(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:
f(f(X)) → f(a(b(f(X))))
f(a(g(X))) → b(X)
b(X) → a(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 4, 8, 9, 10, 11, 12, 13
Node 1 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 1 to 8 labelled f_1(0)
- 1 to 4 labelled b_1(0), a_1(0), a_1(1)
- 4 to 4 labelled #_1(0)
- 8 to 9 labelled a_1(0)
- 9 to 10 labelled b_1(0), a_1(1)
- 10 to 4 labelled f_1(0), b_1(1), a_1(2)
- 10 to 11 labelled f_1(1)
- 11 to 12 labelled a_1(1)
- 12 to 13 labelled b_1(1), a_1(2)
- 13 to 4 labelled f_1(1), b_1(1), a_1(2)
- 13 to 11 labelled f_1(1)