(B1(Aq4(x0)))
Cq0(moveleft(Bq2(x0))) → moveleft(Bq2(Aq0(x0)))
C0(moveleft(Bq2(x0))) → moveleft(Bq2(A0(x0)))
C0'(moveleft(Bq2(x0))) → moveleft(Bq2(A0'(x0)))
Cq1(moveleft(Bq2(x0))) → moveleft(Bq2(Aq1(x0)))
C1'(moveleft(Bq2(x0))) → moveleft(Bq2(A1'(x0)))
C1(moveleft(Bq2(x0))) → moveleft(Bq2(A1(x0)))
Cq2(moveleft(Bq2(x0))) → moveleft(Bq2(Aq2(x0)))
Cq3(moveleft(Bq2(x0))) → moveleft(Bq2(Aq3(x0)))
Cb(moveleft(Bq2(x0))) → moveleft(Bq2(Ab(x0)))
Cq4(moveleft(Bq2(x0))) → moveleft(Bq2(Aq4(x0)))
Cq0(moveleft(Bq3(x0))) → moveleft(Bq3(Aq0(x0)))
C0(moveleft(Bq3(x0))) → moveleft(Bq3(A0(x0)))
C0'(moveleft(Bq3(x0))) → moveleft(Bq3(A0'(x0)))
Cq1(moveleft(Bq3(x0))) → moveleft(Bq3(Aq1(x0)))
C1'(moveleft(Bq3(x0))) → moveleft(Bq3(A1'(x0)))
C1(moveleft(Bq3(x0))) → moveleft(Bq3(A1(x0)))
Cq2(moveleft(Bq3(x0))) → moveleft(Bq3(Aq2(x0)))
Cq3(moveleft(Bq3(x0))) → moveleft(Bq3(Aq3(x0)))
Cb(moveleft(Bq3(x0))) → moveleft(Bq3(Ab(x0)))
Cq4(moveleft(Bq3(x0))) → moveleft(Bq3(Aq4(x0)))
Cq0(moveleft(Bb(x0))) → moveleft(Bb(Aq0(x0)))
C0(moveleft(Bb(x0))) → moveleft(Bb(A0(x0)))
C0'(moveleft(Bb(x0))) → moveleft(Bb(A0'(x0)))
Cq1(moveleft(Bb(x0))) → moveleft(Bb(Aq1(x0)))
C1'(moveleft(Bb(x0))) → moveleft(Bb(A1'(x0)))
C1(moveleft(Bb(x0))) → moveleft(Bb(A1(x0)))
Cq2(moveleft(Bb(x0))) → moveleft(Bb(Aq2(x0)))
Cq3(moveleft(Bb(x0))) → moveleft(Bb(Aq3(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cq4(moveleft(Bb(x0))) → moveleft(Bb(Aq4(x0)))
Cq0(moveleft(Bq4(x0))) → moveleft(Bq4(Aq0(x0)))
C0(moveleft(Bq4(x0))) → moveleft(Bq4(A0(x0)))
C0'(moveleft(Bq4(x0))) → moveleft(Bq4(A0'(x0)))
Cq1(moveleft(Bq4(x0))) → moveleft(Bq4(Aq1(x0)))
C1'(moveleft(Bq4(x0))) → moveleft(Bq4(A1'(x0)))
C1(moveleft(Bq4(x0))) → moveleft(Bq4(A1(x0)))
Cq2(moveleft(Bq4(x0))) → moveleft(Bq4(Aq2(x0)))
Cq3(moveleft(Bq4(x0))) → moveleft(Bq4(Aq3(x0)))
Cb(moveleft(Bq4(x0))) → moveleft(Bq4(Ab(x0)))
Cq4(moveleft(Bq4(x0))) → moveleft(Bq4(Aq4(x0)))
cut(moveleft(Bq0(x0))) → Dq0(cut(goright(x0)))
cut(moveleft(B0(x0))) → D0(cut(goright(x0)))
cut(moveleft(B0'(x0))) → D0'(cut(goright(x0)))
cut(moveleft(Bq1(x0))) → Dq1(cut(goright(x0)))
cut(moveleft(B1'(x0))) → D1'(cut(goright(x0)))
cut(moveleft(B1(x0))) → D1(cut(goright(x0)))
cut(moveleft(Bq2(x0))) → Dq2(cut(goright(x0)))
cut(moveleft(Bq3(x0))) → Dq3(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bq4(x0))) → Dq4(cut(goright(x0)))
