(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)) → a__f(g(f(a)))
mark(f(X)) → a__f(X)
mark(a) → a
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:
2180926, 2180927, 2180928, 2180929, 2180930, 2180931, 2180932, 2180934, 2180935, 2180933
Node 2180926 is start node and node 2180927 is final node.
Those nodes are connect through the following edges:
- 2180926 to 2180927 labelled a__f_1(0), a(0), f_1(0), f_1(1)
- 2180926 to 2180928 labelled g_1(0)
- 2180926 to 2180929 labelled a__f_1(0), f_1(1)
- 2180926 to 2180933 labelled a__f_1(1), f_1(2)
- 2180927 to 2180927 labelled #_1(0)
- 2180928 to 2180927 labelled mark_1(0), a__f_1(1), a(1), f_1(2)
- 2180928 to 2180932 labelled g_1(1)
- 2180928 to 2180933 labelled a__f_1(1), f_1(2)
- 2180929 to 2180930 labelled g_1(0)
- 2180930 to 2180931 labelled f_1(0)
- 2180931 to 2180927 labelled a(0)
- 2180932 to 2180927 labelled mark_1(1), a__f_1(1), a(1), f_1(2)
- 2180932 to 2180932 labelled g_1(1)
- 2180932 to 2180933 labelled a__f_1(1), f_1(2)
- 2180934 to 2180935 labelled f_1(1)
- 2180935 to 2180927 labelled a(1)
- 2180933 to 2180934 labelled g_1(1)