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:
c(b(a(X))) → a(a(b(b(c(c(X))))))
a(X) → e
b(X) → e
c(X) → e
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
c(b(a(X))) → a(a(b(b(c(c(X))))))
a(X) → e
b(X) → e
c(X) → e
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
c(b(a(X))) → a(a(b(b(c(c(X))))))
a(X) → e
b(X) → e
c(X) → e
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 7, 6, 5, 4, 3, 12, 11, 10, 9, 8
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 2 labelled e(0)
- 1 to 3 labelled a_1(0), e(1)
- 2 to 2 labelled #_1(0)
- 7 to 2 labelled c_1(0), e(1)
- 7 to 8 labelled a_1(1), e(2)
- 6 to 7 labelled c_1(0), e(1)
- 5 to 6 labelled b_1(0), e(1)
- 4 to 5 labelled b_1(0), e(1)
- 3 to 4 labelled a_1(0), e(1)
- 12 to 2 labelled c_1(1), e(2)
- 12 to 8 labelled a_1(1), e(2)
- 11 to 12 labelled c_1(1), e(2)
- 10 to 11 labelled b_1(1), e(2)
- 9 to 10 labelled b_1(1), e(2)
- 8 to 9 labelled a_1(1), e(2)