(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(a) → f(b)
g(b) → g(a)

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

f(a) → f(b)
g(b) → g(a)

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

9111257, 9111258, 9111259, 9111260

Node 9111257 is start node and node 9111258 is final node.

Those nodes are connect through the following edges:

  • 9111257 to 9111259 labelled g_1(0)
  • 9111257 to 9111260 labelled f_1(0)
  • 9111258 to 9111258 labelled #_1(0)
  • 9111259 to 9111258 labelled a(0)
  • 9111260 to 9111258 labelled b(0)

(2) TRUE