(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:
7881466, 7881467, 7881468, 7881469, 7881470, 7881471, 7881472, 7881473
Node 7881466 is start node and node 7881467 is final node.
Those nodes are connect through the following edges:
- 7881466 to 7881467 labelled g_1(0), n__g_1(0), f_1(0), n__f_1(0), n__a(0), a(0), activate_1(0), n__g_1(1), n__a(1), n__f_1(1), g_1(1), f_1(1), a(1), activate_1(1), n__a(2), n__g_1(2), n__f_1(2)
- 7881466 to 7881468 labelled f_1(0), n__f_1(1)
- 7881466 to 7881466 labelled g_1(0), n__g_1(1), g_1(1), n__g_1(2)
- 7881466 to 7881471 labelled f_1(1), n__f_1(2)
- 7881467 to 7881467 labelled #_1(0)
- 7881468 to 7881469 labelled n__g_1(0)
- 7881469 to 7881470 labelled n__f_1(0)
- 7881470 to 7881467 labelled n__a(0)
- 7881471 to 7881472 labelled n__g_1(1)
- 7881472 to 7881473 labelled n__f_1(1)
- 7881473 to 7881467 labelled n__a(1)