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(R(x0)) → rotate(cut(CR(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(L(x0)) → rotate(cut(CL(guess(x0))))
begin(a(x0)) → rotate(cut(Ca(guess(x0))))
guess(R(x0)) → CR(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(L(x0)) → CL(guess(x0))
guess(a(x0)) → Ca(guess(x0))
guess(R(x0)) → moveleft(BR(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(L(x0)) → moveleft(BL(wait(x0)))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(end(x0)) → finish(end(x0))
CR(moveleft(BR(x0))) → moveleft(BR(AR(x0)))
Cb(moveleft(BR(x0))) → moveleft(BR(Ab(x0)))
Cc(moveleft(BR(x0))) → moveleft(BR(Ac(x0)))
CL(moveleft(BR(x0))) → moveleft(BR(AL(x0)))
Ca(moveleft(BR(x0))) → moveleft(BR(Aa(x0)))
CR(moveleft(Bb(x0))) → moveleft(Bb(AR(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
CL(moveleft(Bb(x0))) → moveleft(Bb(AL(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
CR(moveleft(Bc(x0))) → moveleft(Bc(AR(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
CL(moveleft(Bc(x0))) → moveleft(Bc(AL(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
CR(moveleft(BL(x0))) → moveleft(BL(AR(x0)))
Cb(moveleft(BL(x0))) → moveleft(BL(Ab(x0)))
Cc(moveleft(BL(x0))) → moveleft(BL(Ac(x0)))
CL(moveleft(BL(x0))) → moveleft(BL(AL(x0)))
Ca(moveleft(BL(x0))) → moveleft(BL(Aa(x0)))
CR(moveleft(Ba(x0))) → moveleft(Ba(AR(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
CL(moveleft(Ba(x0))) → moveleft(Ba(AL(x0)))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
cut(moveleft(BR(x0))) → DR(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(BL(x0))) → DL(cut(goright(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
goright(AR(x0)) → CR(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(AL(x0)) → CL(goright(x0))
goright(Aa(x0)) → Ca(goright(x0))
goright(wait(R(x0))) → moveleft(BR(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(L(x0))) → moveleft(BL(wait(x0)))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CR(finish(x0)) → finish(R(x0))
Cb(finish(x0)) → finish(b(x0))
Cc(finish(x0)) → finish(c(x0))
CL(finish(x0)) → finish(L(x0))
Ca(finish(x0)) → finish(a(x0))
cut(finish(x0)) → finish2(x0)
DR(finish2(x0)) → finish2(R(x0))
Db(finish2(x0)) → finish2(b(x0))
Dc(finish2(x0)) → finish2(c(x0))
DL(finish2(x0)) → finish2(L(x0))
Da(finish2(x0)) → finish2(a(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(R(b(x0))) → begin(b(R(x0)))
rewrite(R(c(x0))) → begin(L(c(x0)))
rewrite(b(L(x0))) → begin(L(b(x0)))
rewrite(a(L(x0))) → begin(a(b(R(x0))))

Proof

1 Termination Assumption

We assume termination of the following TRS
begin(end(x0)) → rewrite(end(x0))
begin(R(x0)) → rotate(cut(CR(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
begin(L(x0)) → rotate(cut(CL(guess(x0))))
begin(a(x0)) → rotate(cut(Ca(guess(x0))))
guess(R(x0)) → CR(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(L(x0)) → CL(guess(x0))
guess(a(x0)) → Ca(guess(x0))
guess(R(x0)) → moveleft(BR(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(L(x0)) → moveleft(BL(wait(x0)))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(end(x0)) → finish(end(x0))
CR(moveleft(BR(x0))) → moveleft(BR(AR(x0)))
Cb(moveleft(BR(x0))) → moveleft(BR(Ab(x0)))
Cc(moveleft(BR(x0))) → moveleft(BR(Ac(x0)))
CL(moveleft(BR(x0))) → moveleft(BR(AL(x0)))
Ca(moveleft(BR(x0))) → moveleft(BR(Aa(x0)))
CR(moveleft(Bb(x0))) → moveleft(Bb(AR(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
CL(moveleft(Bb(x0))) → moveleft(Bb(AL(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
CR(moveleft(Bc(x0))) → moveleft(Bc(AR(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
CL(moveleft(Bc(x0))) → moveleft(Bc(AL(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
CR(moveleft(BL(x0))) → moveleft(BL(AR(x0)))
Cb(moveleft(BL(x0))) → moveleft(BL(Ab(x0)))
Cc(moveleft(BL(x0))) → moveleft(BL(Ac(x0)))
CL(moveleft(BL(x0))) → moveleft(BL(AL(x0)))
Ca(moveleft(BL(x0))) → moveleft(BL(Aa(x0)))
CR(moveleft(Ba(x0))) → moveleft(Ba(AR(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
CL(moveleft(Ba(x0))) → moveleft(Ba(AL(x0)))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
cut(moveleft(BR(x0))) → DR(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
cut(moveleft(BL(x0))) → DL(cut(goright(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
goright(AR(x0)) → CR(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(AL(x0)) → CL(goright(x0))
goright(Aa(x0)) → Ca(goright(x0))
goright(wait(R(x0))) → moveleft(BR(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(L(x0))) → moveleft(BL(wait(x0)))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
CR(finish(x0)) → finish(R(x0))
Cb(finish(x0)) → finish(b(x0))
Cc(finish(x0)) → finish(c(x0))
CL(finish(x0)) → finish(L(x0))
Ca(finish(x0)) → finish(a(x0))
cut(finish(x0)) → finish2(x0)
DR(finish2(x0)) → finish2(R(x0))
Db(finish2(x0)) → finish2(b(x0))
Dc(finish2(x0)) → finish2(c(x0))
DL(finish2(x0)) → finish2(L(x0))
Da(finish2(x0)) → finish2(a(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(R(b(x0))) → begin(b(R(x0)))
rewrite(R(c(x0))) → begin(L(c(x0)))
rewrite(b(L(x0))) → begin(L(b(x0)))
rewrite(a(L(x0))) → begin(a(b(R(x0))))