(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:
10131664, 10131665, 10131668, 10131667, 10131666, 10131671, 10131670, 10131669
Node 10131664 is start node and node 10131665 is final node.
Those nodes are connect through the following edges:
- 10131664 to 10131665 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)
- 10131664 to 10131664 labelled cons_1(0), cons_1(1)
- 10131664 to 10131666 labelled f_1(0)
- 10131664 to 10131669 labelled f_1(1), cons_1(2)
- 10131665 to 10131665 labelled #_1(0)
- 10131668 to 10131665 labelled 0(0)
- 10131667 to 10131668 labelled s_1(0)
- 10131666 to 10131667 labelled p_1(0)
- 10131666 to 10131665 labelled 0(1)
- 10131671 to 10131665 labelled 0(1)
- 10131670 to 10131671 labelled s_1(1)
- 10131669 to 10131670 labelled p_1(1)
- 10131669 to 10131665 labelled 0(2)