(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] 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:
899110, 899111, 899113, 899112, 899115, 899114, 899116, 899117, 899118, 899119
Node 899110 is start node and node 899111 is final node.
Those nodes are connect through the following edges:
- 899110 to 899112 labelled g_1(0)
- 899110 to 899114 labelled f_1(0)
- 899110 to 899111 labelled f_1(0), g_1(0), g_1(1), f_1(1)
- 899110 to 899116 labelled g_1(1)
- 899110 to 899118 labelled f_1(1)
- 899111 to 899111 labelled #_1(0)
- 899113 to 899111 labelled 0(0)
- 899112 to 899113 labelled f_1(0)
- 899115 to 899111 labelled 1(0)
- 899114 to 899115 labelled g_1(0)
- 899116 to 899117 labelled f_1(1)
- 899117 to 899111 labelled 0(1)
- 899118 to 899119 labelled g_1(1)
- 899119 to 899111 labelled 1(1)