/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1 ms]
(6) YES


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

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

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

Q is empty.

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

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

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7, 8, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296

Node 7 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 7 to 35 labelled b_1(0)* 8 to 8 labelled #_1(0)* 35 to 36 labelled a_1(0)* 36 to 37 labelled a_1(0)* 37 to 38 labelled a_1(0)* 38 to 39 labelled b_1(0)* 39 to 40 labelled a_1(0)* 40 to 41 labelled a_1(0)* 41 to 42 labelled b_1(0)* 42 to 43 labelled a_1(0)* 42 to 285 labelled b_1(1)* 43 to 44 labelled a_1(0)* 43 to 285 labelled b_1(1)* 44 to 45 labelled a_1(0)* 44 to 285 labelled b_1(1)* 45 to 46 labelled a_1(0)* 45 to 285 labelled b_1(1)* 46 to 8 labelled a_1(0)* 46 to 285 labelled b_1(1)* 285 to 286 labelled a_1(1)* 286 to 287 labelled a_1(1)* 287 to 288 labelled a_1(1)* 288 to 289 labelled b_1(1)* 289 to 290 labelled a_1(1)* 290 to 291 labelled a_1(1)* 291 to 292 labelled b_1(1)* 292 to 293 labelled a_1(1)* 292 to 285 labelled b_1(1)* 293 to 294 labelled a_1(1)* 293 to 285 labelled b_1(1)* 294 to 295 labelled a_1(1)* 294 to 285 labelled b_1(1)* 295 to 296 labelled a_1(1)* 295 to 285 labelled b_1(1)* 296 to 8 labelled a_1(1)* 296 to 285 labelled b_1(1)


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

(6)
YES