YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

1.1 Bounds

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