(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:
7474238, 7474239, 7474240, 7474241, 7474242, 7474243, 7474244, 7474245, 7474247, 7474248, 7474246, 7474249, 7474250, 7474251
Node 7474238 is start node and node 7474239 is final node.
Those nodes are connect through the following edges:
- 7474238 to 7474240 labelled f_1(0)
- 7474238 to 7474241 labelled f_1(0)
- 7474238 to 7474245 labelled f_1(1)
- 7474239 to 7474239 labelled #_1(0)
- 7474240 to 7474239 labelled g_1(0)
- 7474241 to 7474242 labelled g_1(0)
- 7474242 to 7474243 labelled f_1(0)
- 7474242 to 7474245 labelled f_1(1)
- 7474243 to 7474244 labelled g_1(0)
- 7474244 to 7474239 labelled f_1(0)
- 7474244 to 7474245 labelled f_1(1)
- 7474244 to 7474246 labelled f_1(1)
- 7474244 to 7474250 labelled f_1(2)
- 7474244 to 7474251 labelled f_1(2)
- 7474245 to 7474239 labelled g_1(1)
- 7474245 to 7474243 labelled g_1(1)
- 7474245 to 7474245 labelled g_1(1)
- 7474245 to 7474246 labelled g_1(1)
- 7474245 to 7474250 labelled g_1(1)
- 7474245 to 7474251 labelled g_1(1)
- 7474247 to 7474248 labelled f_1(1)
- 7474247 to 7474251 labelled f_1(2)
- 7474247 to 7474245 labelled f_1(1)
- 7474247 to 7474250 labelled f_1(2)
- 7474248 to 7474249 labelled g_1(1)
- 7474246 to 7474247 labelled g_1(1)
- 7474249 to 7474239 labelled f_1(1)
- 7474249 to 7474245 labelled f_1(1)
- 7474249 to 7474246 labelled f_1(1)
- 7474249 to 7474250 labelled f_1(2)
- 7474249 to 7474251 labelled f_1(2)
- 7474250 to 7474248 labelled g_1(2)
- 7474250 to 7474251 labelled g_1(2)
- 7474251 to 7474239 labelled g_1(2)
- 7474251 to 7474245 labelled g_1(2)
- 7474251 to 7474246 labelled g_1(2)
- 7474251 to 7474250 labelled g_1(2)