(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(X) → g(h(f(X)))
mark(f(X)) → a__f(mark(X))
mark(g(X)) → g(X)
mark(h(X)) → h(mark(X))
a__f(X) → f(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
9714376, 9714377, 9714378, 9714379, 9714380, 9714382, 9714381, 9714383, 9714384, 9714385
Node 9714376 is start node and node 9714377 is final node.
Those nodes are connect through the following edges:
- 9714376 to 9714377 labelled g_1(0), f_1(0)
- 9714376 to 9714378 labelled a__f_1(0), h_1(0), f_1(1)
- 9714376 to 9714379 labelled g_1(0)
- 9714376 to 9714381 labelled g_1(1)
- 9714377 to 9714377 labelled #_1(0)
- 9714378 to 9714377 labelled mark_1(0), g_1(1)
- 9714378 to 9714383 labelled a__f_1(1), h_1(1), f_1(2)
- 9714378 to 9714384 labelled g_1(2)
- 9714379 to 9714380 labelled h_1(0)
- 9714380 to 9714377 labelled f_1(0)
- 9714382 to 9714378 labelled f_1(1)
- 9714381 to 9714382 labelled h_1(1)
- 9714383 to 9714377 labelled mark_1(1), g_1(1)
- 9714383 to 9714383 labelled a__f_1(1), h_1(1), f_1(2)
- 9714383 to 9714384 labelled g_1(2)
- 9714384 to 9714385 labelled h_1(2)
- 9714385 to 9714383 labelled f_1(2)