SRS Standard pair #487514735

details
property	value
status	complete
benchmark	167636.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n110.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	standard
runtime (wallclock)	33.0136899948 seconds
cpu usage	124.233072313
max memory	7.254626304E9
stage attributes
key	value
output-size	814614
starexec-result	YES
output
/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 52 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 2405 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 1352 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 12 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 820 ms]
(12) QDP
(13) PisEmptyProof [EQUIVALENT, 0 ms]
(14) YES


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

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

   0(0(0(1(0(x1))))) -> 2(2(1(1(1(0(x1))))))
   0(1(0(1(2(2(x1)))))) -> 1(1(2(0(0(2(x1))))))
   2(2(0(0(2(2(x1)))))) -> 2(2(1(1(1(2(0(x1)))))))
   0(1(0(0(2(2(2(1(x1)))))))) -> 2(1(1(1(2(0(0(1(1(x1)))))))))
   0(1(2(0(1(1(2(1(x1)))))))) -> 1(0(2(2(1(1(0(1(x1))))))))
   0(2(2(2(2(0(1(2(2(x1))))))))) -> 1(1(1(1(0(1(0(0(2(2(x1))))))))))
   2(0(0(0(1(0(2(0(0(x1))))))))) -> 1(0(0(1(2(0(1(1(1(1(2(x1)))))))))))
   2(2(1(2(0(0(1(1(2(x1))))))))) -> 0(1(1(1(1(1(2(2(2(1(x1))))))))))
   0(0(0(0(0(1(1(0(1(0(1(x1))))))))))) -> 0(1(2(1(0(1(0(0(1(1(1(1(x1))))))))))))
   0(0(1(0(2(0(0(0(0(0(2(x1))))))))))) -> 1(0(0(1(2(1(2(1(0(1(1(1(x1))))))))))))
   0(2(0(1(0(2(0(1(0(1(2(x1))))))))))) -> 1(0(0(2(1(1(1(1(2(1(1(2(0(x1)))))))))))))
   1(0(0(0(2(0(2(1(2(2(0(x1))))))))))) -> 1(0(1(0(0(2(2(2(1(1(1(1(2(x1)))))))))))))
   2(2(1(2(0(2(0(1(0(1(2(x1))))))))))) -> 1(1(1(1(0(2(1(2(2(2(1(0(x1))))))))))))
   1(0(1(0(2(2(0(1(0(0(0(0(x1)))))))))))) -> 1(0(0(2(1(2(0(0(0(1(1(1(1(2(x1))))))))))))))
   1(2(1(2(0(1(2(2(2(0(0(1(x1)))))))))))) -> 1(1(1(1(2(1(1(1(1(1(1(1(1(0(1(1(2(x1)))))))))))))))))
   0(1(2(2(2(2(2(2(0(0(2(2(1(x1))))))))))))) -> 2(2(0(2(2(0(1(0(1(1(1(1(1(2(2(1(x1))))))))))))))))
   0(2(0(1(1(0(2(2(0(0(1(2(0(x1))))))))))))) -> 2(1(2(1(0(2(1(1(1(1(1(1(0(1(x1))))))))))))))
   0(2(0(2(0(1(0(2(2(1(1(0(0(x1))))))))))))) -> 1(1(1(1(0(2(2(2(2(2(1(1(1(2(0(1(x1))))))))))))))))
   2(0(2(0(0(2(2(2(2(1(2(0(2(x1))))))))))))) -> 0(0(2(0(1(0(0(2(1(1(1(1(1(2(1(2(x1))))))))))))))))
   2(1(0(1(1(0(1(0(2(1(2(0(2(x1))))))))))))) -> 1(1(1(1(1(1(0(0(0(1(0(2(2(2(0(2(x1))))))))))))))))
   2(1(1(0(2(2(1(2(0(2(2(1(2(x1))))))))))))) -> 1(1(1(0(2(1(1(1(1(1(0(1(2(2(2(0(x1))))))))))))))))
   2(1(2(0(0(0(1(0(1(0(0(0(0(x1))))))))))))) -> 2(2(0(1(2(0(0(1(1(1(1(1(1(0(x1))))))))))))))
   0(0(0(2(0(1(1(2(1(1(2(0(1(1(x1)))))))))))))) -> 1(1(2(0(2(0(2(2(1(2(0(1(1(1(1(x1)))))))))))))))
