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:
b(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
Q is empty.
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
The set Q is empty.
We have obtained the following QTRS:
a(b(a(a(b(x))))) → b(a(a(b(b(a(a(x)))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(b(x))))) → b(a(a(b(b(a(a(x)))))))
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:
a(b(a(a(b(x))))) → b(a(a(b(b(a(a(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
128, 129, 133, 134, 132, 130, 135, 131, 139, 140, 138, 136, 141, 137, 145, 146, 144, 142, 147, 143, 151, 152, 150, 148, 153, 149
Node 128 is start node and node 129 is final node.
Those nodes are connect through the following edges:
- 128 to 130 labelled b_1(0)
- 129 to 129 labelled #_1(0)
- 133 to 134 labelled b_1(0)
- 134 to 135 labelled a_1(0)
- 134 to 142 labelled b_1(1)
- 132 to 133 labelled b_1(0)
- 130 to 131 labelled a_1(0)
- 135 to 129 labelled a_1(0)
- 135 to 136 labelled b_1(1)
- 131 to 132 labelled a_1(0)
- 139 to 140 labelled b_1(1)
- 140 to 141 labelled a_1(1)
- 140 to 148 labelled b_1(2)
- 138 to 139 labelled b_1(1)
- 136 to 137 labelled a_1(1)
- 141 to 129 labelled a_1(1)
- 141 to 136 labelled b_1(1)
- 137 to 138 labelled a_1(1)
- 145 to 146 labelled b_1(1)
- 146 to 147 labelled a_1(1)
- 146 to 148 labelled b_1(2)
- 144 to 145 labelled b_1(1)
- 142 to 143 labelled a_1(1)
- 147 to 139 labelled a_1(1)
- 147 to 136 labelled b_1(1)
- 143 to 144 labelled a_1(1)
- 151 to 152 labelled b_1(2)
- 152 to 153 labelled a_1(2)
- 152 to 148 labelled b_1(2)
- 150 to 151 labelled b_1(2)
- 148 to 149 labelled a_1(2)
- 153 to 139 labelled a_1(2)
- 153 to 136 labelled b_1(1)
- 149 to 150 labelled a_1(2)