SRS Relative pair #487082297

details
property	value
status	complete
benchmark	88143.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010_relative
run statistics
property	value
solver	AProVE
configuration	standard
runtime (wallclock)	23.7579 seconds
cpu usage	71.4453
user time	69.3799
system time	2.06544
max virtual memory	1.9250636E7
max residence set size	5641912.0
stage attributes
key	value
starexec-result	YES
output
YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) FlatCCProof [EQUIVALENT, 58 ms]
(2) RelTRS
(3) RootLabelingProof [EQUIVALENT, 470 ms]
(4) RelTRS
(5) RelTRSRRRProof [EQUIVALENT, 772 ms]
(6) RelTRS
(7) RelTRSRRRProof [EQUIVALENT, 64 ms]
(8) RelTRS
(9) SIsEmptyProof [EQUIVALENT, 0 ms]
(10) QTRS
(11) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(12) YES


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

(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   0(0(0(1(1(1(2(3(3(1(3(3(2(x1))))))))))))) -> 0(2(2(1(0(1(2(3(0(0(3(2(2(3(1(2(2(x1)))))))))))))))))
   0(0(0(3(3(1(1(1(3(3(1(3(2(x1))))))))))))) -> 3(0(2(1(0(3(3(3(1(2(2(2(1(2(1(2(2(x1)))))))))))))))))
   0(0(2(0(3(1(3(2(1(0(0(2(3(x1))))))))))))) -> 0(2(2(2(1(3(3(3(2(2(0(3(1(3(2(1(2(x1)))))))))))))))))
   0(1(0(0(3(3(2(1(2(0(1(2(3(x1))))))))))))) -> 3(2(2(1(2(2(0(3(0(2(2(2(1(2(2(3(1(x1)))))))))))))))))
   0(1(2(0(1(1(0(2(2(1(2(0(2(x1))))))))))))) -> 2(0(3(3(2(2(1(0(3(3(3(3(2(2(2(3(3(x1)))))))))))))))))
   0(1(2(1(1(1(2(2(0(1(3(2(0(x1))))))))))))) -> 2(3(2(0(1(2(3(0(3(3(2(1(3(3(1(3(3(x1)))))))))))))))))
   0(2(2(0(0(3(1(0(3(2(1(3(0(x1))))))))))))) -> 3(1(2(2(1(3(3(2(2(3(0(2(2(1(1(1(0(x1)))))))))))))))))
   0(2(3(3(1(0(3(3(0(2(3(1(1(x1))))))))))))) -> 2(1(3(2(2(2(0(2(2(2(3(3(2(2(2(0(3(x1)))))))))))))))))
   0(3(0(3(0(2(3(0(0(3(1(2(1(x1))))))))))))) -> 3(1(1(2(2(3(0(1(2(2(2(2(3(2(2(2(0(x1)))))))))))))))))
   0(3(0(3(1(0(1(2(2(0(3(1(3(x1))))))))))))) -> 2(3(2(2(3(0(3(0(3(3(2(2(1(2(2(0(3(x1)))))))))))))))))
