(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
b(c(a(x))) → a(b(a(b(c(x)))))
b(x) → c(c(x))
c(d(x)) → a(b(c(a(x))))
a(a(x)) → a(c(b(a(x))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 42 labelled a_1(0)
- 1 to 45 labelled c_1(0)
- 1 to 46 labelled a_1(0)
- 1 to 49 labelled a_1(0)
- 1 to 76 labelled a_1(1)
- 2 to 2 labelled #_1(0)
- 42 to 43 labelled b_1(0)
- 42 to 58 labelled c_1(1)
- 43 to 44 labelled a_1(0)
- 43 to 76 labelled a_1(1)
- 44 to 45 labelled b_1(0)
- 44 to 59 labelled c_1(1)
- 44 to 68 labelled a_1(1)
- 45 to 2 labelled c_1(0)
- 45 to 62 labelled a_1(1)
- 45 to 86 labelled a_1(2)
- 46 to 47 labelled b_1(0)
- 46 to 60 labelled c_1(1)
- 46 to 68 labelled a_1(1)
- 47 to 48 labelled c_1(0)
- 48 to 2 labelled a_1(0)
- 48 to 65 labelled a_1(1)
- 49 to 50 labelled c_1(0)
- 50 to 51 labelled b_1(0)
- 50 to 61 labelled c_1(1)
- 51 to 2 labelled a_1(0)
- 51 to 65 labelled a_1(1)
- 58 to 43 labelled c_1(1)
- 59 to 45 labelled c_1(1)
- 60 to 47 labelled c_1(1)
- 61 to 51 labelled c_1(1)
- 62 to 63 labelled b_1(1)
- 62 to 72 labelled c_1(2)
- 62 to 79 labelled a_1(2)
- 63 to 64 labelled c_1(1)
- 64 to 2 labelled a_1(1)
- 64 to 65 labelled a_1(1)
- 65 to 66 labelled c_1(1)
- 66 to 67 labelled b_1(1)
- 66 to 73 labelled c_1(2)
- 67 to 2 labelled a_1(1)
- 67 to 65 labelled a_1(1)
- 68 to 69 labelled b_1(1)
- 68 to 74 labelled c_1(2)
- 69 to 70 labelled a_1(1)
- 69 to 89 labelled a_1(2)
- 70 to 71 labelled b_1(1)
- 70 to 75 labelled c_1(2)
- 70 to 68 labelled a_1(1)
- 71 to 2 labelled c_1(1)
- 71 to 62 labelled a_1(1)
- 71 to 65 labelled c_1(1)
- 71 to 86 labelled a_1(2)
- 72 to 63 labelled c_1(2)
- 73 to 67 labelled c_1(2)
- 74 to 69 labelled c_1(2)
- 75 to 71 labelled c_1(2)
- 76 to 77 labelled c_1(1)
- 77 to 78 labelled b_1(1)
- 77 to 83 labelled c_1(2)
- 78 to 68 labelled a_1(1)
- 79 to 80 labelled b_1(2)
- 79 to 84 labelled c_1(3)
- 80 to 81 labelled a_1(2)
- 80 to 89 labelled a_1(2)
- 81 to 82 labelled b_1(2)
- 81 to 85 labelled c_1(3)
- 81 to 68 labelled a_1(1)
- 82 to 2 labelled c_1(2)
- 82 to 62 labelled a_1(1)
- 82 to 65 labelled c_1(2)
- 82 to 86 labelled a_1(2)
- 83 to 78 labelled c_1(2)
- 84 to 80 labelled c_1(3)
- 85 to 82 labelled c_1(3)
- 86 to 87 labelled c_1(2)
- 87 to 88 labelled b_1(2)
- 87 to 92 labelled c_1(3)
- 88 to 79 labelled a_1(2)
- 89 to 90 labelled c_1(2)
- 90 to 91 labelled b_1(2)
- 90 to 93 labelled c_1(3)
- 91 to 68 labelled a_1(2)
- 92 to 88 labelled c_1(3)
- 93 to 91 labelled c_1(3)