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(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(a(x0)) → rotate(cut(Ca(guess(x0))))
begin(B(x0)) → rotate(cut(CB(guess(x0))))
guess(A(x0)) → CA(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(a(x0)) → Ca(guess(x0))
guess(B(x0)) → CB(guess(x0))
guess(A(x0)) → moveleft(BA(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(B(x0)) → moveleft(BB(wait(x0)))
guess(end(x0)) → finish(end(x0))
CA(moveleft(BA(x0))) → moveleft(BA(AA(x0)))
Cb(moveleft(BA(x0))) → moveleft(BA(Ab(x0)))
Ca(moveleft(BA(x0))) → moveleft(BA(Aa(x0)))
CB(moveleft(BA(x0))) → moveleft(BA(AB(x0)))
CA(moveleft(Bb(x0))) → moveleft(Bb(AA(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
CB(moveleft(Bb(x0))) → moveleft(Bb(AB(x0)))
CA(moveleft(Ba(x0))) → moveleft(Ba(AA(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
CB(moveleft(Ba(x0))) → moveleft(Ba(AB(x0)))
CA(moveleft(BB(x0))) → moveleft(BB(AA(x0)))
Cb(moveleft(BB(x0))) → moveleft(BB(Ab(x0)))
Ca(moveleft(BB(x0))) → moveleft(BB(Aa(x0)))
CB(moveleft(BB(x0))) → moveleft(BB(AB(x0)))
cut(moveleft(BA(x0))) → DA(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(BB(x0))) → DB(cut(goright(x0)))
goright(AA(x0)) → CA(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Aa(x0)) → Ca(goright(x0))
goright(AB(x0)) → CB(goright(x0))
goright(wait(A(x0))) → moveleft(BA(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(B(x0))) → moveleft(BB(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CA(finish(x0)) → finish(A(x0))
Cb(finish(x0)) → finish(b(x0))
Ca(finish(x0)) → finish(a(x0))
CB(finish(x0)) → finish(B(x0))
cut(finish(x0)) → finish2(x0)
DA(finish2(x0)) → finish2(A(x0))
Db(finish2(x0)) → finish2(b(x0))
Da(finish2(x0)) → finish2(a(x0))
DB(finish2(x0)) → finish2(B(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(A(b(x0))) → begin(b(a(B(A(x0)))))
rewrite(B(a(x0))) → begin(a(b(A(B(x0)))))
rewrite(A(a(x0))) → begin(x0)
rewrite(B(b(x0))) → begin(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(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(a(x0)) → rotate(cut(Ca(guess(x0))))
begin(B(x0)) → rotate(cut(CB(guess(x0))))
guess(A(x0)) → CA(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(a(x0)) → Ca(guess(x0))
guess(B(x0)) → CB(guess(x0))
guess(A(x0)) → moveleft(BA(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(B(x0)) → moveleft(BB(wait(x0)))
guess(end(x0)) → finish(end(x0))
CA(moveleft(BA(x0))) → moveleft(BA(AA(x0)))
Cb(moveleft(BA(x0))) → moveleft(BA(Ab(x0)))
Ca(moveleft(BA(x0))) → moveleft(BA(Aa(x0)))
CB(moveleft(BA(x0))) → moveleft(BA(AB(x0)))
CA(moveleft(Bb(x0))) → moveleft(Bb(AA(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
CB(moveleft(Bb(x0))) → moveleft(Bb(AB(x0)))
CA(moveleft(Ba(x0))) → moveleft(Ba(AA(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
CB(moveleft(Ba(x0))) → moveleft(Ba(AB(x0)))
CA(moveleft(BB(x0))) → moveleft(BB(AA(x0)))
Cb(moveleft(BB(x0))) → moveleft(BB(Ab(x0)))
Ca(moveleft(BB(x0))) → moveleft(BB(Aa(x0)))
CB(moveleft(BB(x0))) → moveleft(BB(AB(x0)))
cut(moveleft(BA(x0))) → DA(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(BB(x0))) → DB(cut(goright(x0)))
goright(AA(x0)) → CA(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Aa(x0)) → Ca(goright(x0))
goright(AB(x0)) → CB(goright(x0))
goright(wait(A(x0))) → moveleft(BA(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(B(x0))) → moveleft(BB(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CA(finish(x0)) → finish(A(x0))
Cb(finish(x0)) → finish(b(x0))
Ca(finish(x0)) → finish(a(x0))
CB(finish(x0)) → finish(B(x0))
cut(finish(x0)) → finish2(x0)
DA(finish2(x0)) → finish2(A(x0))
Db(finish2(x0)) → finish2(b(x0))
Da(finish2(x0)) → finish2(a(x0))
DB(finish2(x0)) → finish2(B(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(A(b(x0))) → begin(b(a(B(A(x0)))))
rewrite(B(a(x0))) → begin(a(b(A(B(x0)))))
rewrite(A(a(x0))) → begin(x0)
rewrite(B(b(x0))) → begin(x0)