(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:
1750581, 1750582, 1750583, 1750584, 1750585, 1750586, 1750589, 1750587, 1750588
Node 1750581 is start node and node 1750582 is final node.
Those nodes are connect through the following edges:
- 1750581 to 1750582 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)
- 1750581 to 1750581 labelled cons_1(0), cons_1(1)
- 1750581 to 1750583 labelled f_1(0)
- 1750581 to 1750586 labelled cons_1(1)
- 1750581 to 1750587 labelled f_1(1), cons_1(2)
- 1750582 to 1750582 labelled #_1(0)
- 1750583 to 1750584 labelled p_1(0)
- 1750583 to 1750582 labelled 0(1)
- 1750584 to 1750585 labelled s_1(0)
- 1750585 to 1750582 labelled 0(0)
- 1750586 to 1750582 labelled 0(1)
- 1750589 to 1750582 labelled 0(1)
- 1750587 to 1750588 labelled p_1(1)
- 1750587 to 1750582 labelled 0(2)
- 1750588 to 1750589 labelled s_1(1)