(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(c(b(b(x))))) → a(c(b(b(b(a(c(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 11 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 11 to 12 labelled c_1(0)
- 12 to 13 labelled b_1(0)
- 12 to 35 labelled a_1(1)
- 13 to 14 labelled b_1(0)
- 13 to 29 labelled a_1(1)
- 14 to 15 labelled b_1(0)
- 14 to 17 labelled a_1(1)
- 15 to 16 labelled a_1(0)
- 16 to 4 labelled c_1(0)
- 17 to 20 labelled c_1(1)
- 20 to 22 labelled b_1(1)
- 20 to 47 labelled a_1(2)
- 22 to 24 labelled b_1(1)
- 22 to 41 labelled a_1(2)
- 24 to 26 labelled b_1(1)
- 24 to 17 labelled a_1(1)
- 26 to 28 labelled a_1(1)
- 28 to 4 labelled c_1(1)
- 29 to 30 labelled c_1(1)
- 30 to 31 labelled b_1(1)
- 31 to 32 labelled b_1(1)
- 32 to 33 labelled b_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 24 labelled c_1(1)
- 35 to 36 labelled c_1(1)
- 36 to 37 labelled b_1(1)
- 37 to 38 labelled b_1(1)
- 38 to 39 labelled b_1(1)
- 39 to 40 labelled a_1(1)
- 40 to 32 labelled c_1(1)
- 41 to 42 labelled c_1(2)
- 42 to 43 labelled b_1(2)
- 43 to 44 labelled b_1(2)
- 44 to 45 labelled b_1(2)
- 45 to 46 labelled a_1(2)
- 46 to 24 labelled c_1(2)
- 47 to 48 labelled c_1(2)
- 48 to 49 labelled b_1(2)
- 49 to 50 labelled b_1(2)
- 50 to 51 labelled b_1(2)
- 51 to 52 labelled a_1(2)
- 52 to 44 labelled c_1(2)