(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(a)) → f(g(n__f(a)))
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 6, 8, 10, 14, 15, 16
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 6 labelled f_1(0), n__f_1(1)
- 1 to 3 labelled n__f_1(0), f_1(0), a(0), g_1(0), activate_1(0), n__f_1(1), f_1(1), a(1), g_1(1), activate_1(1), n__f_1(2)
- 1 to 14 labelled f_1(1), n__f_1(2)
- 3 to 3 labelled #_1(0)
- 6 to 8 labelled g_1(0)
- 8 to 10 labelled n__f_1(0)
- 10 to 3 labelled a(0)
- 14 to 15 labelled g_1(1)
- 15 to 16 labelled n__f_1(1)
- 16 to 3 labelled a(1)