(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(n__f(n__a)) → f(n__g(f(n__a)))
f(X) → n__f(X)
a → n__a
g(X) → n__g(X)
activate(n__f(X)) → f(X)
activate(n__a) → a
activate(n__g(X)) → g(X)
activate(X) → X
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
8305248, 8305249, 8305251, 8305252, 8305250, 8305253, 8305254, 8305255
Node 8305248 is start node and node 8305249 is final node.
Those nodes are connect through the following edges:
- 8305248 to 8305249 labelled g_1(0), n__g_1(0), f_1(0), n__f_1(0), n__a(0), a(0), activate_1(0), n__f_1(1), n__a(1), n__g_1(1), g_1(1), f_1(1), a(1), activate_1(1), n__a(2), n__g_1(2), n__f_1(2)
- 8305248 to 8305250 labelled f_1(0), n__f_1(1)
- 8305248 to 8305253 labelled f_1(1), n__f_1(2)
- 8305249 to 8305249 labelled #_1(0)
- 8305251 to 8305252 labelled f_1(0), n__f_1(1)
- 8305252 to 8305249 labelled n__a(0)
- 8305250 to 8305251 labelled n__g_1(0)
- 8305253 to 8305254 labelled n__g_1(1)
- 8305254 to 8305255 labelled f_1(1), n__f_1(2)
- 8305255 to 8305249 labelled n__a(1)