(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(g(x)) → g(g(f(x)))
f(g(x)) → g(g(g(x)))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 5, 6, 9, 10
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 5 labelled g_1(0)
- 3 to 3 labelled #_1(0)
- 5 to 6 labelled g_1(0)
- 6 to 3 labelled f_1(0), g_1(0)
- 6 to 9 labelled g_1(1)
- 9 to 10 labelled g_1(1)
- 10 to 3 labelled f_1(1), g_1(1)
- 10 to 9 labelled g_1(1)