(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(a(b(a(b(x))))) → a(b(a(b(a(b(b(a(a(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
5, 6, 23, 24, 25, 26, 28, 30, 32, 34, 176, 177, 178, 179, 180, 181, 182, 184, 198, 199, 200, 201, 202, 203, 204, 205
Node 5 is start node and node 6 is final node.
Those nodes are connected through the following edges:
- 5 to 23 labelled a_1(0)
- 6 to 6 labelled #_1(0)
- 23 to 24 labelled b_1(0)
- 24 to 25 labelled a_1(0)
- 25 to 26 labelled b_1(0)
- 26 to 28 labelled a_1(0)
- 28 to 30 labelled b_1(0)
- 30 to 32 labelled b_1(0)
- 32 to 34 labelled a_1(0)
- 32 to 176 labelled a_1(1)
- 34 to 6 labelled a_1(0)
- 34 to 176 labelled a_1(1)
- 176 to 177 labelled b_1(1)
- 177 to 178 labelled a_1(1)
- 178 to 179 labelled b_1(1)
- 179 to 180 labelled a_1(1)
- 180 to 181 labelled b_1(1)
- 181 to 182 labelled b_1(1)
- 182 to 184 labelled a_1(1)
- 182 to 176 labelled a_1(1)
- 182 to 198 labelled a_1(2)
- 184 to 6 labelled a_1(1)
- 184 to 176 labelled a_1(1)
- 184 to 179 labelled a_1(1)
- 198 to 199 labelled b_1(2)
- 199 to 200 labelled a_1(2)
- 200 to 201 labelled b_1(2)
- 201 to 202 labelled a_1(2)
- 202 to 203 labelled b_1(2)
- 203 to 204 labelled b_1(2)
- 204 to 205 labelled a_1(2)
- 205 to 179 labelled a_1(2)