(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(n__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(activate(X))
activate(X) → X

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

2, 3, 6, 8, 10, 12, 13, 14, 15, 18

Node 2 is start node and node 3 is final node.

Those nodes are connected through the following edges:

• 2 to 6 labelled f_1(0), n__f_1(1)
• 2 to 3 labelled n__f_1(0), n__a(0), n__g_1(0), f_1(0), a(0), g_1(0), activate_1(0), n__f_1(1), n__a(1), n__g_1(1), f_1(1), a(1), g_1(1), activate_1(1), n__f_1(2), n__a(2), n__g_1(2)
• 2 to 12 labelled g_1(0), n__g_1(1)
• 2 to 13 labelled f_1(1), n__f_1(2)
• 2 to 18 labelled g_1(1), n__g_1(2)
• 2 to 2 labelled g_1(1), n__g_1(2)
• 3 to 3 labelled #_1(0)
• 6 to 8 labelled n__g_1(0)
• 8 to 10 labelled n__f_1(0)
• 10 to 3 labelled n__a(0)
• 12 to 3 labelled activate_1(0), f_1(1), a(1), n__f_1(1), n__a(1), n__g_1(1), g_1(1), activate_1(1), n__f_1(2), n__a(2), n__g_1(2)
• 12 to 2 labelled g_1(1), n__g_1(2)
• 12 to 13 labelled f_1(1), n__f_1(2)
• 13 to 14 labelled n__g_1(1)
• 14 to 15 labelled n__f_1(1)
• 15 to 3 labelled n__a(1)
• 18 to 3 labelled activate_1(1), f_1(1), a(1), n__f_1(1), n__a(1), n__g_1(1), g_1(1), n__f_1(2), n__a(2), n__g_1(2)
• 18 to 2 labelled g_1(1), n__g_1(2)
• 18 to 13 labelled f_1(1), n__f_1(2)