(0) Obligation:

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

f(f(x)) → f(x)
f(s(x)) → f(x)
g(s(0)) → g(f(s(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(f(x)) → f(x)
f(s(x)) → f(x)
g(s(0)) → g(f(s(0)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

2928298, 2928299, 2928301, 2928302, 2928300

Node 2928298 is start node and node 2928299 is final node.

Those nodes are connect through the following edges:

  • 2928298 to 2928299 labelled f_1(0), f_1(1)
  • 2928298 to 2928300 labelled g_1(0)
  • 2928299 to 2928299 labelled #_1(0)
  • 2928301 to 2928302 labelled s_1(0)
  • 2928302 to 2928299 labelled 0(0)
  • 2928300 to 2928301 labelled f_1(0)
  • 2928300 to 2928302 labelled f_1(1)

(2) TRUE