(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:
899251, 899252, 899254, 899255, 899253
Node 899251 is start node and node 899252 is final node.
Those nodes are connect through the following edges:
- 899251 to 899252 labelled f_1(0), f_1(1)
- 899251 to 899253 labelled g_1(0)
- 899252 to 899252 labelled #_1(0)
- 899254 to 899255 labelled s_1(0)
- 899255 to 899252 labelled 0(0)
- 899253 to 899254 labelled f_1(0)
- 899253 to 899255 labelled f_1(1)