Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(x1)) → c(b(x1))
b(b(x1)) → a(c(x1))
c(c(x1)) → b(a(x1))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(x1)) → c(b(x1))
b(b(x1)) → a(c(x1))
c(c(x1)) → b(a(x1))
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(a(x1)) → c(b(x1))
b(b(x1)) → a(c(x1))
c(c(x1)) → b(a(x1))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled c_1(0)
- 1 to 4 labelled b_1(0)
- 1 to 5 labelled a_1(0)
- 2 to 2 labelled #_1(0)
- 3 to 2 labelled b_1(0)
- 3 to 7 labelled a_1(1)
- 4 to 2 labelled a_1(0)
- 4 to 8 labelled c_1(1)
- 5 to 2 labelled c_1(0)
- 5 to 6 labelled b_1(1)
- 6 to 2 labelled a_1(1)
- 6 to 8 labelled c_1(1)
- 7 to 2 labelled c_1(1)
- 7 to 6 labelled b_1(1)
- 8 to 2 labelled b_1(1)
- 8 to 7 labelled a_1(1)