(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(1) → f(g(1))
f(f(x)) → f(x)
g(0) → g(f(0))
g(g(x)) → g(x)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
9412279, 9412280, 9412281, 9412282, 9412283, 9412284, 9412286, 9412285, 9412287, 9412288
Node 9412279 is start node and node 9412280 is final node.
Those nodes are connect through the following edges:
- 9412279 to 9412281 labelled g_1(0)
- 9412279 to 9412283 labelled f_1(0)
- 9412279 to 9412280 labelled f_1(0), g_1(0), g_1(1), f_1(1)
- 9412279 to 9412285 labelled g_1(1)
- 9412279 to 9412287 labelled f_1(1)
- 9412280 to 9412280 labelled #_1(0)
- 9412281 to 9412282 labelled f_1(0)
- 9412282 to 9412280 labelled 0(0)
- 9412283 to 9412284 labelled g_1(0)
- 9412284 to 9412280 labelled 1(0)
- 9412286 to 9412280 labelled 0(1)
- 9412285 to 9412286 labelled f_1(1)
- 9412287 to 9412288 labelled g_1(1)
- 9412288 to 9412280 labelled 1(1)