(0) Obligation:

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

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

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

9413098, 9413099, 9413101, 9413100

Node 9413098 is start node and node 9413099 is final node.

Those nodes are connect through the following edges:

  • 9413098 to 9413100 labelled g_1(0)
  • 9413098 to 9413099 labelled f_1(0), f_1(1)
  • 9413099 to 9413099 labelled #_1(0)
  • 9413101 to 9413099 labelled 0(0)
  • 9413100 to 9413101 labelled f_1(0)

(2) TRUE