   1(0(0(1(2(2(2(3(2(3(2(0(1(x1))))))))))))) -> 1(2(1(0(2(2(1(2(1(0(3(3(2(2(2(3(3(x1)))))))))))))))))
   1(0(2(3(0(3(2(3(2(2(3(2(3(x1))))))))))))) -> 1(3(2(2(1(2(2(2(3(3(2(2(3(1(2(1(2(x1)))))))))))))))))
   1(3(1(0(1(1(3(2(2(1(1(2(1(x1))))))))))))) -> 1(2(3(2(3(2(1(2(2(2(2(2(2(0(1(2(2(x1)))))))))))))))))
   2(0(0(1(3(0(3(1(3(0(1(2(1(x1))))))))))))) -> 2(2(3(3(0(1(0(0(3(3(3(1(0(2(2(1(2(x1)))))))))))))))))
   2(0(0(2(3(0(3(1(0(0(2(1(3(x1))))))))))))) -> 2(0(2(1(2(2(2(2(3(2(3(1(3(3(1(3(1(x1)))))))))))))))))
   2(1(0(2(2(0(0(1(3(2(0(3(3(x1))))))))))))) -> 2(0(2(2(1(3(2(1(1(1(2(2(1(3(3(3(3(x1)))))))))))))))))
   2(1(0(3(0(3(0(3(3(0(2(1(1(x1))))))))))))) -> 2(2(0(1(2(1(1(0(2(2(2(3(2(3(0(2(2(x1)))))))))))))))))
   2(1(1(2(0(1(1(3(0(2(3(0(1(x1))))))))))))) -> 2(2(3(3(3(3(3(2(1(0(1(2(2(3(3(2(2(x1)))))))))))))))))
   2(1(1(3(3(0(3(2(3(2(1(1(3(x1))))))))))))) -> 2(3(2(3(2(2(3(3(2(1(2(2(3(3(0(1(3(x1)))))))))))))))))
   2(1(1(3(3(3(0(3(0(3(0(0(2(x1))))))))))))) -> 2(0(2(2(0(2(1(3(3(3(2(3(3(2(3(3(2(x1)))))))))))))))))
   2(2(0(0(1(0(2(3(0(3(0(1(0(x1))))))))))))) -> 2(2(2(1(0(2(0(1(3(1(3(0(3(3(3(3(2(x1)))))))))))))))))
   2(2(0(0(3(0(2(2(3(0(1(3(3(x1))))))))))))) -> 2(2(1(1(0(1(2(1(2(0(2(2(2(0(2(2(2(x1)))))))))))))))))
   2(2(0(3(0(1(0(2(3(2(3(1(2(x1))))))))))))) -> 2(2(0(2(2(2(1(0(0(3(1(3(1(3(3(2(2(x1)))))))))))))))))
   2(2(1(0(2(1(2(1(1(0(1(2(0(x1))))))))))))) -> 2(2(0(2(0(3(1(2(2(0(1(2(2(2(2(2(2(x1)))))))))))))))))
   2(3(1(1(0(2(3(1(2(3(3(1(1(x1))))))))))))) -> 2(2(2(1(2(1(1(2(0(2(0(0(3(0(1(3(3(x1)))))))))))))))))
   2(3(2(0(3(0(1(3(2(2(2(0(2(x1))))))))))))) -> 2(1(2(2(3(0(0(1(3(2(2(3(2(2(3(3(2(x1)))))))))))))))))
   2(3(2(1(1(1(3(2(3(2(3(2(1(x1))))))))))))) -> 2(2(2(0(3(2(2(0(2(3(2(3(0(2(2(0(2(x1)))))))))))))))))
   3(0(2(3(0(1(0(3(3(0(0(1(0(x1))))))))))))) -> 3(0(0(1(2(2(3(3(3(2(0(1(2(0(3(3(2(x1)))))))))))))))))

