(3) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(a(c(b(c(b(x)))))) → c(b(c(b(c(b(a(a(a(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 3, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 63, 64, 65, 66, 67, 68, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 95, 96, 97, 98, 99, 100, 109, 110, 111, 112, 113, 114, 115, 116
Node 2 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 2 to 13 labelled c_1(0)
- 3 to 3 labelled #_1(0)
- 13 to 14 labelled b_1(0)
- 14 to 15 labelled c_1(0)
- 15 to 16 labelled b_1(0)
- 16 to 17 labelled c_1(0)
- 17 to 18 labelled b_1(0)
- 18 to 19 labelled a_1(0)
- 18 to 29 labelled c_1(1)
- 19 to 20 labelled a_1(0)
- 19 to 21 labelled c_1(1)
- 20 to 3 labelled a_1(0)
- 20 to 21 labelled c_1(1)
- 21 to 22 labelled b_1(1)
- 22 to 23 labelled c_1(1)
- 23 to 24 labelled b_1(1)
- 24 to 25 labelled c_1(1)
- 25 to 26 labelled b_1(1)
- 26 to 27 labelled a_1(1)
- 26 to 45 labelled c_1(2)
- 27 to 28 labelled a_1(1)
- 27 to 21 labelled c_1(1)
- 28 to 3 labelled a_1(1)
- 28 to 21 labelled c_1(1)
- 29 to 30 labelled b_1(1)
- 30 to 31 labelled c_1(1)
- 31 to 32 labelled b_1(1)
- 32 to 33 labelled c_1(1)
- 33 to 34 labelled b_1(1)
- 34 to 35 labelled a_1(1)
- 35 to 36 labelled a_1(1)
- 35 to 59 labelled c_1(2)
- 36 to 24 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 c_1(2)
- 49 to 50 labelled b_1(2)
- 50 to 51 labelled a_1(2)
- 51 to 52 labelled a_1(2)
- 51 to 59 labelled c_1(2)
- 52 to 24 labelled a_1(2)
- 59 to 61 labelled b_1(2)
- 61 to 63 labelled c_1(2)
- 63 to 64 labelled b_1(2)
- 64 to 65 labelled c_1(2)
- 65 to 66 labelled b_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 68 labelled a_1(2)
- 67 to 77 labelled c_1(3)
- 68 to 46 labelled a_1(2)
- 77 to 78 labelled b_1(3)
- 78 to 79 labelled c_1(3)
- 79 to 80 labelled b_1(3)
- 80 to 81 labelled c_1(3)
- 81 to 82 labelled b_1(3)
- 82 to 83 labelled a_1(3)
- 82 to 109 labelled c_1(4)
- 83 to 84 labelled a_1(3)
- 84 to 50 labelled a_1(3)
- 84 to 93 labelled c_1(3)
- 93 to 94 labelled b_1(3)
- 94 to 95 labelled c_1(3)
- 95 to 96 labelled b_1(3)
- 96 to 97 labelled c_1(3)
- 97 to 98 labelled b_1(3)
- 98 to 99 labelled a_1(3)
- 99 to 100 labelled a_1(3)
- 100 to 64 labelled a_1(3)
- 109 to 110 labelled b_1(4)
- 110 to 111 labelled c_1(4)
- 111 to 112 labelled b_1(4)
- 112 to 113 labelled c_1(4)
- 113 to 114 labelled b_1(4)
- 114 to 115 labelled a_1(4)
- 115 to 116 labelled a_1(4)
- 116 to 96 labelled a_1(4)