Derivational Complexity: TRS pair #487102880

details

property	value
status	complete
benchmark	45720.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)	3.61867 seconds
cpu usage	11.4231
user time	10.6591
system time	0.764005
max virtual memory	1.8546712E7
max residence set size	2658712.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 30 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 665 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (12) BEST
        (13) proven lower bound
            (14) LowerBoundPropagationProof [FINISHED, 0 ms]
            (15) BOUNDS(n^1, INF)
        (16) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
   0(2(1(x1))) -> 3(1(3(0(2(x1)))))
   0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
   0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
   0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
   1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
   0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
   0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
   0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
   0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
   0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
   0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
   0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
   0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
   0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
   0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
   0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
   0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
   0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
   1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
   1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
   0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
   0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
   0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
   0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
   0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
   0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
   0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
   0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
   0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
   0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
   0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
   0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
   1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
   1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
   1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
   1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
   1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
   0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
   0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
   0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
   0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
   0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
   0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
   0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
   0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
   0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
   0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
   0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
   0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
   0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
   0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
   0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
   0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
   1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
   1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
   1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
   1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
   1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
   1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
   1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
   1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
   1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
   1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
   0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))

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job log

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actions all output return to Derivational Complexity: TRS