/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) 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(b(a(a(b(b(a(a(b(x1))))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(b(x1))))))))))))))

Q is empty.

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

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

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264

Node 239 is start node and node 240 is final node.

Those nodes are connected through the following edges:

* 239 to 241 labelled a_1(0)* 240 to 240 labelled #_1(0)* 241 to 242 labelled a_1(0)* 242 to 243 labelled b_1(0)* 243 to 244 labelled b_1(0)* 244 to 245 labelled a_1(0)* 245 to 246 labelled a_1(0)* 246 to 247 labelled b_1(0)* 246 to 253 labelled a_1(1)* 247 to 248 labelled a_1(0)* 248 to 249 labelled a_1(0)* 249 to 250 labelled b_1(0)* 249 to 253 labelled a_1(1)* 250 to 251 labelled a_1(0)* 251 to 252 labelled a_1(0)* 252 to 240 labelled b_1(0)* 252 to 253 labelled a_1(1)* 253 to 254 labelled a_1(1)* 254 to 255 labelled b_1(1)* 255 to 256 labelled b_1(1)* 256 to 257 labelled a_1(1)* 257 to 258 labelled a_1(1)* 258 to 259 labelled b_1(1)* 258 to 253 labelled a_1(1)* 259 to 260 labelled a_1(1)* 260 to 261 labelled a_1(1)* 261 to 262 labelled b_1(1)* 261 to 253 labelled a_1(1)* 262 to 263 labelled a_1(1)* 263 to 264 labelled a_1(1)* 264 to 240 labelled b_1(1)* 264 to 253 labelled a_1(1)


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

(4)
YES