YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

t(o(x0)) → m(a(x0))
t(e(x0)) → n(s(x0))
a(l(x0)) → a(t(x0))
o(m(a(x0))) → t(e(n(x0)))
s(a(x0)) → l(a(t(o(m(a(t(e(x0))))))))
n(s(x0)) → a(l(a(t(x0))))

Proof

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
o(t(x0)) → a(m(x0))
e(t(x0)) → s(n(x0))
l(a(x0)) → t(a(x0))
a(m(o(x0))) → n(e(t(x0)))
a(s(x0)) → e(t(a(m(o(t(a(l(x0))))))))
s(n(x0)) → t(a(l(a(x0))))

1.1 Bounds

The given TRS is match-bounded by 4. This is shown by the following automaton.