YES Termination w.r.t. Q proof of SK90_4.46.ari

(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:

1, 3, 6, 8

Node 1 is start node and node 3 is final node.

Those nodes are connected through the following edges:

  • 1 to 6 labelled f_1(0)
  • 1 to 8 labelled g_1(0)
  • 3 to 3 labelled #_1(0)
  • 6 to 3 labelled b(0)
  • 8 to 3 labelled a(0)

(2) YES