(0) Obligation:

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

f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(0)) → 0

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(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(0)) → 0

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

8844968, 8844969, 8844970, 8844971, 8844972

Node 8844968 is start node and node 8844969 is final node.

Those nodes are connect through the following edges:

  • 8844968 to 8844969 labelled 0(0)
  • 8844968 to 8844968 labelled cons_1(0)
  • 8844968 to 8844970 labelled f_1(0), cons_1(1)
  • 8844969 to 8844969 labelled #_1(0)
  • 8844970 to 8844971 labelled p_1(0)
  • 8844970 to 8844969 labelled 0(1)
  • 8844971 to 8844972 labelled s_1(0)
  • 8844972 to 8844969 labelled 0(0)

(2) TRUE