(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:
9776634, 9776635, 9776636, 9776637, 9776638, 9776639, 9776640, 9776641
Node 9776634 is start node and node 9776635 is final node.
Those nodes are connect through the following edges:
- 9776634 to 9776635 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__g_1(1), n__a(1), g_1(1), f_1(1), a(1), activate_1(1), n__f_1(2), n__a(2), n__g_1(2)
- 9776634 to 9776636 labelled f_1(0), n__f_1(1)
- 9776634 to 9776634 labelled g_1(0), n__g_1(1), g_1(1), n__g_1(2)
- 9776634 to 9776639 labelled f_1(1), n__f_1(2)
- 9776635 to 9776635 labelled #_1(0)
- 9776636 to 9776637 labelled n__g_1(0)
- 9776637 to 9776638 labelled n__f_1(0)
- 9776638 to 9776635 labelled n__a(0)
- 9776639 to 9776640 labelled n__g_1(1)
- 9776640 to 9776641 labelled n__f_1(1)
- 9776641 to 9776635 labelled n__a(1)