(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:
9629135, 9629136, 9629137, 9629138, 9629139, 9629140, 9629142, 9629141
Node 9629135 is start node and node 9629136 is final node.
Those nodes are connect through the following edges:
- 9629135 to 9629136 labelled a_1(0), b_1(0), a_1(1)
- 9629135 to 9629137 labelled f_1(0)
- 9629136 to 9629136 labelled #_1(0)
- 9629137 to 9629138 labelled a_1(0)
- 9629138 to 9629139 labelled b_1(0), a_1(1)
- 9629139 to 9629136 labelled f_1(0), b_1(1), a_1(2)
- 9629139 to 9629140 labelled f_1(1)
- 9629140 to 9629141 labelled a_1(1)
- 9629142 to 9629136 labelled f_1(1), b_1(1), a_1(2)
- 9629142 to 9629140 labelled f_1(1)
- 9629141 to 9629142 labelled b_1(1), a_1(2)