(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
f(f(X)) → f(g(f(g(f(X)))))
f(g(f(X))) → f(g(X))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 6, 7, 9, 10, 13, 14, 15, 16, 17, 23, 26
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 6 labelled f_1(0)
- 2 to 17 labelled f_1(1)
- 2 to 13 labelled f_1(1)
- 2 to 23 labelled f_1(2)
- 2 to 26 labelled f_1(2)
- 4 to 4 labelled #_1(0)
- 6 to 7 labelled g_1(0)
- 6 to 4 labelled g_1(0)
- 7 to 9 labelled f_1(0)
- 7 to 13 labelled f_1(1)
- 7 to 23 labelled f_1(2)
- 7 to 17 labelled f_1(1)
- 7 to 26 labelled f_1(2)
- 9 to 10 labelled g_1(0)
- 10 to 4 labelled f_1(0)
- 10 to 13 labelled f_1(1)
- 10 to 23 labelled f_1(2)
- 10 to 26 labelled f_1(2)
- 13 to 14 labelled g_1(1)
- 13 to 4 labelled g_1(1)
- 14 to 15 labelled f_1(1)
- 14 to 26 labelled f_1(2)
- 14 to 13 labelled f_1(1)
- 14 to 23 labelled f_1(2)
- 15 to 16 labelled g_1(1)
- 16 to 4 labelled f_1(1)
- 16 to 13 labelled f_1(1)
- 16 to 23 labelled f_1(2)
- 16 to 26 labelled f_1(2)
- 17 to 9 labelled g_1(1)
- 17 to 13 labelled g_1(1)
- 17 to 23 labelled g_1(1)
- 17 to 17 labelled g_1(1)
- 17 to 26 labelled g_1(1)
- 23 to 15 labelled g_1(2)
- 23 to 26 labelled g_1(2)
- 26 to 4 labelled g_1(2)
- 26 to 13 labelled g_1(2)
- 26 to 23 labelled g_1(2)