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) → s(0)
f(s(0)) → s(0)
f(s(s(x))) → f(f(s(x)))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → s(0)
f(s(0)) → s(0)
f(s(s(x))) → f(f(s(x)))
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
f(0) → s(0)
f(s(0)) → s(0)
f(s(s(x))) → f(f(s(x)))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 5, 4, 7, 6, 8, 9
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled s_1(0)
- 1 to 4 labelled f_1(0)
- 1 to 8 labelled s_1(1)
- 2 to 2 labelled #_1(0)
- 3 to 2 labelled 0(0)
- 5 to 2 labelled s_1(0)
- 4 to 5 labelled f_1(0)
- 4 to 6 labelled f_1(1)
- 4 to 8 labelled s_1(1)
- 4 to 9 labelled s_1(2)
- 7 to 2 labelled s_1(1)
- 6 to 7 labelled f_1(1)
- 6 to 6 labelled f_1(1)
- 6 to 8 labelled s_1(1)
- 6 to 9 labelled s_1(2)
- 8 to 2 labelled 0(1)
- 9 to 2 labelled 0(2)