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(l(x0)) → rotate(cut(Cl(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(r(x0)) → rotate(cut(Cr(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(l(x0)) → Cl(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(r(x0)) → Cr(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(l(x0)) → moveleft(Bl(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(r(x0)) → moveleft(Br(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cl(moveleft(Ba(x0))) → moveleft(Ba(Al(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
Cr(moveleft(Ba(x0))) → moveleft(Ba(Ar(x0)))
Ca(moveleft(Bl(x0))) → moveleft(Bl(Aa(x0)))
Cl(moveleft(Bl(x0))) → moveleft(Bl(Al(x0)))
Cc(moveleft(Bl(x0))) → moveleft(Bl(Ac(x0)))
Cr(moveleft(Bl(x0))) → moveleft(Bl(Ar(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
Cl(moveleft(Bc(x0))) → moveleft(Bc(Al(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cr(moveleft(Bc(x0))) → moveleft(Bc(Ar(x0)))
Ca(moveleft(Br(x0))) → moveleft(Br(Aa(x0)))
Cl(moveleft(Br(x0))) → moveleft(Br(Al(x0)))
Cc(moveleft(Br(x0))) → moveleft(Br(Ac(x0)))
Cr(moveleft(Br(x0))) → moveleft(Br(Ar(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bl(x0))) → Dl(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Br(x0))) → Dr(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(Al(x0)) → Cl(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Ar(x0)) → Cr(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(l(x0))) → moveleft(Bl(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(r(x0))) → moveleft(Br(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cl(finish(x0)) → finish(l(x0))
Cc(finish(x0)) → finish(c(x0))
Cr(finish(x0)) → finish(r(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Dl(finish2(x0)) → finish2(l(x0))
Dc(finish2(x0)) → finish2(c(x0))
Dr(finish2(x0)) → finish2(r(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(l(x0))) → begin(l(a(x0)))
rewrite(a(c(x0))) → begin(c(a(x0)))
rewrite(c(a(r(x0)))) → begin(r(a(x0)))
rewrite(l(r(a(a(x0))))) → begin(a(a(l(c(c(c(r(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(l(x0)) → rotate(cut(Cl(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(r(x0)) → rotate(cut(Cr(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(l(x0)) → Cl(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(r(x0)) → Cr(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(l(x0)) → moveleft(Bl(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(r(x0)) → moveleft(Br(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cl(moveleft(Ba(x0))) → moveleft(Ba(Al(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
Cr(moveleft(Ba(x0))) → moveleft(Ba(Ar(x0)))
Ca(moveleft(Bl(x0))) → moveleft(Bl(Aa(x0)))
Cl(moveleft(Bl(x0))) → moveleft(Bl(Al(x0)))
Cc(moveleft(Bl(x0))) → moveleft(Bl(Ac(x0)))
Cr(moveleft(Bl(x0))) → moveleft(Bl(Ar(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
Cl(moveleft(Bc(x0))) → moveleft(Bc(Al(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
Cr(moveleft(Bc(x0))) → moveleft(Bc(Ar(x0)))
Ca(moveleft(Br(x0))) → moveleft(Br(Aa(x0)))
Cl(moveleft(Br(x0))) → moveleft(Br(Al(x0)))
Cc(moveleft(Br(x0))) → moveleft(Br(Ac(x0)))
Cr(moveleft(Br(x0))) → moveleft(Br(Ar(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bl(x0))) → Dl(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(Br(x0))) → Dr(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(Al(x0)) → Cl(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(Ar(x0)) → Cr(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(l(x0))) → moveleft(Bl(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(r(x0))) → moveleft(Br(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cl(finish(x0)) → finish(l(x0))
Cc(finish(x0)) → finish(c(x0))
Cr(finish(x0)) → finish(r(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Dl(finish2(x0)) → finish2(l(x0))
Dc(finish2(x0)) → finish2(c(x0))
Dr(finish2(x0)) → finish2(r(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(l(x0))) → begin(l(a(x0)))
rewrite(a(c(x0))) → begin(c(a(x0)))
rewrite(c(a(r(x0)))) → begin(r(a(x0)))
rewrite(l(r(a(a(x0))))) → begin(a(a(l(c(c(c(r(x0))))))))