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(p(x0)) → rotate(cut(Cp(guess(x0))))
begin(A(x0)) → rotate(cut(CA(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(p(x0)) → Cp(guess(x0))
guess(A(x0)) → CA(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(p(x0)) → moveleft(Bp(wait(x0)))
guess(A(x0)) → moveleft(BA(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cp(moveleft(Ba(x0))) → moveleft(Ba(Ap(x0)))
CA(moveleft(Ba(x0))) → moveleft(Ba(AA(x0)))
Ca(moveleft(Bp(x0))) → moveleft(Bp(Aa(x0)))
Cp(moveleft(Bp(x0))) → moveleft(Bp(Ap(x0)))
CA(moveleft(Bp(x0))) → moveleft(Bp(AA(x0)))
Ca(moveleft(BA(x0))) → moveleft(BA(Aa(x0)))
Cp(moveleft(BA(x0))) → moveleft(BA(Ap(x0)))
CA(moveleft(BA(x0))) → moveleft(BA(AA(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bp(x0))) → Dp(cut(goright(x0)))
cut(moveleft(BA(x0))) → DA(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(Ap(x0)) → Cp(goright(x0))
goright(AA(x0)) → CA(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(p(x0))) → moveleft(Bp(wait(x0)))
goright(wait(A(x0))) → moveleft(BA(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cp(finish(x0)) → finish(p(x0))
CA(finish(x0)) → finish(A(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Dp(finish2(x0)) → finish2(p(x0))
DA(finish2(x0)) → finish2(A(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(p(x0))) → begin(p(a(A(x0))))
rewrite(a(A(x0))) → begin(A(a(x0)))
rewrite(p(A(A(x0)))) → begin(a(p(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(p(x0)) → rotate(cut(Cp(guess(x0))))
begin(A(x0)) → rotate(cut(CA(guess(x0))))
guess(a(x0)) → Ca(guess(x0))
guess(p(x0)) → Cp(guess(x0))
guess(A(x0)) → CA(guess(x0))
guess(a(x0)) → moveleft(Ba(wait(x0)))
guess(p(x0)) → moveleft(Bp(wait(x0)))
guess(A(x0)) → moveleft(BA(wait(x0)))
guess(end(x0)) → finish(end(x0))
Ca(moveleft(Ba(x0))) → moveleft(Ba(Aa(x0)))
Cp(moveleft(Ba(x0))) → moveleft(Ba(Ap(x0)))
CA(moveleft(Ba(x0))) → moveleft(Ba(AA(x0)))
Ca(moveleft(Bp(x0))) → moveleft(Bp(Aa(x0)))
Cp(moveleft(Bp(x0))) → moveleft(Bp(Ap(x0)))
CA(moveleft(Bp(x0))) → moveleft(Bp(AA(x0)))
Ca(moveleft(BA(x0))) → moveleft(BA(Aa(x0)))
Cp(moveleft(BA(x0))) → moveleft(BA(Ap(x0)))
CA(moveleft(BA(x0))) → moveleft(BA(AA(x0)))
cut(moveleft(Ba(x0))) → Da(cut(goright(x0)))
cut(moveleft(Bp(x0))) → Dp(cut(goright(x0)))
cut(moveleft(BA(x0))) → DA(cut(goright(x0)))
goright(Aa(x0)) → Ca(goright(x0))
goright(Ap(x0)) → Cp(goright(x0))
goright(AA(x0)) → CA(goright(x0))
goright(wait(a(x0))) → moveleft(Ba(wait(x0)))
goright(wait(p(x0))) → moveleft(Bp(wait(x0)))
goright(wait(A(x0))) → moveleft(BA(wait(x0)))
goright(wait(end(x0))) → finish(end(x0))
Ca(finish(x0)) → finish(a(x0))
Cp(finish(x0)) → finish(p(x0))
CA(finish(x0)) → finish(A(x0))
cut(finish(x0)) → finish2(x0)
Da(finish2(x0)) → finish2(a(x0))
Dp(finish2(x0)) → finish2(p(x0))
DA(finish2(x0)) → finish2(A(x0))
rotate(finish2(x0)) → rewrite(x0)
rewrite(a(p(x0))) → begin(p(a(A(x0))))
rewrite(a(A(x0))) → begin(A(a(x0)))
rewrite(p(A(A(x0)))) → begin(a(p(x0)))