(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(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(X)
activate(X) → X
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
10145946, 10145947, 10145949, 10145950, 10145948, 10145952, 10145953, 10145951
Node 10145946 is start node and node 10145947 is final node.
Those nodes are connect through the following edges:
- 10145946 to 10145947 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__g_1(2), n__a(2)
- 10145946 to 10145948 labelled f_1(0), n__f_1(1)
- 10145946 to 10145951 labelled f_1(1), n__f_1(2)
- 10145947 to 10145947 labelled #_1(0)
- 10145949 to 10145950 labelled f_1(0), n__f_1(1)
- 10145950 to 10145947 labelled n__a(0)
- 10145948 to 10145949 labelled n__g_1(0)
- 10145952 to 10145953 labelled f_1(1), n__f_1(2)
- 10145953 to 10145947 labelled n__a(1)
- 10145951 to 10145952 labelled n__g_1(1)