YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(a(a(x0))) → b#(x0)
b#(a(a(x0))) → b#(b(x0))
b#(a(a(x0))) → a#(b(b(x0)))
b#(a(a(x0))) → a#(a(b(b(x0))))
b#(b(x0)) → a#(c(x0))

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.