Derivational Complexity: TRS Innermost pair #487106298

details
property	value
status	complete
benchmark	24100.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
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.683 seconds
cpu usage	929.717
user time	922.298
system time	7.41844
max virtual memory	1.8750496E7
max residence set size	1.5358476E7
stage attributes
key	value
starexec-result	WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 41 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) CpxTrsMatchBoundsProof [FINISHED, 479 ms]
(8) BOUNDS(1, n^1)


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

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   0(0(1(0(1(2(0(3(3(4(x1)))))))))) -> 4(2(3(4(2(1(1(4(2(0(x1))))))))))
   0(0(1(5(2(3(0(1(5(5(x1)))))))))) -> 0(0(1(3(1(2(5(0(5(5(x1))))))))))
   0(0(4(0(1(0(2(0(3(3(x1)))))))))) -> 0(0(4(0(1(0(0(2(3(3(x1))))))))))
   0(0(5(3(4(5(1(5(3(0(x1)))))))))) -> 0(0(3(1(5(4(5(5(3(0(x1))))))))))
   0(2(2(0(1(0(3(4(0(0(x1)))))))))) -> 0(2(2(0(1(3(0(0(4(0(x1))))))))))
   0(3(2(0(5(0(4(3(5(3(x1)))))))))) -> 0(3(2(0(0(5(4(3(5(3(x1))))))))))
   0(4(3(3(5(1(2(4(3(3(x1)))))))))) -> 0(4(3(3(1(5(2(4(3(3(x1))))))))))
   0(5(2(4(0(0(1(3(4(3(x1)))))))))) -> 0(5(4(2(0(0(1(3(4(3(x1))))))))))
   0(5(5(0(4(0(3(1(2(1(x1)))))))))) -> 0(5(4(5(0(0(3(1(2(1(x1))))))))))
   1(0(0(0(4(0(0(5(0(4(x1)))))))))) -> 2(4(5(5(1(0(5(5(0(2(x1))))))))))
   1(0(0(5(3(4(0(1(4(3(x1)))))))))) -> 1(0(0(5(1(3(0(4(4(3(x1))))))))))
   1(0(1(0(5(5(0(1(3(2(x1)))))))))) -> 1(0(1(5(0(5(0(1(3(2(x1))))))))))
   1(1(3(2(1(0(5(3(3(4(x1)))))))))) -> 1(1(2(3(1(0(5(3(3(4(x1))))))))))
   1(2(1(5(1(5(1(3(4(3(x1)))))))))) -> 1(2(1(3(5(4(5(1(3(1(x1))))))))))
   1(3(0(2(3(2(4(1(2(0(x1)))))))))) -> 1(3(0(1(2(3(2(4(2(0(x1))))))))))
   1(3(2(2(2(5(2(0(1(0(x1)))))))))) -> 1(3(2(2(2(2(5(0(1(0(x1))))))))))
   1(4(5(2(2(4(0(0(3(5(x1)))))))))) -> 4(2(5(0(1(3(0(4(2(5(x1))))))))))
   1(5(0(4(1(3(2(3(3(3(x1)))))))))) -> 1(5(4(0(3(1(2(3(3(3(x1))))))))))
   1(5(1(2(0(2(5(1(3(2(x1)))))))))) -> 1(5(1(0(2(2(5(1(3(2(x1))))))))))
