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(1) → f(g(1))
f(f(x)) → f(x)
g(0) → g(f(0))
g(g(x)) → g(x)
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(1) → f(g(1))
f(f(x)) → f(x)
g(0) → g(f(0))
g(g(x)) → g(x)
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(1) → f(g(1))
f(f(x)) → f(x)
g(0) → g(f(0))
g(g(x)) → g(x)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 4, 3, 5, 6, 8, 7, 9, 10
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled g_1(0)
- 1 to 5 labelled f_1(0)
- 1 to 2 labelled f_1(0), g_1(0), g_1(1), f_1(1)
- 1 to 7 labelled g_1(1)
- 1 to 9 labelled f_1(1)
- 2 to 2 labelled #_1(0)
- 4 to 2 labelled 0(0)
- 3 to 4 labelled f_1(0)
- 5 to 6 labelled g_1(0)
- 6 to 2 labelled 1(0)
- 8 to 2 labelled 0(1)
- 7 to 8 labelled f_1(1)
- 9 to 10 labelled g_1(1)
- 10 to 2 labelled 1(1)