(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(l(x)) → l(a(x))
r(a(a(x))) → a(a(r(x)))
b(l(x)) → b(a(r(x)))
r(b(x)) → l(b(x))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 3 labelled l_1(0)
- 1 to 4 labelled a_1(0), b_1(0)
- 1 to 13 labelled l_1(1)
- 1 to 14 labelled b_1(1)
- 2 to 2 labelled #_1(0)
- 3 to 2 labelled a_1(0), b_1(0)
- 3 to 8 labelled l_1(1)
- 3 to 9 labelled b_1(1)
- 3 to 17 labelled b_1(2)
- 4 to 5 labelled a_1(0)
- 4 to 12 labelled l_1(1)
- 5 to 2 labelled r_1(0)
- 5 to 9 labelled a_1(1)
- 5 to 11 labelled l_1(1)
- 5 to 19 labelled l_1(2)
- 8 to 2 labelled a_1(1)
- 8 to 8 labelled l_1(1)
- 9 to 10 labelled a_1(1)
- 9 to 16 labelled l_1(2)
- 10 to 2 labelled r_1(1)
- 10 to 9 labelled a_1(1)
- 10 to 11 labelled l_1(1)
- 10 to 19 labelled l_1(2)
- 11 to 2 labelled b_1(1)
- 11 to 9 labelled b_1(1)
- 11 to 17 labelled b_1(2)
- 12 to 11 labelled a_1(1)
- 12 to 19 labelled a_1(1)
- 13 to 12 labelled a_1(1)
- 14 to 15 labelled a_1(1)
- 15 to 12 labelled r_1(1)
- 15 to 17 labelled a_1(2)
- 16 to 11 labelled a_1(2)
- 16 to 19 labelled a_1(2)
- 17 to 18 labelled a_1(2)
- 18 to 16 labelled r_1(2)
- 18 to 20 labelled a_1(3)
- 19 to 16 labelled a_1(2)
- 20 to 21 labelled a_1(3)
- 21 to 16 labelled r_1(3)
- 21 to 20 labelled a_1(3)