YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

a(l(x0)) → l(a(x0))
r(a(a(x0))) → a(a(r(x0)))
b(l(x0)) → b(a(r(x0)))
r(b(x0)) → l(b(x0))

Proof

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
l(a(x0)) → a(l(x0))
a(a(r(x0))) → r(a(a(x0)))
l(b(x0)) → r(a(b(x0)))
b(r(x0)) → b(l(x0))

1.1 Bounds

The given TRS is match-bounded by 3. This is shown by the following automaton.