(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:
a(b(x)) → b(a(x))
b(a(x)) → a(a(c(b(x))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 19 labelled b_1(0)
- 3 to 20 labelled a_1(0)
- 3 to 23 labelled a_1(1)
- 4 to 4 labelled #_1(0)
- 19 to 4 labelled a_1(0)
- 19 to 26 labelled b_1(1)
- 19 to 27 labelled a_1(2)
- 20 to 21 labelled a_1(0)
- 21 to 22 labelled c_1(0)
- 22 to 4 labelled b_1(0)
- 22 to 23 labelled a_1(1)
- 23 to 24 labelled a_1(1)
- 24 to 25 labelled c_1(1)
- 25 to 4 labelled b_1(1)
- 25 to 23 labelled a_1(1)
- 25 to 27 labelled b_1(1)
- 25 to 30 labelled a_1(2)
- 26 to 4 labelled a_1(1)
- 26 to 26 labelled b_1(1)
- 26 to 27 labelled a_1(2)
- 27 to 28 labelled a_1(2)
- 28 to 29 labelled c_1(2)
- 29 to 4 labelled b_1(2)
- 29 to 23 labelled a_1(1)
- 29 to 27 labelled b_1(2)
- 29 to 33 labelled a_1(3)
- 30 to 31 labelled a_1(2)
- 31 to 32 labelled c_1(2)
- 32 to 28 labelled b_1(2)
- 33 to 34 labelled a_1(3)
- 34 to 35 labelled c_1(3)
- 35 to 28 labelled b_1(3)