(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:
c(b(a(X))) → a(a(b(b(c(c(X))))))
a(X) → e
b(X) → e
c(X) → e
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
9629383, 9629384, 9629386, 9629387, 9629389, 9629388, 9629385, 9629394, 9629390, 9629392, 9629393, 9629391
Node 9629383 is start node and node 9629384 is final node.
Those nodes are connect through the following edges:
- 9629383 to 9629384 labelled e(0)
- 9629383 to 9629385 labelled a_1(0), e(1)
- 9629384 to 9629384 labelled #_1(0)
- 9629386 to 9629387 labelled b_1(0), e(1)
- 9629387 to 9629388 labelled b_1(0), e(1)
- 9629389 to 9629384 labelled c_1(0), e(1)
- 9629389 to 9629390 labelled a_1(1), e(2)
- 9629388 to 9629389 labelled c_1(0), e(1)
- 9629385 to 9629386 labelled a_1(0), e(1)
- 9629394 to 9629384 labelled c_1(1), e(2)
- 9629394 to 9629390 labelled a_1(1), e(2)
- 9629390 to 9629391 labelled a_1(1), e(2)
- 9629392 to 9629393 labelled b_1(1), e(2)
- 9629393 to 9629394 labelled c_1(1), e(2)
- 9629391 to 9629392 labelled b_1(1), e(2)