(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
g(0) → 0
g(s(x)) → f(g(x))
f(0) → 0
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 7
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 4 labelled 0(0), 0(1)
- 2 to 5 labelled f_1(0)
- 4 to 4 labelled #_1(0)
- 5 to 4 labelled g_1(0), 0(1), 0(2)
- 5 to 7 labelled f_1(1)
- 7 to 4 labelled g_1(1), 0(1), 0(2)
- 7 to 7 labelled f_1(1)