(3) 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:
s(f(x)) → s(p(f(f(s(x)))))
0'(f(x)) → 0'(x)
s(p(x)) → x
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
751745, 751746, 751747, 751748, 751749, 751750, 751751, 751752, 751753, 751754
Node 751745 is start node and node 751746 is final node.
Those nodes are connect through the following edges:
- 751745 to 751746 labelled p_1(0), 0'_1(0), f_1(0), s_1(0), 0'_1(1), p_1(1), f_1(1), s_1(1)
- 751745 to 751747 labelled s_1(0)
- 751745 to 751751 labelled s_1(1)
- 751745 to 751749 labelled f_1(1)
- 751745 to 751753 labelled f_1(2)
- 751746 to 751746 labelled #_1(0)
- 751747 to 751748 labelled p_1(0)
- 751748 to 751749 labelled f_1(0)
- 751749 to 751750 labelled f_1(0)
- 751750 to 751746 labelled s_1(0), p_1(1), f_1(1), s_1(1), 0'_1(1)
- 751750 to 751751 labelled s_1(1)
- 751750 to 751753 labelled f_1(2)
- 751751 to 751752 labelled p_1(1)
- 751752 to 751753 labelled f_1(1)
- 751753 to 751754 labelled f_1(1)
- 751754 to 751746 labelled s_1(1), p_1(1), f_1(1), 0'_1(1)
- 751754 to 751751 labelled s_1(1)
- 751754 to 751753 labelled f_1(2)