(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(l(x)) → l(a(x))
a(c(x)) → c(a(x))
c(a(r(x))) → r(a(x))
l(r(a(x))) → a(l(c(c(r(x)))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 5, 7, 8, 9, 10, 22, 23, 24, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 51, 56, 57, 58, 59, 60, 61
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 5 labelled l_1(0), c_1(0), r_1(0)
- 1 to 7 labelled a_1(0)
- 1 to 22 labelled l_1(1)
- 1 to 23 labelled r_1(1)
- 1 to 35 labelled a_1(1)
- 1 to 39 labelled l_1(2)
- 2 to 2 labelled #_1(0)
- 5 to 2 labelled a_1(0)
- 5 to 23 labelled l_1(1), c_1(1), r_1(1)
- 5 to 40 labelled a_1(2)
- 5 to 51 labelled l_1(3)
- 7 to 8 labelled l_1(0)
- 8 to 9 labelled c_1(0)
- 9 to 10 labelled c_1(0)
- 10 to 2 labelled r_1(0)
- 22 to 8 labelled a_1(1)
- 22 to 24 labelled c_1(1)
- 23 to 2 labelled a_1(1)
- 23 to 23 labelled l_1(1), c_1(1), r_1(1)
- 23 to 40 labelled a_1(2)
- 23 to 51 labelled l_1(3)
- 24 to 9 labelled a_1(1)
- 24 to 34 labelled c_1(1)
- 24 to 23 labelled r_1(1)
- 34 to 10 labelled a_1(1)
- 35 to 36 labelled l_1(1)
- 36 to 37 labelled c_1(1)
- 37 to 38 labelled c_1(1)
- 38 to 2 labelled r_1(1)
- 38 to 40 labelled r_1(1)
- 39 to 36 labelled a_1(2)
- 39 to 56 labelled c_1(2)
- 40 to 41 labelled l_1(2)
- 41 to 42 labelled c_1(2)
- 42 to 43 labelled c_1(2)
- 43 to 2 labelled r_1(2)
- 43 to 40 labelled r_1(2)
- 51 to 41 labelled a_1(3)
- 51 to 57 labelled c_1(3)
- 56 to 37 labelled a_1(2)
- 56 to 58 labelled c_1(2)
- 56 to 60 labelled r_1(2)
- 56 to 5 labelled r_1(2)
- 57 to 42 labelled a_1(3)
- 57 to 59 labelled c_1(3)
- 57 to 61 labelled r_1(3)
- 58 to 38 labelled a_1(2)
- 59 to 43 labelled a_1(3)
- 60 to 2 labelled a_1(2)
- 60 to 23 labelled l_1(1), c_1(1), r_1(1)
- 60 to 40 labelled a_1(2)
- 60 to 51 labelled l_1(3)
- 61 to 2 labelled a_1(3)
- 61 to 40 labelled a_1(3), a_1(2)
- 61 to 23 labelled l_1(1), c_1(1), r_1(1)
- 61 to 51 labelled l_1(3)