YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

1.1 Bounds

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