(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:
8483900, 8483901, 8483902, 8483903, 8483904, 8483905, 8483906, 8483907, 8483908, 8483909, 8483910, 8483911
Node 8483900 is start node and node 8483901 is final node.
Those nodes are connect through the following edges:
- 8483900 to 8483901 labelled g_1(0), f_1(0), g_1(1), f_1(1)
- 8483900 to 8483902 labelled mark_1(0)
- 8483900 to 8483900 labelled active_1(0), mark_1(0), active_1(1), mark_1(1)
- 8483900 to 8483904 labelled active_1(0), g_1(1)
- 8483900 to 8483905 labelled active_1(1)
- 8483900 to 8483906 labelled mark_1(1)
- 8483900 to 8483909 labelled active_1(2)
- 8483900 to 8483910 labelled mark_1(2)
- 8483900 to 8483911 labelled active_1(3)
- 8483901 to 8483901 labelled #_1(0)
- 8483902 to 8483903 labelled f_1(0)
- 8483903 to 8483904 labelled g_1(0)
- 8483904 to 8483901 labelled c(0)
- 8483905 to 8483903 labelled f_1(1)
- 8483906 to 8483907 labelled f_1(1)
- 8483907 to 8483908 labelled g_1(1)
- 8483908 to 8483901 labelled c(1)
- 8483909 to 8483907 labelled f_1(2)
- 8483909 to 8483901 labelled f_1(2), g_1(2), g_1(1), f_1(1)
- 8483909 to 8483904 labelled g_1(2)
- 8483910 to 8483908 labelled g_1(2)
- 8483911 to 8483908 labelled g_1(3)