(3) 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:
a(b(c(a(b(a(b(x))))))) → c(a(b(a(b(b(c(a(b(a(x))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 23, 24, 25, 26, 27, 28, 29, 30, 31, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 3 labelled c_1(0)
- 2 to 2 labelled #_1(0)
- 3 to 4 labelled a_1(0)
- 4 to 5 labelled b_1(0)
- 5 to 6 labelled a_1(0)
- 6 to 7 labelled b_1(0)
- 7 to 8 labelled b_1(0)
- 8 to 9 labelled c_1(0)
- 9 to 10 labelled a_1(0)
- 9 to 41 labelled c_1(1)
- 10 to 11 labelled b_1(0)
- 11 to 2 labelled a_1(0)
- 11 to 23 labelled c_1(1)
- 23 to 24 labelled a_1(1)
- 24 to 25 labelled b_1(1)
- 25 to 26 labelled a_1(1)
- 26 to 27 labelled b_1(1)
- 27 to 28 labelled b_1(1)
- 28 to 29 labelled c_1(1)
- 29 to 30 labelled a_1(1)
- 29 to 50 labelled c_1(2)
- 30 to 31 labelled b_1(1)
- 31 to 2 labelled a_1(1)
- 31 to 23 labelled c_1(1)
- 41 to 42 labelled a_1(1)
- 42 to 43 labelled b_1(1)
- 43 to 44 labelled a_1(1)
- 44 to 45 labelled b_1(1)
- 45 to 46 labelled b_1(1)
- 46 to 47 labelled c_1(1)
- 47 to 48 labelled a_1(1)
- 47 to 50 labelled c_1(2)
- 48 to 49 labelled b_1(1)
- 49 to 27 labelled a_1(1)
- 49 to 23 labelled c_1(1)
- 50 to 51 labelled a_1(2)
- 51 to 52 labelled b_1(2)
- 52 to 53 labelled a_1(2)
- 53 to 54 labelled b_1(2)
- 54 to 55 labelled b_1(2)
- 55 to 56 labelled c_1(2)
- 56 to 57 labelled a_1(2)
- 56 to 50 labelled c_1(2)
- 57 to 58 labelled b_1(2)
- 58 to 27 labelled a_1(2)
- 58 to 23 labelled c_1(1)