(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
f(f(a)) → f(g(n__f(n__a)))
f(X) → n__f(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__a) → a
activate(X) → X
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 8, 9, 11, 12, 13, 18, 19, 20
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 5 labelled f_1(0), n__f_1(1)
- 2 to 4 labelled n__f_1(0), n__a(0), a(0), f_1(0), g_1(0), activate_1(0), n__a(1), n__f_1(1), a(1), f_1(1), g_1(1), activate_1(1), n__a(2), n__f_1(2)
- 2 to 11 labelled f_1(1), n__f_1(2)
- 2 to 2 labelled f_1(1), n__f_1(2)
- 2 to 18 labelled f_1(2), n__f_1(3)
- 4 to 4 labelled #_1(0)
- 5 to 8 labelled g_1(0)
- 5 to 4 labelled activate_1(0), a(1), f_1(1), g_1(1), n__f_1(1), n__a(1), activate_1(1), n__a(2), n__f_1(2)
- 5 to 2 labelled f_1(1), n__f_1(2)
- 5 to 11 labelled f_1(1), n__f_1(2)
- 5 to 18 labelled f_1(2), n__f_1(3)
- 8 to 9 labelled n__f_1(0)
- 9 to 4 labelled n__a(0)
- 11 to 12 labelled g_1(1)
- 11 to 4 labelled activate_1(1), a(1), f_1(1), g_1(1), n__f_1(1), n__a(1), n__a(2), n__f_1(2)
- 11 to 2 labelled f_1(1), n__f_1(2)
- 11 to 11 labelled f_1(1), n__f_1(2)
- 11 to 18 labelled f_1(2), n__f_1(3)
- 12 to 13 labelled n__f_1(1)
- 13 to 4 labelled n__a(1)
- 18 to 19 labelled g_1(2)
- 19 to 20 labelled n__f_1(2)
- 20 to 4 labelled n__a(2)