(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(b(a(x)))) → a(b(a(a(c(a(b(c(a(b(x))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 6, 7, 9, 11, 13, 15, 17, 18, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 50, 51, 52, 53, 54, 55, 56, 57, 58
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 6 labelled a_1(0)
- 3 to 3 labelled #_1(0)
- 6 to 7 labelled b_1(0)
- 7 to 9 labelled a_1(0)
- 9 to 11 labelled a_1(0)
- 11 to 13 labelled c_1(0)
- 11 to 32 labelled a_1(1)
- 13 to 15 labelled a_1(0)
- 15 to 17 labelled b_1(0)
- 17 to 18 labelled c_1(0)
- 17 to 23 labelled a_1(1)
- 18 to 21 labelled a_1(0)
- 21 to 3 labelled b_1(0)
- 23 to 24 labelled b_1(1)
- 24 to 25 labelled a_1(1)
- 25 to 26 labelled a_1(1)
- 26 to 27 labelled c_1(1)
- 26 to 50 labelled a_1(2)
- 27 to 28 labelled a_1(1)
- 28 to 29 labelled b_1(1)
- 29 to 30 labelled c_1(1)
- 29 to 23 labelled a_1(1)
- 30 to 31 labelled a_1(1)
- 31 to 3 labelled b_1(1)
- 32 to 33 labelled b_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 35 labelled a_1(1)
- 35 to 36 labelled c_1(1)
- 36 to 37 labelled a_1(1)
- 37 to 38 labelled b_1(1)
- 38 to 39 labelled c_1(1)
- 39 to 40 labelled a_1(1)
- 40 to 23 labelled b_1(1)
- 50 to 51 labelled b_1(2)
- 51 to 52 labelled a_1(2)
- 52 to 53 labelled a_1(2)
- 53 to 54 labelled c_1(2)
- 54 to 55 labelled a_1(2)
- 55 to 56 labelled b_1(2)
- 56 to 57 labelled c_1(2)
- 57 to 58 labelled a_1(2)
- 58 to 23 labelled b_1(2)