(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:
1066774, 1066775, 1066776, 1066777, 1066778, 1066779
Node 1066774 is start node and node 1066775 is final node.
Those nodes are connect through the following edges:
- 1066774 to 1066776 labelled g_1(0)
- 1066775 to 1066775 labelled #_1(0)
- 1066776 to 1066777 labelled g_1(0)
- 1066777 to 1066775 labelled f_1(0), g_1(0)
- 1066777 to 1066778 labelled g_1(1)
- 1066778 to 1066779 labelled g_1(1)
- 1066779 to 1066775 labelled f_1(1), g_1(1)
- 1066779 to 1066778 labelled g_1(1)