YES Termination w.r.t. Q proof of Transformed_CSR_04_Ex25_Luc06_L.ari

Termination w.r.t. Q of the given QTRS could be proven:

0 QTRS
↳1 RFCMatchBoundsTRSProof (⇔, 0 ms)
↳2 YES

(0) Obligation:

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

f(f(X)) → c
c → d
h(X) → c

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

f(f(X)) → c
c → d
h(X) → c

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

2, 4

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

  • 2 to 4 labelled c(0), d(0), d(1)
  • 4 to 4 labelled #_1(0)

(2) YES