(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:
a__f(f(a)) → c(f(g(f(a))))
mark(f(X)) → a__f(mark(X))
mark(a) → a
mark(c(X)) → c(X)
mark(g(X)) → g(mark(X))
a__f(X) → f(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
8279410, 8279411, 8279412, 8279414, 8279415, 8279413, 8279416, 8279417, 8279418, 8279419, 8279421, 8279420, 8279423, 8279424, 8279425, 8279422
Node 8279410 is start node and node 8279411 is final node.
Those nodes are connect through the following edges:
- 8279410 to 8279411 labelled c_1(0), a(0), f_1(0)
- 8279410 to 8279412 labelled a__f_1(0), g_1(0), f_1(1)
- 8279410 to 8279413 labelled c_1(0)
- 8279410 to 8279418 labelled c_1(1)
- 8279411 to 8279411 labelled #_1(0)
- 8279412 to 8279411 labelled mark_1(0), c_1(1), a(1)
- 8279412 to 8279417 labelled a__f_1(1), g_1(1), f_1(2)
- 8279412 to 8279422 labelled c_1(2)
- 8279414 to 8279415 labelled g_1(0)
- 8279415 to 8279416 labelled f_1(0)
- 8279413 to 8279414 labelled f_1(0)
- 8279416 to 8279411 labelled a(0)
- 8279417 to 8279411 labelled mark_1(1), c_1(1), a(1)
- 8279417 to 8279417 labelled a__f_1(1), g_1(1), f_1(2)
- 8279417 to 8279422 labelled c_1(2)
- 8279418 to 8279419 labelled f_1(1)
- 8279419 to 8279420 labelled g_1(1)
- 8279421 to 8279411 labelled a(1)
- 8279420 to 8279421 labelled f_1(1)
- 8279423 to 8279424 labelled g_1(2)
- 8279424 to 8279425 labelled f_1(2)
- 8279425 to 8279411 labelled a(2)
- 8279422 to 8279423 labelled f_1(2)