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(a(x0)) → rotate(cut(Ca(guess(x0))))
begin(s(x0)) → rotate(cut(Cs(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(s(x0)) → Cs(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(s(x0)) → moveleft(Bs(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cs(moveleft(Ba(x0))) → moveleft(Ba(As(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Ca(moveleft(Bs(x0))) → moveleft(Bs(Aa(x0)))
Cs(moveleft(Bs(x0))) → moveleft(Bs(As(x0)))
Cb(moveleft(Bs(x0))) → moveleft(Bs(Ab(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
Cs(moveleft(Bb(x0))) → moveleft(Bb(As(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bs(x0))) → Ds(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(As(x0)) → Cs(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(s(x0))) → moveleft(Bs(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cs(finish(x0)) → finish(s(x0))
Cb(finish(x0)) → finish(b(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Ds(finish2(x0)) → finish2(s(x0))
Db(finish2(x0)) → finish2(b(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(a(s(s(x0))))) → begin(s(s(a(a(x0)))))
rewrite(b(b(a(a(b(b(s(s(x0))))))))) → begin(a(a(b(b(s(s(a(a(x0)))))))))
rewrite(b(b(a(a(b(b(b(b(x0))))))))) → begin(a(a(b(b(a(a(b(b(x0)))))))))
rewrite(a(a(b(b(a(a(a(a(x0))))))))) → begin(b(b(a(a(b(b(a(a(x0)))))))))

Proof

1 Termination Assumption

We assume termination of the following TRS
begin(end(x0)) → rewrite(end(x0))
begin(a(x0)) → rotate(cut(Ca(guess(x0))))
begin(s(x0)) → rotate(cut(Cs(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(s(x0)) → Cs(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(s(x0)) → moveleft(Bs(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cs(moveleft(Ba(x0))) → moveleft(Ba(As(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Ca(moveleft(Bs(x0))) → moveleft(Bs(Aa(x0)))
Cs(moveleft(Bs(x0))) → moveleft(Bs(As(x0)))
Cb(moveleft(Bs(x0))) → moveleft(Bs(Ab(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
Cs(moveleft(Bb(x0))) → moveleft(Bb(As(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bs(x0))) → Ds(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(As(x0)) → Cs(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(s(x0))) → moveleft(Bs(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cs(finish(x0)) → finish(s(x0))
Cb(finish(x0)) → finish(b(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Ds(finish2(x0)) → finish2(s(x0))
Db(finish2(x0)) → finish2(b(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(a(s(s(x0))))) → begin(s(s(a(a(x0)))))
rewrite(b(b(a(a(b(b(s(s(x0))))))))) → begin(a(a(b(b(s(s(a(a(x0)))))))))
rewrite(b(b(a(a(b(b(b(b(x0))))))))) → begin(a(a(b(b(a(a(b(b(x0)))))))))
rewrite(a(a(b(b(a(a(a(a(x0))))))))) → begin(b(b(a(a(b(b(a(a(x0)))))))))