   1(5(3(0(5(5(4(0(4(0(x1)))))))))) -> 1(5(3(0(5(4(5(0(4(0(x1))))))))))
   2(0(0(4(3(2(1(3(3(4(x1)))))))))) -> 2(0(0(3(4(2(1(3(3(4(x1))))))))))
   2(1(0(3(3(2(1(2(2(5(x1)))))))))) -> 2(1(0(3(2(3(1(2(2(5(x1))))))))))
   2(1(2(4(4(3(5(2(4(1(x1)))))))))) -> 2(1(2(4(3(1(4(4(2(5(x1))))))))))
   2(1(3(4(1(3(2(4(2(1(x1)))))))))) -> 2(1(3(4(1(2(3(4(2(1(x1))))))))))
   2(1(4(0(5(3(4(5(5(0(x1)))))))))) -> 2(4(1(5(0(3(4(5(5(0(x1))))))))))
   2(3(5(0(1(3(4(5(5(2(x1)))))))))) -> 2(3(5(0(3(1(4(5(5(2(x1))))))))))
   2(4(0(1(4(1(4(3(3(4(x1)))))))))) -> 2(4(0(4(4(3(1(1(3(4(x1))))))))))
   2(5(1(1(4(5(4(0(4(2(x1)))))))))) -> 2(5(1(1(5(4(4(0(4(2(x1))))))))))
   2(5(1(3(0(3(4(3(5(0(x1)))))))))) -> 2(5(1(3(3(4(0(3(5(0(x1))))))))))
   3(0(1(4(0(3(5(1(4(5(x1)))))))))) -> 3(0(1(1(3(4(5(0(4(5(x1))))))))))
   3(0(2(0(4(3(1(4(3(1(x1)))))))))) -> 1(0(5(0(0(5(2(5(5(2(x1))))))))))
   3(0(4(3(2(4(0(5(2(0(x1)))))))))) -> 3(0(0(2(4(5(0(4(2(3(x1))))))))))
   3(2(0(1(2(4(0(0(5(3(x1)))))))))) -> 3(2(0(1(4(2(3(0(5(0(x1))))))))))
   3(3(5(2(1(5(3(0(4(5(x1)))))))))) -> 3(3(1(4(2(5(5(3(0(5(x1))))))))))
   3(4(2(1(4(3(3(1(3(5(x1)))))))))) -> 3(1(1(3(5(5(0(3(0(5(x1))))))))))
   3(4(5(0(5(1(4(0(5(3(x1)))))))))) -> 3(4(5(0(5(4(1(0(5(3(x1))))))))))
   3(5(0(3(4(2(0(0(3(0(x1)))))))))) -> 3(5(0(3(0(4(2(0(3(0(x1))))))))))
   3(5(1(3(2(0(2(4(2(3(x1)))))))))) -> 3(2(3(1(4(5(0(2(3(2(x1))))))))))
   4(0(4(2(4(3(4(3(4(1(x1)))))))))) -> 4(4(2(3(4(0(3(4(4(1(x1))))))))))
   4(1(3(2(2(0(2(0(1(3(x1)))))))))) -> 4(2(3(2(1(0(2(0(1(3(x1))))))))))
   4(2(5(0(5(1(0(3(1(0(x1)))))))))) -> 4(2(5(0(5(0(1(3(1(0(x1))))))))))
   4(3(2(0(0(0(3(0(0(3(x1)))))))))) -> 4(3(0(2(0(0(3(0(0(3(x1))))))))))
   4(4(0(0(4(3(3(5(3(2(x1)))))))))) -> 4(4(0(4(0(3(3(5(3(2(x1))))))))))
   4(5(1(0(4(3(5(5(5(1(x1)))))))))) -> 4(5(1(0(3(4(5(5(5(1(x1))))))))))
   4(5(1(3(5(1(3(4(1(2(x1)))))))))) -> 4(5(1(3(5(1(3(1(4(2(x1))))))))))
   5(0(3(5(2(3(0(3(4(4(x1)))))))))) -> 5(0(3(5(2(3(3(0(4(4(x1))))))))))
   5(1(0(1(3(2(1(0(2(0(x1)))))))))) -> 5(1(0(1(2(3(1(0(0(2(x1))))))))))
