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(b(a(b(a(a(a(x1))))))) → a(a(a(a(b(a(b(a(b(x1)))))))))
Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(b(a(a(a(x1))))))) → a(a(a(a(b(a(b(a(b(x1)))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(b(a(b(a(a(a(x1))))))) → a(a(a(a(b(a(b(a(b(x1)))))))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
Q is empty.
We were given the following TRS:
a(b(a(b(a(a(a(x1))))))) → a(a(a(a(b(a(b(a(b(x1)))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS:
b(a(b(a(a(a(x1)))))) → a(a(a(b(a(b(a(b(x1))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(a(a(a(x1)))))) → a(a(a(b(a(b(a(b(x1))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(b(a(b(a(a(a(x1))))))) → a(a(a(a(b(a(b(a(b(x1)))))))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
Q is empty.
We were given the following TRS:
a(a(a(b(a(b(a(x))))))) → b(a(b(a(b(a(a(a(a(x)))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS:
a(a(a(b(a(b(x)))))) → b(a(b(a(b(a(a(a(x))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(b(a(b(x)))))) → b(a(b(a(b(a(a(a(x))))))))
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(a(b(a(b(x)))))) → b(a(b(a(b(a(a(a(x))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
387, 388, 392, 393, 390, 391, 389, 395, 394, 399, 400, 397, 398, 396, 402, 401
Node 387 is start node and node 388 is final node.
Those nodes are connect through the following edges:
- 387 to 389 labelled b_1(0)
- 388 to 388 labelled #_1(0)
- 392 to 393 labelled b_1(0)
- 393 to 394 labelled a_1(0)
- 393 to 396 labelled b_1(1)
- 390 to 391 labelled b_1(0)
- 391 to 392 labelled a_1(0)
- 389 to 390 labelled a_1(0)
- 395 to 388 labelled a_1(0)
- 395 to 396 labelled b_1(1)
- 394 to 395 labelled a_1(0)
- 394 to 396 labelled b_1(1)
- 399 to 400 labelled b_1(1)
- 400 to 401 labelled a_1(1)
- 400 to 396 labelled b_1(1)
- 397 to 398 labelled b_1(1)
- 398 to 399 labelled a_1(1)
- 396 to 397 labelled a_1(1)
- 402 to 388 labelled a_1(1)
- 402 to 396 labelled b_1(1)
- 401 to 402 labelled a_1(1)
- 401 to 396 labelled b_1(1)