(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:

472402, 472403, 472405, 472406, 472404

Node 472402 is start node and node 472403 is final node.

Those nodes are connect through the following edges:

  • 472402 to 472403 labelled 0(0)
  • 472402 to 472402 labelled cons_1(0)
  • 472402 to 472404 labelled f_1(0), cons_1(1)
  • 472403 to 472403 labelled #_1(0)
  • 472405 to 472406 labelled s_1(0)
  • 472406 to 472403 labelled 0(0)
  • 472404 to 472405 labelled p_1(0)
  • 472404 to 472403 labelled 0(1)

(2) TRUE