YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Bounds

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