(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:
1449162, 1449163, 1449166, 1449165, 1449164, 1449169, 1449167, 1449168
Node 1449162 is start node and node 1449163 is final node.
Those nodes are connect through the following edges:
- 1449162 to 1449163 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__g_1(2), n__f_1(2), n__a(2)
- 1449162 to 1449164 labelled f_1(0), n__f_1(1)
- 1449162 to 1449162 labelled g_1(0), n__g_1(1), g_1(1), n__g_1(2)
- 1449162 to 1449167 labelled f_1(1), n__f_1(2)
- 1449163 to 1449163 labelled #_1(0)
- 1449166 to 1449163 labelled n__a(0)
- 1449165 to 1449166 labelled n__f_1(0)
- 1449164 to 1449165 labelled n__g_1(0)
- 1449169 to 1449163 labelled n__a(1)
- 1449167 to 1449168 labelled n__g_1(1)
- 1449168 to 1449169 labelled n__f_1(1)