(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:
9559662, 9559663, 9559665, 9559664, 9559667, 9559666, 9559669, 9559668, 9559671, 9559670, 9559673, 9559672, 9559674, 9559675
Node 9559662 is start node and node 9559663 is final node.
Those nodes are connect through the following edges:
- 9559662 to 9559663 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)
- 9559662 to 9559664 labelled g_1(0)
- 9559662 to 9559666 labelled f_1(0)
- 9559662 to 9559668 labelled f_1(0)
- 9559662 to 9559674 labelled g_1(1)
- 9559662 to 9559670 labelled f_1(1)
- 9559662 to 9559672 labelled f_1(1)
- 9559663 to 9559663 labelled #_1(0)
- 9559665 to 9559663 labelled 0(0), 1(0)
- 9559664 to 9559665 labelled d_1(0)
- 9559667 to 9559663 labelled f_1(0)
- 9559667 to 9559670 labelled f_1(1)
- 9559667 to 9559672 labelled f_1(1)
- 9559666 to 9559667 labelled c_1(0)
- 9559669 to 9559663 labelled f_1(0)
- 9559669 to 9559670 labelled f_1(1)
- 9559669 to 9559672 labelled f_1(1)
- 9559668 to 9559669 labelled d_1(0)
- 9559671 to 9559663 labelled f_1(1)
- 9559671 to 9559670 labelled f_1(1)
- 9559671 to 9559672 labelled f_1(1)
- 9559670 to 9559671 labelled c_1(1)
- 9559673 to 9559663 labelled f_1(1)
- 9559673 to 9559670 labelled f_1(1)
- 9559673 to 9559672 labelled f_1(1)
- 9559672 to 9559673 labelled d_1(1)
- 9559674 to 9559675 labelled d_1(1)
- 9559675 to 9559663 labelled 0(1), 1(1)