(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:
a(b(x)) → d(x)
b(a(x)) → a(b(x))
d(c(x)) → f(a(b(b(c(x)))))
d(f(x)) → f(a(b(x)))
a(f(x)) → a(x)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 16, 17, 18, 19, 20, 21, 22, 23, 24
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 4 labelled d_1(0), a_1(0), d_1(1), a_1(1)
- 2 to 16 labelled a_1(0)
- 2 to 17 labelled f_1(0)
- 2 to 2 labelled f_1(0)
- 2 to 21 labelled f_1(1), a_1(1), a_1(2)
- 4 to 4 labelled #_1(0)
- 16 to 4 labelled b_1(0), d_1(2)
- 16 to 22 labelled a_1(1)
- 16 to 23 labelled d_1(2)
- 16 to 21 labelled f_1(1), a_1(2)
- 17 to 18 labelled a_1(0)
- 17 to 19 labelled d_1(1)
- 18 to 19 labelled b_1(0)
- 19 to 20 labelled b_1(0)
- 20 to 4 labelled c_1(0)
- 21 to 22 labelled a_1(1)
- 21 to 23 labelled d_1(2)
- 21 to 4 labelled d_1(2)
- 21 to 21 labelled f_1(1), a_1(2)
- 22 to 23 labelled b_1(1), d_1(2)
- 22 to 4 labelled b_1(1), d_1(2)
- 22 to 22 labelled a_1(1)
- 22 to 21 labelled f_1(1), a_1(2)
- 23 to 24 labelled b_1(1)
- 24 to 4 labelled c_1(1)