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(C(x0)) → rotate(cut(CC(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(B(x0)) → rotate(cut(CB(guess(x0))))
guess(C(x0)) → CC(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(B(x0)) → CB(guess(x0))
guess(C(x0)) → moveleft(BC(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(B(x0)) → moveleft(BB(wait(x0)))
guess(end(x0)) → finish(end(x0))
CC(moveleft(BC(x0))) → moveleft(BC(AC(x0)))
Cc(moveleft(BC(x0))) → moveleft(BC(Ac(x0)))
Cb(moveleft(BC(x0))) → moveleft(BC(Ab(x0)))
CB(moveleft(BC(x0))) → moveleft(BC(AB(x0)))
CC(moveleft(Bc(x0))) → moveleft(Bc(AC(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
CB(moveleft(Bc(x0))) → moveleft(Bc(AB(x0)))
CC(moveleft(Bb(x0))) → moveleft(Bb(AC(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
CB(moveleft(Bb(x0))) → moveleft(Bb(AB(x0)))
CC(moveleft(BB(x0))) → moveleft(BB(AC(x0)))
Cc(moveleft(BB(x0))) → moveleft(BB(Ac(x0)))
Cb(moveleft(BB(x0))) → moveleft(BB(Ab(x0)))
CB(moveleft(BB(x0))) → moveleft(BB(AB(x0)))
cut(moveleft(BC(x0))) → DC(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(BB(x0))) → DB(cut(goright(x0)))
goright(AC(x0)) → CC(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(AB(x0)) → CB(goright(x0))
goright(wait(C(x0))) → moveleft(BC(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(B(x0))) → moveleft(BB(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CC(finish(x0)) → finish(C(x0))
Cc(finish(x0)) → finish(c(x0))
Cb(finish(x0)) → finish(b(x0))
CB(finish(x0)) → finish(B(x0))
cut(finish(x0)) → finish2(x0)
DC(finish2(x0)) → finish2(C(x0))
Dc(finish2(x0)) → finish2(c(x0))
Db(finish2(x0)) → finish2(b(x0))
DB(finish2(x0)) → finish2(B(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(C(C(x0))) → begin(c(c(x0)))
rewrite(c(c(c(c(x0))))) → begin(x0)
rewrite(b(b(b(b(x0))))) → begin(B(B(x0)))
rewrite(B(B(B(B(x0))))) → begin(b(b(x0)))
rewrite(c(c(B(B(c(c(b(b(c(c(x0))))))))))) → begin(B(B(c(c(b(b(c(c(B(B(c(c(b(b(x0)))))))))))))))
rewrite(b(b(B(B(x0))))) → begin(x0)
rewrite(B(B(b(b(x0))))) → begin(x0)
rewrite(c(c(C(C(x0))))) → begin(x0)
rewrite(C(C(c(c(x0))))) → begin(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
begin(end(x0)) → rewrite(end(x0))
begin(C(x0)) → rotate(cut(CC(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(B(x0)) → rotate(cut(CB(guess(x0))))
guess(C(x0)) → CC(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(B(x0)) → CB(guess(x0))
guess(C(x0)) → moveleft(BC(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(B(x0)) → moveleft(BB(wait(x0)))
guess(end(x0)) → finish(end(x0))
CC(moveleft(BC(x0))) → moveleft(BC(AC(x0)))
Cc(moveleft(BC(x0))) → moveleft(BC(Ac(x0)))
Cb(moveleft(BC(x0))) → moveleft(BC(Ab(x0)))
CB(moveleft(BC(x0))) → moveleft(BC(AB(x0)))
CC(moveleft(Bc(x0))) → moveleft(Bc(AC(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
CB(moveleft(Bc(x0))) → moveleft(Bc(AB(x0)))
CC(moveleft(Bb(x0))) → moveleft(Bb(AC(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
CB(moveleft(Bb(x0))) → moveleft(Bb(AB(x0)))
CC(moveleft(BB(x0))) → moveleft(BB(AC(x0)))
Cc(moveleft(BB(x0))) → moveleft(BB(Ac(x0)))
Cb(moveleft(BB(x0))) → moveleft(BB(Ab(x0)))
CB(moveleft(BB(x0))) → moveleft(BB(AB(x0)))
cut(moveleft(BC(x0))) → DC(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(BB(x0))) → DB(cut(goright(x0)))
goright(AC(x0)) → CC(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(AB(x0)) → CB(goright(x0))
goright(wait(C(x0))) → moveleft(BC(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(B(x0))) → moveleft(BB(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CC(finish(x0)) → finish(C(x0))
Cc(finish(x0)) → finish(c(x0))
Cb(finish(x0)) → finish(b(x0))
CB(finish(x0)) → finish(B(x0))
cut(finish(x0)) → finish2(x0)
DC(finish2(x0)) → finish2(C(x0))
Dc(finish2(x0)) → finish2(c(x0))
Db(finish2(x0)) → finish2(b(x0))
DB(finish2(x0)) → finish2(B(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(C(C(x0))) → begin(c(c(x0)))
rewrite(c(c(c(c(x0))))) → begin(x0)
rewrite(b(b(b(b(x0))))) → begin(B(B(x0)))
rewrite(B(B(B(B(x0))))) → begin(b(b(x0)))
rewrite(c(c(B(B(c(c(b(b(c(c(x0))))))))))) → begin(B(B(c(c(b(b(c(c(B(B(c(c(b(b(x0)))))))))))))))
rewrite(b(b(B(B(x0))))) → begin(x0)
rewrite(B(B(b(b(x0))))) → begin(x0)
rewrite(c(c(C(C(x0))))) → begin(x0)
rewrite(C(C(c(c(x0))))) → begin(x0)