YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

1.1 Bounds

The given TRS is match-bounded by 2. This is shown by the following automaton.