YES Termination w.r.t. Q proof of Transformed_CSR_04_Ex23_Luc06_L.ari

(0) Obligation:

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

f(f(a)) → c

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(f(a)) → c

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

1, 4

Node 1 is start node and node 4 is final node.

Those nodes are connected through the following edges:

  • 1 to 4 labelled c(0)
  • 4 to 4 labelled #_1(0)

(2) YES