goright(Aq0(x0)) → Cq0(goright(x0))
goright(A0(x0)) → C0(goright(x0))
goright(A0'(x0)) → C0'(goright(x0))
goright(Aq1(x0)) → Cq1(goright(x0))
goright(A1'(x0)) → C1'(goright(x0))
goright(A1(x0)) → C1(goright(x0))
goright(Aq2(x0)) → Cq2(goright(x0))
goright(Aq3(x0)) → Cq3(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Aq4(x0)) → Cq4(goright(x0))
goright(wait(q0(x0))) → moveleft(Bq0(wait(x0)))
goright(wait(0(x0))) → moveleft(B0(wait(x0)))
goright(wait(0'(x0))) → moveleft(B0'(wait(x0)))
goright(wait(q1(x0))) → moveleft(Bq1(wait(x0)))
goright(wait(1'(x0))) → moveleft(B1'(wait(x0)))
goright(wait(1(x0))) → moveleft(B1(wait(x0)))
goright(wait(q2(x0))) → moveleft(Bq2(wait(x0)))
goright(wait(q3(x0))) → moveleft(Bq3(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(q4(x0))) → moveleft(Bq4(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Cq0(finish(x0)) → finish(q0(x0))
C0(finish(x0)) → finish(0(x0))
C0'(finish(x0)) → finish(0'(x0))
Cq1(finish(x0)) → finish(q1(x0))
C1'(finish(x0)) → finish(1'(x0))
C1(finish(x0)) → finish(1(x0))
Cq2(finish(x0)) → finish(q2(x0))
Cq3(finish(x0)) → finish(q3(x0))
Cb(finish(x0)) → finish(b(x0))
Cq4(finish(x0)) → finish(q4(x0))
cut(finish(x0)) → finish2(x0)
Dq0(finish2(x0)) → finish2(q0(x0))
D0(finish2(x0)) → finish2(0(x0))
D0'(finish2(x0)) → finish2(0'(x0))
Dq1(finish2(x0)) → finish2(q1(x0))
D1'(finish2(x0)) → finish2(1'(x0))
D1(finish2(x0)) → finish2(1(x0))
Dq2(finish2(x0)) → finish2(q2(x0))
Dq3(finish2(x0)) → finish2(q3(x0))
Db(finish2(x0)) → finish2(b(x0))
Dq4(finish2(x0)) → finish2(q4(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(q0(0(x0))) → begin(0'(q1(x0)))
rewrite(q1(0(x0))) → begin(0(q1(x0)))
rewrite(q1(1'(x0))) → begin(1'(q1(x0)))
rewrite(0(q1(1(x0)))) → begin(q2(0(1'(x0))))
rewrite(0'(q1(1(x0)))) → begin(q2(0'(1'(x0))))
rewrite(1'(q1(1(x0)))) → begin(q2(1'(1'(x0))))
rewrite(0(q2(0(x0)))) → begin(q2(0(0(x0))))
rewrite(0'(q2(0(x0)))) → begin(q2(0'(0(x0))))
rewrite(1'(q2(0(x0)))) → begin(q2(1'(0(x0))))
rewrite(0(q2(1'(x0)))) → begin(q2(0(1'(x0))))
rewrite(0'(q2(1'(x0)))) → begin(q2(0'(1'(x0))))
rewrite(1'(q2(1'(x0)))) → begin(q2(1'(1'(x0))))
rewrite(q2(0'(x0))) → begin(0'(q0(x0)))
rewrite(q0(1'(x0))) → begin(1'(q3(x0)))
rewrite(q3(1'(x0))) → begin(1'(q3(x0)))
rewrite(q3(b(x0))) → begin(b(q4(x0)))