(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:
9555482, 9555483, 9555484, 9555485, 9555487, 9555486
Node 9555482 is start node and node 9555483 is final node.
Those nodes are connect through the following edges:
- 9555482 to 9555484 labelled g_1(0)
- 9555483 to 9555483 labelled #_1(0)
- 9555484 to 9555485 labelled g_1(0)
- 9555485 to 9555483 labelled f_1(0), g_1(0)
- 9555485 to 9555486 labelled g_1(1)
- 9555487 to 9555483 labelled f_1(1), g_1(1)
- 9555487 to 9555486 labelled g_1(1)
- 9555486 to 9555487 labelled g_1(1)