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

Proof

1 Rule Removal

Using the linear polynomial interpretation over the arctic semiring over the integers
[a(x1)] = 0 · x1 + -∞
[b(x1)] = 4 · x1 + -∞
[c(x1)] = 0 · x1 + -∞
the rules
a(b(x0)) → b(a(a(x0)))
a(a(x0)) → a(c(a(x0)))
remain.

1.1 String Reversal

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

1.1.1 Bounds

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