(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:
a(b(x)) → b(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:
3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 5 labelled b_1(0)
- 3 to 6 labelled a_1(0)
- 3 to 8 labelled a_1(1)
- 4 to 4 labelled #_1(0)
- 5 to 4 labelled a_1(0)
- 5 to 10 labelled b_1(1)
- 5 to 11 labelled a_1(2)
- 6 to 7 labelled c_1(0)
- 7 to 4 labelled b_1(0)
- 7 to 8 labelled a_1(1)
- 8 to 9 labelled c_1(1)
- 9 to 4 labelled b_1(1)
- 9 to 8 labelled a_1(1)
- 9 to 11 labelled b_1(1)
- 10 to 4 labelled a_1(1)
- 10 to 10 labelled b_1(1)
- 10 to 11 labelled a_1(2)
- 11 to 12 labelled c_1(2)
- 12 to 4 labelled b_1(2)
- 12 to 8 labelled a_1(1)
- 12 to 11 labelled b_1(2)