(3) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 6. This implies Q-termination of R.
The following rules were used to construct the certificate:
c(c(x)) → b(a(x))
b(x) → a(a(x))
b(b(b(x))) → b(c(a(x)))
a(c(a(x))) → c(c(a(x)))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 73, 74, 75, 76, 77, 78, 79, 80
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 5 labelled b_1(0), a_1(0)
- 1 to 6 labelled b_1(0), c_1(0)
- 1 to 8 labelled a_1(1)
- 1 to 9 labelled b_1(1)
- 1 to 12 labelled a_1(2)
- 1 to 40 labelled c_1(1)
- 1 to 42 labelled c_1(2)
- 1 to 48 labelled b_1(1)
- 1 to 50 labelled b_1(2)
- 1 to 51 labelled b_1(3)
- 1 to 52 labelled a_1(3)
- 1 to 53 labelled a_1(4)
- 2 to 2 labelled #_1(0)
- 5 to 2 labelled a_1(0)
- 5 to 10 labelled c_1(1)
- 5 to 13 labelled b_1(2)
- 5 to 32 labelled a_1(3)
- 6 to 7 labelled c_1(0)
- 6 to 14 labelled b_1(1)
- 6 to 33 labelled a_1(2)
- 6 to 54 labelled b_1(2)
- 6 to 62 labelled a_1(3)
- 7 to 2 labelled a_1(0)
- 7 to 10 labelled c_1(1)
- 7 to 13 labelled b_1(2)
- 7 to 32 labelled a_1(3)
- 8 to 5 labelled a_1(1)
- 8 to 6 labelled a_1(1)
- 8 to 10 labelled c_1(1)
- 8 to 13 labelled b_1(2)
- 8 to 32 labelled a_1(3)
- 8 to 42 labelled c_1(2)
- 8 to 51 labelled b_1(3)
- 8 to 53 labelled a_1(4)
- 9 to 7 labelled a_1(1)
- 9 to 42 labelled c_1(2)
- 9 to 51 labelled b_1(3)
- 9 to 53 labelled a_1(4)
- 10 to 11 labelled c_1(1)
- 10 to 34 labelled b_1(2)
- 10 to 37 labelled a_1(3)
- 10 to 56 labelled b_1(3)
- 10 to 63 labelled a_1(4)
- 11 to 2 labelled a_1(1)
- 11 to 10 labelled c_1(1)
- 11 to 13 labelled b_1(2)
- 11 to 32 labelled a_1(3), a_1(1)
- 12 to 9 labelled a_1(2)
- 12 to 48 labelled a_1(2)
- 12 to 58 labelled c_1(2)
- 12 to 64 labelled b_1(3)
- 12 to 54 labelled c_1(2)
- 12 to 73 labelled a_1(4)
- 13 to 11 labelled a_1(2)
- 13 to 42 labelled c_1(2)
- 13 to 51 labelled b_1(3)
- 13 to 53 labelled a_1(4)
- 14 to 10 labelled a_1(1)
- 14 to 35 labelled c_1(2)
- 14 to 38 labelled b_1(3)
- 14 to 39 labelled a_1(4)
- 32 to 13 labelled a_1(3)
- 33 to 14 labelled a_1(2)
- 33 to 60 labelled c_1(3)
- 33 to 65 labelled b_1(4)
- 33 to 74 labelled a_1(5)
- 34 to 10 labelled a_1(2)
- 34 to 35 labelled c_1(2)
- 34 to 38 labelled b_1(3)
- 34 to 39 labelled a_1(4)
- 35 to 36 labelled c_1(2)
- 35 to 34 labelled b_1(2)
- 35 to 37 labelled a_1(3)
- 35 to 56 labelled b_1(3)
- 35 to 63 labelled a_1(4)
- 36 to 2 labelled a_1(2)
- 36 to 10 labelled c_1(1)
- 36 to 13 labelled b_1(2)
- 36 to 32 labelled a_1(2), a_1(3)
- 37 to 34 labelled a_1(3)
- 37 to 60 labelled c_1(3)
- 37 to 65 labelled b_1(4)
- 37 to 74 labelled a_1(5)
- 38 to 36 labelled a_1(3)
- 38 to 42 labelled c_1(2)
- 38 to 51 labelled b_1(3)
- 38 to 53 labelled a_1(4)
- 39 to 38 labelled a_1(4)
- 40 to 41 labelled c_1(1)
- 41 to 37 labelled a_1(1)
- 41 to 63 labelled a_1(1)
- 42 to 43 labelled c_1(2)
- 43 to 37 labelled a_1(2)
- 43 to 63 labelled a_1(2)
- 48 to 49 labelled c_1(1)
- 49 to 38 labelled a_1(1)
- 49 to 51 labelled a_1(1)
- 50 to 41 labelled a_1(2)
- 51 to 43 labelled a_1(3)
- 52 to 50 labelled a_1(3)
- 53 to 51 labelled a_1(4)
- 54 to 55 labelled c_1(2)
- 55 to 51 labelled a_1(2)
- 56 to 57 labelled c_1(3)
- 57 to 51 labelled a_1(3)
- 58 to 59 labelled c_1(2)
- 59 to 38 labelled a_1(2)
- 60 to 61 labelled c_1(3)
- 61 to 37 labelled a_1(3)
- 61 to 63 labelled a_1(3)
- 62 to 54 labelled a_1(3)
- 62 to 56 labelled c_1(3)
- 62 to 77 labelled b_1(4)
- 62 to 79 labelled a_1(5)
- 63 to 56 labelled a_1(4)
- 63 to 75 labelled c_1(4)
- 63 to 78 labelled b_1(5)
- 63 to 80 labelled a_1(6)
- 64 to 59 labelled a_1(3)
- 64 to 55 labelled a_1(3)
- 65 to 61 labelled a_1(4)
- 73 to 64 labelled a_1(4)
- 74 to 65 labelled a_1(5)
- 75 to 76 labelled c_1(4)
- 76 to 51 labelled a_1(4)
- 77 to 57 labelled a_1(4)
- 78 to 76 labelled a_1(5)
- 79 to 77 labelled a_1(5)
- 80 to 78 labelled a_1(6)