(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:
b(a(a(b(b(a(x)))))) → a(a(b(b(a(a(a(b(b(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 85 labelled a_1(0)
- 3 to 3 labelled #_1(0)
- 85 to 86 labelled a_1(0)
- 86 to 87 labelled b_1(0)
- 87 to 88 labelled b_1(0)
- 88 to 89 labelled a_1(0)
- 89 to 90 labelled a_1(0)
- 90 to 91 labelled a_1(0)
- 91 to 92 labelled b_1(0)
- 91 to 101 labelled a_1(1)
- 92 to 3 labelled b_1(0)
- 92 to 93 labelled a_1(1)
- 93 to 94 labelled a_1(1)
- 94 to 95 labelled b_1(1)
- 95 to 96 labelled b_1(1)
- 96 to 97 labelled a_1(1)
- 97 to 98 labelled a_1(1)
- 98 to 99 labelled a_1(1)
- 99 to 100 labelled b_1(1)
- 99 to 109 labelled a_1(2)
- 100 to 3 labelled b_1(1)
- 100 to 93 labelled a_1(1)
- 101 to 102 labelled a_1(1)
- 102 to 103 labelled b_1(1)
- 103 to 104 labelled b_1(1)
- 104 to 105 labelled a_1(1)
- 105 to 106 labelled a_1(1)
- 106 to 107 labelled a_1(1)
- 107 to 108 labelled b_1(1)
- 107 to 109 labelled a_1(2)
- 108 to 97 labelled b_1(1)
- 108 to 93 labelled a_1(1)
- 109 to 110 labelled a_1(2)
- 110 to 111 labelled b_1(2)
- 111 to 112 labelled b_1(2)
- 112 to 113 labelled a_1(2)
- 113 to 114 labelled a_1(2)
- 114 to 115 labelled a_1(2)
- 115 to 116 labelled b_1(2)
- 115 to 109 labelled a_1(2)
- 116 to 97 labelled b_1(2)
- 116 to 93 labelled a_1(1)