The relative TRS consists of the following S rules:

   1(3(2(0(2(1(2(1(2(2(1(2(0(x1))))))))))))) -> 3(2(1(2(1(2(2(1(2(2(0(2(2(0(2(2(2(x1)))))))))))))))))


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(1) FlatCCProof (EQUIVALENT)
We used flat context closure [ROOTLAB]

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

(2)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   0(0(0(1(1(1(2(3(3(1(3(3(2(x1))))))))))))) -> 0(2(2(1(0(1(2(3(0(0(3(2(2(3(1(2(2(x1)))))))))))))))))
   0(0(2(0(3(1(3(2(1(0(0(2(3(x1))))))))))))) -> 0(2(2(2(1(3(3(3(2(2(0(3(1(3(2(1(2(x1)))))))))))))))))
   1(0(0(1(2(2(2(3(2(3(2(0(1(x1))))))))))))) -> 1(2(1(0(2(2(1(2(1(0(3(3(2(2(2(3(3(x1)))))))))))))))))
   1(0(2(3(0(3(2(3(2(2(3(2(3(x1))))))))))))) -> 1(3(2(2(1(2(2(2(3(3(2(2(3(1(2(1(2(x1)))))))))))))))))
   1(3(1(0(1(1(3(2(2(1(1(2(1(x1))))))))))))) -> 1(2(3(2(3(2(1(2(2(2(2(2(2(0(1(2(2(x1)))))))))))))))))
   2(0(0(1(3(0(3(1(3(0(1(2(1(x1))))))))))))) -> 2(2(3(3(0(1(0(0(3(3(3(1(0(2(2(1(2(x1)))))))))))))))))
   2(0(0(2(3(0(3(1(0(0(2(1(3(x1))))))))))))) -> 2(0(2(1(2(2(2(2(3(2(3(1(3(3(1(3(1(x1)))))))))))))))))
   2(1(0(2(2(0(0(1(3(2(0(3(3(x1))))))))))))) -> 2(0(2(2(1(3(2(1(1(1(2(2(1(3(3(3(3(x1)))))))))))))))))
   2(1(0(3(0(3(0(3(3(0(2(1(1(x1))))))))))))) -> 2(2(0(1(2(1(1(0(2(2(2(3(2(3(0(2(2(x1)))))))))))))))))
   2(1(1(2(0(1(1(3(0(2(3(0(1(x1))))))))))))) -> 2(2(3(3(3(3(3(2(1(0(1(2(2(3(3(2(2(x1)))))))))))))))))
   2(1(1(3(3(0(3(2(3(2(1(1(3(x1))))))))))))) -> 2(3(2(3(2(2(3(3(2(1(2(2(3(3(0(1(3(x1)))))))))))))))))
   2(1(1(3(3(3(0(3(0(3(0(0(2(x1))))))))))))) -> 2(0(2(2(0(2(1(3(3(3(2(3(3(2(3(3(2(x1)))))))))))))))))
   2(2(0(0(1(0(2(3(0(3(0(1(0(x1))))))))))))) -> 2(2(2(1(0(2(0(1(3(1(3(0(3(3(3(3(2(x1)))))))))))))))))
   2(2(0(0(3(0(2(2(3(0(1(3(3(x1))))))))))))) -> 2(2(1(1(0(1(2(1(2(0(2(2(2(0(2(2(2(x1)))))))))))))))))
   2(2(0(3(0(1(0(2(3(2(3(1(2(x1))))))))))))) -> 2(2(0(2(2(2(1(0(0(3(1(3(1(3(3(2(2(x1)))))))))))))))))
   2(2(1(0(2(1(2(1(1(0(1(2(0(x1))))))))))))) -> 2(2(0(2(0(3(1(2(2(0(1(2(2(2(2(2(2(x1)))))))))))))))))
   2(3(1(1(0(2(3(1(2(3(3(1(1(x1))))))))))))) -> 2(2(2(1(2(1(1(2(0(2(0(0(3(0(1(3(3(x1)))))))))))))))))
   2(3(2(0(3(0(1(3(2(2(2(0(2(x1))))))))))))) -> 2(1(2(2(3(0(0(1(3(2(2(3(2(2(3(3(2(x1)))))))))))))))))
   2(3(2(1(1(1(3(2(3(2(3(2(1(x1))))))))))))) -> 2(2(2(0(3(2(2(0(2(3(2(3(0(2(2(0(2(x1)))))))))))))))))
   3(0(2(3(0(1(0(3(3(0(0(1(0(x1))))))))))))) -> 3(0(0(1(2(2(3(3(3(2(0(1(2(0(3(3(2(x1)))))))))))))))))
   0(0(0(0(3(3(1(1(1(3(3(1(3(2(x1)))))))))))))) -> 0(3(0(2(1(0(3(3(3(1(2(2(2(1(2(1(2(2(x1))))))))))))))))))
   1(0(0(0(3(3(1(1(1(3(3(1(3(2(x1)))))))))))))) -> 1(3(0(2(1(0(3(3(3(1(2(2(2(1(2(1(2(2(x1))))))))))))))))))
   2(0(0(0(3(3(1(1(1(3(3(1(3(2(x1)))))))))))))) -> 2(3(0(2(1(0(3(3(3(1(2(2(2(1(2(1(2(2(x1))))))))))))))))))
   3(0(0(0(3(3(1(1(1(3(3(1(3(2(x1)))))))))))))) -> 3(3(0(2(1(0(3(3(3(1(2(2(2(1(2(1(2(2(x1))))))))))))))))))
   0(0(1(0(0(3(3(2(1(2(0(1(2(3(x1)))))))))))))) -> 0(3(2(2(1(2(2(0(3(0(2(2(2(1(2(2(3(1(x1))))))))))))))))))
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