(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:
1358528, 1358529, 1358530, 1358531, 1358532, 1358534, 1358533, 1358535, 1358536, 1358537
Node 1358528 is start node and node 1358529 is final node.
Those nodes are connect through the following edges:
- 1358528 to 1358529 labelled g_1(0), f_1(0)
- 1358528 to 1358530 labelled a__f_1(0), h_1(0), f_1(1)
- 1358528 to 1358531 labelled g_1(0)
- 1358528 to 1358533 labelled g_1(1)
- 1358529 to 1358529 labelled #_1(0)
- 1358530 to 1358529 labelled mark_1(0), g_1(1)
- 1358530 to 1358535 labelled a__f_1(1), h_1(1), f_1(2)
- 1358530 to 1358536 labelled g_1(2)
- 1358531 to 1358532 labelled h_1(0)
- 1358532 to 1358529 labelled f_1(0)
- 1358534 to 1358530 labelled f_1(1)
- 1358533 to 1358534 labelled h_1(1)
- 1358535 to 1358529 labelled mark_1(1), g_1(1)
- 1358535 to 1358535 labelled a__f_1(1), h_1(1), f_1(2)
- 1358535 to 1358536 labelled g_1(2)
- 1358536 to 1358537 labelled h_1(2)
- 1358537 to 1358535 labelled f_1(2)