   5(1(1(5(1(5(1(1(4(3(x1)))))))))) -> 5(1(1(5(1(3(1(5(4(1(x1))))))))))
   5(3(0(0(3(4(4(2(3(2(x1)))))))))) -> 5(3(0(0(4(3(4(2(3(2(x1))))))))))
   5(5(3(1(5(5(3(2(0(5(x1)))))))))) -> 5(5(3(1(5(5(2(3(0(5(x1))))))))))
   0(3(5(4(1(5(1(5(1(2(0(x1))))))))))) -> 3(1(3(1(0(5(1(2(4(5(x1))))))))))
   1(2(4(0(4(3(4(0(0(3(2(x1))))))))))) -> 1(1(4(1(4(4(3(2(1(1(x1))))))))))
   1(3(2(3(3(0(2(4(2(3(2(x1))))))))))) -> 2(0(2(5(4(5(5(5(0(5(x1))))))))))
   2(0(4(3(4(5(3(0(0(0(5(x1))))))))))) -> 2(4(4(4(2(0(4(2(4(2(x1))))))))))
   2(4(0(0(5(5(1(3(5(1(4(x1))))))))))) -> 2(2(0(0(0(5(3(2(0(5(x1))))))))))
   3(0(2(4(1(1(2(1(5(2(0(x1))))))))))) -> 2(1(5(3(3(1(1(2(0(2(x1))))))))))
   3(2(4(4(2(4(5(4(1(5(1(x1))))))))))) -> 2(1(4(1(5(5(4(2(0(2(x1))))))))))
   4(0(1(2(3(1(0(2(2(4(5(x1))))))))))) -> 0(5(2(4(5(0(4(5(5(0(x1))))))))))
   4(2(0(3(4(2(1(1(3(3(0(x1))))))))))) -> 1(0(5(5(3(2(2(1(5(4(x1))))))))))
   4(2(0(5(4(5(5(3(2(5(4(x1))))))))))) -> 4(1(3(2(0(0(5(2(4(1(x1))))))))))
   4(2(1(5(3(5(4(1(4(4(3(x1))))))))))) -> 4(0(5(2(3(5(4(3(2(2(x1))))))))))
   4(4(4(0(3(3(4(3(4(5(4(x1))))))))))) -> 3(2(2(4(0(0(1(0(4(5(x1))))))))))
   4(5(5(4(4(4(2(5(2(5(3(x1))))))))))) -> 0(4(0(3(2(4(1(0(0(0(x1))))))))))
   5(3(2(0(0(5(3(1(4(1(0(x1))))))))))) -> 4(4(5(5(0(1(0(2(3(0(x1))))))))))
   5(5(4(0(2(4(5(2(3(4(3(x1))))))))))) -> 1(0(2(1(4(5(1(2(4(5(x1))))))))))
   1(0(2(1(4(3(4(5(2(3(3(1(x1)))))))))))) -> 4(4(5(5(2(2(2(4(0(3(x1))))))))))
   1(2(1(1(1(1(2(5(2(2(4(5(x1)))))))))))) -> 3(2(0(1(0(1(1(0(0(0(x1))))))))))
   3(2(0(0(4(2(3(3(5(5(2(2(x1)))))))))))) -> 1(3(0(3(4(1(3(4(2(3(x1))))))))))
   3(2(0(0(5(4(5(0(5(4(2(5(x1)))))))))))) -> 0(3(0(4(0(1(4(4(4(4(x1))))))))))
   3(2(0(2(0(3(4(4(4(4(1(3(x1)))))))))))) -> 1(1(1(0(5(3(0(0(1(5(x1))))))))))
   4(0(5(0(1(1(0(4(3(5(3(5(x1)))))))))))) -> 2(5(3(4(0(4(4(5(3(1(x1))))))))))
   5(2(0(2(5(5(1(5(5(1(5(1(x1)))))))))))) -> 1(1(3(4(0(5(4(3(2(4(x1))))))))))
   5(2(1(5(5(5(2(0(4(5(2(4(x1)))))))))))) -> 1(1(4(5(4(3(4(2(2(5(x1))))))))))
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actions all output return to Derivational Complexity: TRS Innermost