(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
active(c) → mark(f(g(c)))
active(f(g(X))) → mark(g(X))
mark(c) → active(c)
mark(f(X)) → active(f(X))
mark(g(X)) → active(g(X))
f(mark(X)) → f(X)
f(active(X)) → f(X)
g(mark(X)) → g(X)
g(active(X)) → g(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
41184, 41185, 41187, 41188, 41186, 41190, 41191, 41189, 41192, 41193, 41194, 41195
Node 41184 is start node and node 41185 is final node.
Those nodes are connect through the following edges:
- 41184 to 41185 labelled g_1(0), f_1(0), f_1(1), g_1(1)
- 41184 to 41186 labelled mark_1(0)
- 41184 to 41184 labelled active_1(0), mark_1(0), mark_1(1), active_1(1)
- 41184 to 41188 labelled active_1(0), g_1(1)
- 41184 to 41189 labelled mark_1(1)
- 41184 to 41192 labelled active_1(1)
- 41184 to 41193 labelled active_1(2)
- 41184 to 41194 labelled mark_1(2)
- 41184 to 41195 labelled active_1(3)
- 41185 to 41185 labelled #_1(0)
- 41187 to 41188 labelled g_1(0)
- 41188 to 41185 labelled c(0)
- 41186 to 41187 labelled f_1(0)
- 41190 to 41191 labelled g_1(1)
- 41191 to 41185 labelled c(1)
- 41189 to 41190 labelled f_1(1)
- 41192 to 41185 labelled f_1(1), g_1(1)
- 41192 to 41187 labelled f_1(1)
- 41193 to 41185 labelled g_1(2), f_1(2), f_1(1), g_1(1)
- 41193 to 41190 labelled f_1(2)
- 41193 to 41188 labelled g_1(2)
- 41194 to 41191 labelled g_1(2)
- 41195 to 41191 labelled g_1(3)