(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:
a__f(f(a)) → a__f(g(f(a)))
mark(f(X)) → a__f(mark(X))
mark(a) → a
mark(g(X)) → g(X)
a__f(X) → f(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 4, 6, 8, 10, 11, 15, 16, 17, 18, 19, 20
Node 1 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 1 to 6 labelled a__f_1(0), f_1(1)
- 1 to 4 labelled a(0), g_1(0), f_1(0)
- 1 to 15 labelled a__f_1(1), f_1(2)
- 4 to 4 labelled #_1(0)
- 6 to 8 labelled g_1(0)
- 6 to 4 labelled mark_1(0), a(1), g_1(1)
- 6 to 11 labelled a__f_1(1), f_1(2)
- 6 to 18 labelled a__f_1(2), f_1(3)
- 8 to 10 labelled f_1(0)
- 10 to 4 labelled a(0)
- 11 to 4 labelled mark_1(1), a(1), g_1(1)
- 11 to 11 labelled a__f_1(1), f_1(2)
- 11 to 18 labelled a__f_1(2), f_1(3)
- 15 to 16 labelled g_1(1)
- 16 to 17 labelled f_1(1)
- 17 to 4 labelled a(1)
- 18 to 19 labelled g_1(2)
- 19 to 20 labelled f_1(2)
- 20 to 4 labelled a(2)