(3) 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(a(b(a(x)))) → a(b(a(b(c(x)))))
b(c(a(x))) → a(b(c(b(a(a(x))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 4, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58
Node 1 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 1 to 14 labelled a_1(0)
- 1 to 18 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 14 to 15 labelled b_1(0)
- 15 to 16 labelled a_1(0)
- 16 to 17 labelled b_1(0)
- 16 to 36 labelled a_1(1)
- 17 to 4 labelled c_1(0)
- 18 to 19 labelled b_1(0)
- 19 to 20 labelled c_1(0)
- 20 to 21 labelled b_1(0)
- 21 to 22 labelled a_1(0)
- 21 to 32 labelled a_1(1)
- 22 to 4 labelled a_1(0)
- 22 to 32 labelled a_1(1)
- 32 to 33 labelled b_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 35 labelled b_1(1)
- 34 to 36 labelled a_1(1)
- 34 to 45 labelled a_1(2)
- 35 to 4 labelled c_1(1)
- 35 to 34 labelled c_1(1)
- 36 to 37 labelled b_1(1)
- 37 to 38 labelled c_1(1)
- 38 to 39 labelled b_1(1)
- 39 to 40 labelled a_1(1)
- 39 to 32 labelled a_1(1)
- 39 to 50 labelled a_1(2)
- 40 to 4 labelled a_1(1)
- 40 to 32 labelled a_1(1)
- 45 to 46 labelled b_1(2)
- 46 to 47 labelled c_1(2)
- 47 to 48 labelled b_1(2)
- 48 to 49 labelled a_1(2)
- 49 to 36 labelled a_1(2)
- 49 to 45 labelled a_1(2)
- 50 to 51 labelled b_1(2)
- 51 to 52 labelled a_1(2)
- 52 to 53 labelled b_1(2)
- 52 to 45 labelled a_1(2)
- 52 to 54 labelled a_1(3)
- 53 to 34 labelled c_1(2)
- 54 to 55 labelled b_1(3)
- 55 to 56 labelled c_1(3)
- 56 to 57 labelled b_1(3)
- 57 to 58 labelled a_1(3)
- 58 to 45 labelled a_1(3)