Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 1. 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(0)) → 0
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 5, 3, 4
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 2 labelled 0(0)
- 1 to 1 labelled cons_1(0)
- 1 to 3 labelled f_1(0), cons_1(1)
- 2 to 2 labelled #_1(0)
- 5 to 2 labelled 0(0)
- 3 to 4 labelled p_1(0)
- 3 to 2 labelled 0(1)
- 4 to 5 labelled s_1(0)