   2(1(2(0(1(2(1(2(1(2(1(1(0(0(x1)))))))))))))) -> 1(1(2(0(2(1(2(2(1(2(1(1(0(0(x1))))))))))))))
   1(2(0(1(0(0(1(2(2(0(0(0(0(0(2(x1))))))))))))))) -> 1(1(1(2(1(0(1(1(1(1(2(2(1(1(0(0(0(x1)))))))))))))))))
   2(1(1(0(0(0(0(1(0(1(2(2(1(2(1(x1))))))))))))))) -> 2(0(1(1(1(1(2(2(1(1(2(2(1(1(1(2(x1))))))))))))))))
   0(1(0(1(0(1(0(1(0(2(1(1(0(0(0(2(x1)))))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(0(0(0(2(x1))))))))))))))))
   1(0(2(2(1(0(1(0(1(1(2(2(1(2(0(0(x1)))))))))))))))) -> 1(1(1(1(1(1(1(1(1(1(2(1(2(2(2(2(2(0(2(x1)))))))))))))))))))
   2(0(0(0(2(2(0(2(1(0(1(0(2(2(1(1(x1)))))))))))))))) -> 2(1(1(1(1(0(0(0(1(1(2(1(2(0(2(1(1(1(x1))))))))))))))))))
   2(1(2(1(2(0(1(2(0(2(0(0(1(0(2(0(x1)))))))))))))))) -> 1(1(1(0(1(2(2(1(0(1(2(2(2(1(1(1(2(x1)))))))))))))))))
   2(2(0(2(2(0(2(2(1(2(0(2(1(0(2(2(x1)))))))))))))))) -> 1(2(1(1(1(2(2(0(1(2(2(1(1(1(2(2(1(1(1(x1)))))))))))))))))))
   0(2(2(0(0(2(1(2(2(0(2(1(0(0(0(0(2(x1))))))))))))))))) -> 0(1(0(2(1(2(2(1(2(1(2(2(0(1(1(1(1(2(2(x1)))))))))))))))))))
   1(1(2(0(0(0(2(0(0(1(1(0(0(2(1(2(2(x1))))))))))))))))) -> 1(1(2(1(1(1(1(2(2(1(1(2(1(0(0(0(1(1(0(x1)))))))))))))))))))
   2(2(2(2(0(1(0(2(2(0(2(0(0(0(0(0(0(x1))))))))))))))))) -> 0(1(2(1(2(2(0(1(0(0(0(1(1(1(1(2(2(1(x1))))))))))))))))))
   0(2(2(2(2(0(2(0(0(1(1(1(0(2(2(1(1(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(1(1(1(1(0(2(2(1(1(1(2(1(2(2(x1))))))))))))))))))))
   1(2(2(0(2(2(0(0(1(2(1(2(0(1(0(2(1(2(x1)))))))))))))))))) -> 1(0(0(2(2(1(0(2(1(1(2(0(1(1(1(1(0(2(0(0(x1))))))))))))))))))))
   2(1(2(0(2(0(0(2(2(1(2(2(0(2(0(2(2(1(x1)))))))))))))))))) -> 0(2(0(0(1(1(1(2(0(2(0(1(0(2(0(2(2(1(1(x1)))))))))))))))))))
   0(0(2(2(0(0(1(0(0(1(1(2(1(0(1(0(2(1(2(x1))))))))))))))))))) -> 0(0(2(2(0(0(1(1(2(0(0(1(0(2(1(0(1(1(1(1(1(1(1(x1)))))))))))))))))))))))
   0(1(0(0(1(1(0(0(0(1(0(0(2(1(2(1(2(0(1(x1))))))))))))))))))) -> 2(0(0(2(2(1(1(1(2(0(0(2(0(1(1(0(2(1(0(1(x1))))))))))))))))))))
   0(1(2(0(2(1(0(2(0(2(2(1(2(1(2(2(0(2(2(x1))))))))))))))))))) -> 0(2(0(2(0(1(1(1(1(1(2(2(2(0(2(2(0(2(2(2(x1))))))))))))))))))))
   0(1(2(1(2(2(0(1(0(1(0(2(0(1(0(1(0(1(0(x1))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(0(0(0(0(1(2(0(2(2(x1)))))))))))))))))))
   0(0(0(0(0(2(1(2(2(2(1(0(2(0(1(2(2(0(1(2(x1)))))))))))))))))))) -> 0(2(2(1(1(1(1(1(1(2(2(2(2(1(0(2(0(0(0(0(0(2(x1))))))))))))))))))))))
   0(1(0(1(2(1(0(1(0(0(2(1(2(0(1(0(2(0(1(2(x1)))))))))))))))))))) -> 2(1(2(1(1(2(0(1(0(1(2(2(0(0(0(1(1(1(2(2(2(x1)))))))))))))))))))))
   1(0(2(1(1(2(2(0(1(1(1(2(0(2(0(2(2(2(0(2(x1)))))))))))))))))))) -> 1(1(2(1(2(1(2(2(1(1(1(1(2(2(0(2(1(0(0(0(1(x1)))))))))))))))))))))
   1(2(1(1(2(1(1(2(1(0(1(1(1(2(0(1(2(2(0(0(x1)))))))))))))))))))) -> 1(1(1(1(0(1(0(0(0(1(1(1(1(0(0(1(0(1(2(1(2(x1)))))))))))))))))))))
