YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

1.1 Bounds

The given TRS is match-bounded by 1. This is shown by the following automaton.