(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:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(X)) → X
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
8291034, 8291035, 8291038, 8291037, 8291036, 8291041, 8291039, 8291040
Node 8291034 is start node and node 8291035 is final node.
Those nodes are connect through the following edges:
- 8291034 to 8291035 labelled 0(0), f_1(0), cons_1(0), p_1(0), s_1(0), 0(1), f_1(1), cons_1(1), p_1(1), s_1(1)
- 8291034 to 8291034 labelled cons_1(0), cons_1(1)
- 8291034 to 8291036 labelled f_1(0)
- 8291034 to 8291039 labelled f_1(1), cons_1(2)
- 8291035 to 8291035 labelled #_1(0)
- 8291038 to 8291035 labelled 0(0)
- 8291037 to 8291038 labelled s_1(0)
- 8291036 to 8291037 labelled p_1(0)
- 8291036 to 8291035 labelled 0(1)
- 8291041 to 8291035 labelled 0(1)
- 8291039 to 8291040 labelled p_1(1)
- 8291039 to 8291035 labelled 0(2)
- 8291040 to 8291041 labelled s_1(1)