   2(0(0(1(2(0(2(2(2(2(0(0(1(1(2(1(2(2(2(2(x1)))))))))))))))))))) -> 1(0(1(0(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(0(2(1(x1))))))))))))))))))))))
   2(0(0(2(0(0(1(0(0(0(1(1(2(0(0(1(1(0(2(1(x1)))))))))))))))))))) -> 0(1(1(0(2(2(1(1(1(2(2(1(0(2(0(1(1(1(1(2(1(x1)))))))))))))))))))))
   2(2(0(0(1(1(2(1(1(0(1(2(0(1(2(0(2(2(0(0(x1)))))))))))))))))))) -> 1(2(0(2(2(2(0(0(0(1(1(1(0(1(1(0(1(1(1(1(1(2(2(x1)))))))))))))))))))))))
   0(1(0(1(1(0(1(2(1(2(2(2(1(2(1(0(2(2(0(0(0(x1))))))))))))))))))))) -> 1(0(2(0(0(0(1(0(1(1(1(0(0(2(1(1(1(1(0(1(0(0(1(x1)))))))))))))))))))))))
   2(0(1(1(1(0(1(0(2(0(1(1(2(1(0(1(1(2(2(0(1(x1))))))))))))))))))))) -> 2(1(1(1(2(0(0(0(2(0(1(2(0(1(0(2(1(1(1(1(1(x1)))))))))))))))))))))
   2(0(2(2(0(1(0(1(0(2(0(1(0(2(2(2(2(0(1(2(0(x1))))))))))))))))))))) -> 1(1(1(2(1(0(0(0(1(2(1(2(2(1(1(1(1(2(1(0(0(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))))
   0(0(2(2(1(2(0(1(0(0(2(1(1(2(0(2(1(0(1(0(0(0(x1)))))))))))))))))))))) -> 2(1(0(2(2(2(1(1(1(1(1(1(1(1(2(0(1(0(0(0(1(1(0(0(x1))))))))))))))))))))))))
   0(1(0(2(1(1(2(1(2(2(0(1(1(2(0(1(2(0(2(1(2(1(x1)))))))))))))))))))))) -> 1(2(1(1(0(0(0(1(2(1(0(2(1(1(2(0(1(2(0(1(1(1(1(x1)))))))))))))))))))))))
   0(2(2(0(2(0(0(1(2(1(2(0(2(0(0(0(1(0(2(2(1(0(x1)))))))))))))))))))))) -> 0(0(1(1(1(2(2(0(1(2(0(1(2(1(1(1(1(0(2(0(1(0(1(x1)))))))))))))))))))))))
   1(1(2(1(0(1(1(2(2(2(2(2(0(1(1(0(2(2(0(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(1(0(2(0(1(0(1(0(2(0(0(1(2(2(0(0(1(1(2(1(x1)))))))))))))))))))))))
   2(1(1(1(2(2(0(1(0(1(0(2(0(0(0(0(1(2(0(2(2(2(x1)))))))))))))))))))))) -> 1(2(1(2(0(1(1(1(1(0(0(1(1(0(2(1(2(1(1(0(0(0(1(x1)))))))))))))))))))))))
   2(1(2(0(1(1(2(2(0(1(1(0(1(2(1(0(2(2(2(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(1(1(2(0(1(1(1(2(2(2(1(0(1(1(2(0(2(1(0(0(x1)))))))))))))))))))))))
   2(1(2(2(0(2(1(2(0(2(0(2(0(2(2(0(0(1(0(0(2(1(x1)))))))))))))))))))))) -> 0(2(1(0(0(1(0(2(1(2(1(1(0(0(0(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))
   2(1(2(2(1(0(2(0(1(0(2(1(1(0(0(2(0(0(1(1(0(2(x1)))))))))))))))))))))) -> 2(2(2(0(2(0(0(0(1(2(0(0(2(0(2(0(2(0(2(1(1(1(1(x1)))))))))))))))))))))))
   0(0(1(2(2(1(2(1(2(0(1(1(0(2(2(0(0(2(1(0(0(1(2(x1))))))))))))))))))))))) -> 2(0(1(1(0(1(2(2(0(2(1(1(2(0(1(1(1(1(0(2(2(1(1(1(x1))))))))))))))))))))))))
   0(2(0(0(1(1(0(2(1(1(0(1(2(2(1(0(0(0(0(0(2(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(0(2(2(2(0(0(1(0(2(1(2(0(1(0(0(0(0(0(2(x1)))))))))))))))))))))))
   0(2(2(1(2(1(0(2(1(2(0(1(0(1(1(1(2(2(0(2(0(2(1(x1))))))))))))))))))))))) -> 2(0(1(1(1(1(1(1(1(2(0(2(2(1(1(1(0(2(0(2(2(2(1(1(0(x1)))))))))))))))))))))))))
   1(0(2(2(2(1(2(1(1(0(0(1(0(0(0(2(0(2(2(2(2(2(1(x1))))))))))))))))))))))) -> 1(1(1(2(0(0(1(0(2(1(1(2(2(1(1(1(2(0(1(0(0(1(1(0(1(x1)))))))))))))))))))))))))
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