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(s(x0)) → rotate(cut(Cs(guess(x0))))
begin(p(x0)) → rotate(cut(Cp(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(s(x0)) → Cs(guess(x0))
guess(p(x0)) → Cp(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(s(x0)) → moveleft(Bs(wait(x0)))
guess(p(x0)) → moveleft(Bp(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cs(moveleft(Ba(x0))) → moveleft(Ba(As(x0)))
Cp(moveleft(Ba(x0))) → moveleft(Ba(Ap(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
Ca(moveleft(Bs(x0))) → moveleft(Bs(Aa(x0)))
Cs(moveleft(Bs(x0))) → moveleft(Bs(As(x0)))
Cp(moveleft(Bs(x0))) → moveleft(Bs(Ap(x0)))
Cb(moveleft(Bs(x0))) → moveleft(Bs(Ab(x0)))
Cc(moveleft(Bs(x0))) → moveleft(Bs(Ac(x0)))
Ca(moveleft(Bp(x0))) → moveleft(Bp(Aa(x0)))
Cs(moveleft(Bp(x0))) → moveleft(Bp(As(x0)))
Cp(moveleft(Bp(x0))) → moveleft(Bp(Ap(x0)))
Cb(moveleft(Bp(x0))) → moveleft(Bp(Ab(x0)))
Cc(moveleft(Bp(x0))) → moveleft(Bp(Ac(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
Cs(moveleft(Bb(x0))) → moveleft(Bb(As(x0)))
Cp(moveleft(Bb(x0))) → moveleft(Bb(Ap(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
Cs(moveleft(Bc(x0))) → moveleft(Bc(As(x0)))
Cp(moveleft(Bc(x0))) → moveleft(Bc(Ap(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bs(x0))) → Ds(cut(goright(x0)))
cut(moveleft(Bp(x0))) → Dp(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(As(x0)) → Cs(goright(x0))
goright(Ap(x0)) → Cp(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(s(x0))) → moveleft(Bs(wait(x0)))
goright(wait(p(x0))) → moveleft(Bp(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cs(finish(x0)) → finish(s(x0))
Cp(finish(x0)) → finish(p(x0))
Cb(finish(x0)) → finish(b(x0))
Cc(finish(x0)) → finish(c(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Ds(finish2(x0)) → finish2(s(x0))
Dp(finish2(x0)) → finish2(p(x0))
Db(finish2(x0)) → finish2(b(x0))
Dc(finish2(x0)) → finish2(c(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(s(x0))) → begin(s(s(s(p(s(b(p(p(s(s(x0)))))))))))
rewrite(b(s(x0))) → begin(s(s(s(p(p(s(s(c(p(s(p(s(x0)))))))))))))
rewrite(c(s(x0))) → begin(p(s(p(s(a(p(s(p(s(x0))))))))))
rewrite(p(p(s(x0)))) → begin(p(x0))
rewrite(p(s(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(s(x0)) → rotate(cut(Cs(guess(x0))))
begin(p(x0)) → rotate(cut(Cp(guess(x0))))
begin(b(x0)) → rotate(cut(Cb(guess(x0))))
begin(c(x0)) → rotate(cut(Cc(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(s(x0)) → Cs(guess(x0))
guess(p(x0)) → Cp(guess(x0))
guess(b(x0)) → Cb(guess(x0))
guess(c(x0)) → Cc(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(s(x0)) → moveleft(Bs(wait(x0)))
guess(p(x0)) → moveleft(Bp(wait(x0)))
guess(b(x0)) → moveleft(Bb(wait(x0)))
guess(c(x0)) → moveleft(Bc(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cs(moveleft(Ba(x0))) → moveleft(Ba(As(x0)))
Cp(moveleft(Ba(x0))) → moveleft(Ba(Ap(x0)))
Cb(moveleft(Ba(x0))) → moveleft(Ba(Ab(x0)))
Cc(moveleft(Ba(x0))) → moveleft(Ba(Ac(x0)))
Ca(moveleft(Bs(x0))) → moveleft(Bs(Aa(x0)))
Cs(moveleft(Bs(x0))) → moveleft(Bs(As(x0)))
Cp(moveleft(Bs(x0))) → moveleft(Bs(Ap(x0)))
Cb(moveleft(Bs(x0))) → moveleft(Bs(Ab(x0)))
Cc(moveleft(Bs(x0))) → moveleft(Bs(Ac(x0)))
Ca(moveleft(Bp(x0))) → moveleft(Bp(Aa(x0)))
Cs(moveleft(Bp(x0))) → moveleft(Bp(As(x0)))
Cp(moveleft(Bp(x0))) → moveleft(Bp(Ap(x0)))
Cb(moveleft(Bp(x0))) → moveleft(Bp(Ab(x0)))
Cc(moveleft(Bp(x0))) → moveleft(Bp(Ac(x0)))
Ca(moveleft(Bb(x0))) → moveleft(Bb(Aa(x0)))
Cs(moveleft(Bb(x0))) → moveleft(Bb(As(x0)))
Cp(moveleft(Bb(x0))) → moveleft(Bb(Ap(x0)))
Cb(moveleft(Bb(x0))) → moveleft(Bb(Ab(x0)))
Cc(moveleft(Bb(x0))) → moveleft(Bb(Ac(x0)))
Ca(moveleft(Bc(x0))) → moveleft(Bc(Aa(x0)))
Cs(moveleft(Bc(x0))) → moveleft(Bc(As(x0)))
Cp(moveleft(Bc(x0))) → moveleft(Bc(Ap(x0)))
Cb(moveleft(Bc(x0))) → moveleft(Bc(Ab(x0)))
Cc(moveleft(Bc(x0))) → moveleft(Bc(Ac(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bs(x0))) → Ds(cut(goright(x0)))
cut(moveleft(Bp(x0))) → Dp(cut(goright(x0)))
cut(moveleft(Bb(x0))) → Db(cut(goright(x0)))
cut(moveleft(Bc(x0))) → Dc(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(As(x0)) → Cs(goright(x0))
goright(Ap(x0)) → Cp(goright(x0))
goright(Ab(x0)) → Cb(goright(x0))
goright(Ac(x0)) → Cc(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(s(x0))) → moveleft(Bs(wait(x0)))
goright(wait(p(x0))) → moveleft(Bp(wait(x0)))
goright(wait(b(x0))) → moveleft(Bb(wait(x0)))
goright(wait(c(x0))) → moveleft(Bc(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cs(finish(x0)) → finish(s(x0))
Cp(finish(x0)) → finish(p(x0))
Cb(finish(x0)) → finish(b(x0))
Cc(finish(x0)) → finish(c(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Ds(finish2(x0)) → finish2(s(x0))
Dp(finish2(x0)) → finish2(p(x0))
Db(finish2(x0)) → finish2(b(x0))
Dc(finish2(x0)) → finish2(c(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(s(x0))) → begin(s(s(s(p(s(b(p(p(s(s(x0)))))))))))
rewrite(b(s(x0))) → begin(s(s(s(p(p(s(s(c(p(s(p(s(x0)))))))))))))
rewrite(c(s(x0))) → begin(p(s(p(s(a(p(s(p(s(x0))))))))))
rewrite(p(p(s(x0)))) → begin(p(x0))
rewrite(p(s(x0))) → begin(x0)