(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:
7336624, 7336625, 7336627, 7336626, 7336628, 7336629
Node 7336624 is start node and node 7336625 is final node.
Those nodes are connect through the following edges:
- 7336624 to 7336626 labelled g_1(0)
- 7336625 to 7336625 labelled #_1(0)
- 7336627 to 7336625 labelled f_1(0), g_1(0)
- 7336627 to 7336628 labelled g_1(1)
- 7336626 to 7336627 labelled g_1(0)
- 7336628 to 7336629 labelled g_1(1)
- 7336629 to 7336625 labelled f_1(1), g_1(1)
- 7336629 to 7336628 labelled g_1(1)