(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(b(x))))) → a(b(a(b(b(a(b(b(c(a(b(c(a(x)))))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 29 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 29 to 30 labelled b_1(0)
- 30 to 31 labelled a_1(0)
- 31 to 32 labelled b_1(0)
- 32 to 33 labelled b_1(0)
- 33 to 34 labelled a_1(0)
- 34 to 35 labelled b_1(0)
- 35 to 36 labelled b_1(0)
- 36 to 37 labelled c_1(0)
- 36 to 65 labelled a_1(1)
- 37 to 38 labelled a_1(0)
- 38 to 39 labelled b_1(0)
- 39 to 40 labelled c_1(0)
- 39 to 53 labelled a_1(1)
- 40 to 4 labelled a_1(0)
- 53 to 54 labelled b_1(1)
- 54 to 55 labelled a_1(1)
- 55 to 56 labelled b_1(1)
- 56 to 57 labelled b_1(1)
- 57 to 58 labelled a_1(1)
- 58 to 59 labelled b_1(1)
- 59 to 60 labelled b_1(1)
- 60 to 61 labelled c_1(1)
- 60 to 101 labelled a_1(2)
- 61 to 62 labelled a_1(1)
- 62 to 63 labelled b_1(1)
- 63 to 64 labelled c_1(1)
- 63 to 53 labelled a_1(1)
- 64 to 4 labelled a_1(1)
- 65 to 66 labelled b_1(1)
- 66 to 67 labelled a_1(1)
- 67 to 68 labelled b_1(1)
- 68 to 69 labelled b_1(1)
- 69 to 70 labelled a_1(1)
- 70 to 71 labelled b_1(1)
- 71 to 72 labelled b_1(1)
- 72 to 73 labelled c_1(1)
- 73 to 74 labelled a_1(1)
- 74 to 75 labelled b_1(1)
- 75 to 76 labelled c_1(1)
- 76 to 54 labelled a_1(1)
- 101 to 102 labelled b_1(2)
- 102 to 103 labelled a_1(2)
- 103 to 104 labelled b_1(2)
- 104 to 105 labelled b_1(2)
- 105 to 106 labelled a_1(2)
- 106 to 107 labelled b_1(2)
- 107 to 108 labelled b_1(2)
- 108 to 109 labelled c_1(2)
- 109 to 110 labelled a_1(2)
- 110 to 111 labelled b_1(2)
- 111 to 112 labelled c_1(2)
- 112 to 54 labelled a_1(2)