(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:
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(0)) → g(d(1))
g(c(1)) → g(d(0))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7342752, 7342753, 7342754, 7342755, 7342756, 7342757, 7342758, 7342759, 7342761, 7342760, 7342763, 7342762, 7342764, 7342765
Node 7342752 is start node and node 7342753 is final node.
Those nodes are connect through the following edges:
- 7342752 to 7342753 labelled f_1(0), 1(0), c_1(0), g_1(0), 0(0), d_1(0), f_1(1), 1(1), c_1(1), g_1(1), 0(1), d_1(1), 0(2), 1(2)
- 7342752 to 7342754 labelled g_1(0)
- 7342752 to 7342756 labelled f_1(0)
- 7342752 to 7342758 labelled f_1(0)
- 7342752 to 7342760 labelled g_1(1)
- 7342752 to 7342762 labelled f_1(1)
- 7342752 to 7342764 labelled f_1(1)
- 7342753 to 7342753 labelled #_1(0)
- 7342754 to 7342755 labelled d_1(0)
- 7342755 to 7342753 labelled 0(0), 1(0)
- 7342756 to 7342757 labelled c_1(0)
- 7342757 to 7342753 labelled f_1(0)
- 7342757 to 7342762 labelled f_1(1)
- 7342757 to 7342764 labelled f_1(1)
- 7342758 to 7342759 labelled d_1(0)
- 7342759 to 7342753 labelled f_1(0)
- 7342759 to 7342762 labelled f_1(1)
- 7342759 to 7342764 labelled f_1(1)
- 7342761 to 7342753 labelled 0(1), 1(1)
- 7342760 to 7342761 labelled d_1(1)
- 7342763 to 7342753 labelled f_1(1)
- 7342763 to 7342762 labelled f_1(1)
- 7342763 to 7342764 labelled f_1(1)
- 7342762 to 7342763 labelled c_1(1)
- 7342764 to 7342765 labelled d_1(1)
- 7342765 to 7342753 labelled f_1(1)
- 7342765 to 7342762 labelled f_1(1)
- 7342765 to 7342764 labelled f_1(1)