(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:
c(a(a(b(c(a(x)))))) → a(a(b(c(c(a(a(b(c(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 13, 14, 15, 16, 17, 18, 19, 20, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 13 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 13 to 14 labelled a_1(0)
- 14 to 15 labelled b_1(0)
- 15 to 16 labelled c_1(0)
- 15 to 53 labelled a_1(1)
- 16 to 17 labelled c_1(0)
- 16 to 45 labelled a_1(1)
- 17 to 18 labelled a_1(0)
- 18 to 19 labelled a_1(0)
- 19 to 20 labelled b_1(0)
- 20 to 4 labelled c_1(0)
- 20 to 45 labelled a_1(1)
- 45 to 46 labelled a_1(1)
- 46 to 47 labelled b_1(1)
- 47 to 48 labelled c_1(1)
- 47 to 61 labelled a_1(2)
- 48 to 49 labelled c_1(1)
- 48 to 45 labelled a_1(1)
- 49 to 50 labelled a_1(1)
- 50 to 51 labelled a_1(1)
- 51 to 52 labelled b_1(1)
- 52 to 4 labelled c_1(1)
- 52 to 45 labelled a_1(1)
- 53 to 54 labelled a_1(1)
- 54 to 55 labelled b_1(1)
- 55 to 56 labelled c_1(1)
- 56 to 57 labelled c_1(1)
- 56 to 69 labelled a_1(2)
- 57 to 58 labelled a_1(1)
- 58 to 59 labelled a_1(1)
- 59 to 60 labelled b_1(1)
- 60 to 45 labelled c_1(1)
- 61 to 62 labelled a_1(2)
- 62 to 63 labelled b_1(2)
- 63 to 64 labelled c_1(2)
- 64 to 65 labelled c_1(2)
- 64 to 69 labelled a_1(2)
- 65 to 66 labelled a_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 68 labelled b_1(2)
- 68 to 45 labelled c_1(2)
- 69 to 70 labelled a_1(2)
- 70 to 71 labelled b_1(2)
- 71 to 72 labelled c_1(2)
- 72 to 73 labelled c_1(2)
- 73 to 74 labelled a_1(2)
- 74 to 75 labelled a_1(2)
- 75 to 76 labelled b_1(2)
- 76 to 46 labelled c_1(2)