YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(6) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(b(c(a(a(b(b(c(a(x1)))))))))) -> a(a(b(b(c(a(b(b(c(a(a(b(b(c(x1))))))))))))))

Q is empty.

----------------------------------------

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(c(b(b(a(a(c(b(b(a(x1)))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(a(x1))))))))))))))

Q is empty.

----------------------------------------

(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(c(b(b(a(a(c(b(b(a(x1)))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(a(x1))))))))))))))

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))

----------------------------------------

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))

Q is empty.

----------------------------------------

(5) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
366, 367, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 414, 418, 421, 424, 427, 430, 433, 436, 437, 438, 439, 440

Node 366 is start node and node 367 is final node.

Those nodes are connected through the following edges:

* 366 to 380 labelled c_1(0)* 367 to 367 labelled #_1(0)* 380 to 381 labelled b_1(0)* 381 to 382 labelled b_1(0)* 382 to 383 labelled a_1(0)* 383 to 384 labelled a_1(0)* 384 to 385 labelled c_1(0)* 385 to 386 labelled b_1(0)* 386 to 387 labelled b_1(0)* 387 to 388 labelled a_1(0)* 387 to 414 labelled c_1(1)* 388 to 389 labelled c_1(0)* 389 to 390 labelled b_1(0)* 390 to 391 labelled b_1(0)* 391 to 367 labelled a_1(0)* 391 to 414 labelled c_1(1)* 414 to 418 labelled b_1(1)* 418 to 421 labelled b_1(1)* 421 to 424 labelled a_1(1)* 424 to 427 labelled a_1(1)* 427 to 430 labelled c_1(1)* 430 to 433 labelled b_1(1)* 433 to 436 labelled b_1(1)* 436 to 437 labelled a_1(1)* 436 to 414 labelled c_1(1)* 437 to 438 labelled c_1(1)* 438 to 439 labelled b_1(1)* 439 to 440 labelled b_1(1)* 440 to 367 labelled a_1(1)* 440 to 414 labelled c_1(1)


----------------------------------------

(6)
YES