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(g(x0)) → rotate(cut(Cg(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(f(x0)) → rotate(cut(Cf(guess(x0))))
guess(g(x0)) → Cg(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(f(x0)) → Cf(guess(x0))
guess(g(x0)) → moveleft(Bg(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(f(x0)) → moveleft(Bf(wait(x0)))
guess(end(x0)) → finish(end(x0))
Cg(moveleft(Bg(x0))) → moveleft(Bg(Ag(x0)))
Cc(moveleft(Bg(x0))) → moveleft(Bg(Ac(x0)))
Cf(moveleft(Bg(x0))) → moveleft(Bg(Af(x0)))
Cg(moveleft(Bc(x0))) → moveleft(Bc(Ag(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cf(moveleft(Bc(x0))) → moveleft(Bc(Af(x0)))
Cg(moveleft(Bf(x0))) → moveleft(Bf(Ag(x0)))
Cc(moveleft(Bf(x0))) → moveleft(Bf(Ac(x0)))
Cf(moveleft(Bf(x0))) → moveleft(Bf(Af(x0)))
cut(moveleft(Bg(x0))) → Dg(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Bf(x0))) → Df(cut(goright(x0)))
goright(Ag(x0)) → Cg(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Af(x0)) → Cf(goright(x0))
goright(wait(g(x0))) → moveleft(Bg(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(f(x0))) → moveleft(Bf(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Cg(finish(x0)) → finish(g(x0))
Cc(finish(x0)) → finish(c(x0))
Cf(finish(x0)) → finish(f(x0))
cut(finish(x0)) → finish2(x0)
Dg(finish2(x0)) → finish2(g(x0))
Dc(finish2(x0)) → finish2(c(x0))
Df(finish2(x0)) → finish2(f(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(g(c(x0))) → begin(g(f(c(x0))))
rewrite(g(f(c(x0)))) → begin(g(f(f(c(x0)))))
rewrite(g(g(x0))) → begin(g(f(g(x0))))
rewrite(f(f(g(x0)))) → begin(g(f(x0)))

Proof

1 Termination Assumption

We assume termination of the following TRS
begin(end(x0)) → rewrite(end(x0))
begin(g(x0)) → rotate(cut(Cg(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(f(x0)) → rotate(cut(Cf(guess(x0))))
guess(g(x0)) → Cg(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(f(x0)) → Cf(guess(x0))
guess(g(x0)) → moveleft(Bg(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(f(x0)) → moveleft(Bf(wait(x0)))
guess(end(x0)) → finish(end(x0))
Cg(moveleft(Bg(x0))) → moveleft(Bg(Ag(x0)))
Cc(moveleft(Bg(x0))) → moveleft(Bg(Ac(x0)))
Cf(moveleft(Bg(x0))) → moveleft(Bg(Af(x0)))
Cg(moveleft(Bc(x0))) → moveleft(Bc(Ag(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cf(moveleft(Bc(x0))) → moveleft(Bc(Af(x0)))
Cg(moveleft(Bf(x0))) → moveleft(Bf(Ag(x0)))
Cc(moveleft(Bf(x0))) → moveleft(Bf(Ac(x0)))
Cf(moveleft(Bf(x0))) → moveleft(Bf(Af(x0)))
cut(moveleft(Bg(x0))) → Dg(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Bf(x0))) → Df(cut(goright(x0)))
goright(Ag(x0)) → Cg(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Af(x0)) → Cf(goright(x0))
goright(wait(g(x0))) → moveleft(Bg(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(f(x0))) → moveleft(Bf(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Cg(finish(x0)) → finish(g(x0))
Cc(finish(x0)) → finish(c(x0))
Cf(finish(x0)) → finish(f(x0))
cut(finish(x0)) → finish2(x0)
Dg(finish2(x0)) → finish2(g(x0))
Dc(finish2(x0)) → finish2(c(x0))
Df(finish2(x0)) → finish2(f(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(g(c(x0))) → begin(g(f(c(x0))))
rewrite(g(f(c(x0)))) → begin(g(f(f(c(x0)))))
rewrite(g(g(x0))) → begin(g(f(g(x0))))
rewrite(f(f(g(x0)))) → begin(g(f(x0)))