(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(a(b(x))) → b(b(a(a(x))))
b(a(x)) → a(c(b(x)))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 22, 23, 24, 25, 26, 29, 30, 36, 37, 38, 39, 40, 41, 42, 43, 53, 54, 55, 56
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 3 labelled b_1(0)
- 1 to 6 labelled a_1(0)
- 1 to 36 labelled a_1(1)
- 2 to 2 labelled #_1(0)
- 3 to 4 labelled b_1(0)
- 3 to 22 labelled a_1(1)
- 4 to 5 labelled a_1(0)
- 4 to 24 labelled b_1(1)
- 4 to 40 labelled a_1(2)
- 5 to 2 labelled a_1(0)
- 5 to 24 labelled b_1(1)
- 5 to 40 labelled a_1(2)
- 6 to 7 labelled c_1(0)
- 7 to 2 labelled b_1(0)
- 7 to 29 labelled a_1(1)
- 22 to 23 labelled c_1(1)
- 23 to 5 labelled b_1(1)
- 23 to 29 labelled a_1(1)
- 23 to 40 labelled b_1(1)
- 23 to 53 labelled a_1(2)
- 24 to 25 labelled b_1(1)
- 24 to 38 labelled a_1(2)
- 24 to 53 labelled a_1(2)
- 25 to 26 labelled a_1(1)
- 25 to 24 labelled b_1(1)
- 25 to 40 labelled a_1(2)
- 26 to 2 labelled a_1(1)
- 26 to 24 labelled b_1(1)
- 26 to 40 labelled a_1(2)
- 29 to 30 labelled c_1(1)
- 30 to 2 labelled b_1(1)
- 30 to 29 labelled a_1(1)
- 36 to 37 labelled c_1(1)
- 37 to 22 labelled b_1(1)
- 38 to 39 labelled c_1(2)
- 39 to 26 labelled b_1(2)
- 39 to 42 labelled a_1(2)
- 39 to 55 labelled a_1(3)
- 40 to 41 labelled c_1(2)
- 41 to 38 labelled b_1(2)
- 41 to 53 labelled b_1(2)
- 42 to 43 labelled c_1(2)
- 43 to 2 labelled b_1(2)
- 43 to 29 labelled a_1(1)
- 53 to 54 labelled c_1(2)
- 54 to 40 labelled b_1(2)
- 55 to 56 labelled c_1(3)
- 56 to 40 labelled b_1(3)