(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:
1210693, 1210694, 1210695, 1210696, 1210697, 1210698, 1210699, 1210700
Node 1210693 is start node and node 1210694 is final node.
Those nodes are connect through the following edges:
- 1210693 to 1210694 labelled a_1(0), b_1(0), a_1(1)
- 1210693 to 1210695 labelled f_1(0)
- 1210694 to 1210694 labelled #_1(0)
- 1210695 to 1210696 labelled a_1(0)
- 1210696 to 1210697 labelled b_1(0), a_1(1)
- 1210697 to 1210694 labelled f_1(0), b_1(1), a_1(2)
- 1210697 to 1210698 labelled f_1(1)
- 1210698 to 1210699 labelled a_1(1)
- 1210699 to 1210700 labelled b_1(1), a_1(2)
- 1210700 to 1210694 labelled f_1(1), b_1(1), a_1(2)
- 1210700 to 1210698 labelled f_1(1)