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(b(b(a(b(x1)))))) → a(b(b(a(a(b(b(a(x1))))))))
Q is empty.
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(b(b(a(b(x1)))))) → a(b(b(a(a(b(b(a(x1))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(b(b(a(b(x1)))))) → a(b(b(a(a(b(b(a(x1))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(b(b(a(a(x)))))) → a(b(b(a(a(b(b(a(x))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(a(a(x)))))) → a(b(b(a(a(b(b(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:
b(a(b(b(a(a(x)))))) → a(b(b(a(a(b(b(a(x))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
141, 142, 148, 149, 147, 144, 145, 143, 146, 155, 156, 154, 151, 152, 150, 153, 162, 163, 161, 158, 159, 157, 160, 169, 170, 168, 165, 166, 164, 167
Node 141 is start node and node 142 is final node.
Those nodes are connect through the following edges:
- 141 to 143 labelled a_1(0)
- 142 to 142 labelled #_1(0)
- 148 to 149 labelled b_1(0)
- 148 to 150 labelled a_1(1)
- 149 to 142 labelled a_1(0)
- 147 to 148 labelled b_1(0)
- 147 to 157 labelled a_1(1)
- 144 to 145 labelled b_1(0)
- 145 to 146 labelled a_1(0)
- 143 to 144 labelled b_1(0)
- 146 to 147 labelled a_1(0)
- 155 to 156 labelled b_1(1)
- 155 to 150 labelled a_1(1)
- 156 to 142 labelled a_1(1)
- 154 to 155 labelled b_1(1)
- 154 to 164 labelled a_1(2)
- 151 to 152 labelled b_1(1)
- 152 to 153 labelled a_1(1)
- 150 to 151 labelled b_1(1)
- 153 to 154 labelled a_1(1)
- 162 to 163 labelled b_1(1)
- 162 to 150 labelled a_1(1)
- 163 to 154 labelled a_1(1)
- 161 to 162 labelled b_1(1)
- 161 to 164 labelled a_1(2)
- 158 to 159 labelled b_1(1)
- 159 to 160 labelled a_1(1)
- 157 to 158 labelled b_1(1)
- 160 to 161 labelled a_1(1)
- 169 to 170 labelled b_1(2)
- 169 to 150 labelled a_1(1)
- 170 to 154 labelled a_1(2)
- 168 to 169 labelled b_1(2)
- 168 to 164 labelled a_1(2)
- 165 to 166 labelled b_1(2)
- 166 to 167 labelled a_1(2)
- 164 to 165 labelled b_1(2)
- 167 to 168 labelled a_1(2)