/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

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


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

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

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

Q is empty.

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

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

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

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

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

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

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

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

Q is empty.

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

(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466

Node 343 is start node and node 344 is final node.

Those nodes are connected through the following edges:

* 343 to 345 labelled a_1(0)* 344 to 344 labelled #_1(0)* 345 to 346 labelled a_1(0)* 346 to 347 labelled a_1(0)* 347 to 348 labelled b_1(0)* 348 to 349 labelled b_1(0)* 349 to 350 labelled a_1(0)* 350 to 351 labelled a_1(0)* 351 to 352 labelled a_1(0)* 352 to 353 labelled b_1(0)* 352 to 455 labelled a_1(1)* 353 to 354 labelled a_1(0)* 354 to 355 labelled a_1(0)* 355 to 356 labelled a_1(0)* 356 to 344 labelled b_1(0)* 356 to 455 labelled a_1(1)* 455 to 456 labelled a_1(1)* 456 to 457 labelled a_1(1)* 457 to 458 labelled b_1(1)* 458 to 459 labelled b_1(1)* 459 to 460 labelled a_1(1)* 460 to 461 labelled a_1(1)* 461 to 462 labelled a_1(1)* 462 to 463 labelled b_1(1)* 462 to 455 labelled a_1(1)* 463 to 464 labelled a_1(1)* 464 to 465 labelled a_1(1)* 465 to 466 labelled a_1(1)* 466 to 344 labelled b_1(1)* 466 to 455 labelled a_1(1)


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

(4)
YES