YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

a(a(b(b(x0)))) → b(b(b(a(a(a(x0))))))
a(c(x0)) → c(a(x0))
b(c(x0)) → c(b(x0))

Proof

1 String Reversal

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

1.1 Bounds

The given TRS is match-bounded by 5. This is shown by the following automaton.