Derivational Complexity: TRS Innermost pair #487106780

details

property	value
status	complete
benchmark	157388.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	4.49572 seconds
cpu usage	14.7588
user time	13.7604
system time	0.998471
max virtual memory	1.8414612E7
max residence set size	3721112.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 70 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 947 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 7 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 (innermost) 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(1(x1)))) -> 0(0(2(1(3(1(x1))))))
   0(1(0(1(x1)))) -> 2(1(0(2(0(1(x1))))))
   0(1(0(1(x1)))) -> 2(1(3(1(0(0(x1))))))
   4(1(0(1(x1)))) -> 1(0(4(2(1(x1)))))
   4(1(0(1(x1)))) -> 4(1(0(2(1(x1)))))
   4(1(0(1(x1)))) -> 0(2(1(3(4(1(x1))))))
   4(1(0(1(x1)))) -> 0(4(2(1(3(1(x1))))))
   4(1(0(1(x1)))) -> 1(0(2(4(1(3(x1))))))
   4(1(0(1(x1)))) -> 1(0(4(2(2(1(x1))))))
   4(1(0(1(x1)))) -> 1(0(4(5(2(1(x1))))))
   4(1(0(1(x1)))) -> 4(0(2(1(3(1(x1))))))
   4(1(0(1(x1)))) -> 4(1(0(2(1(3(x1))))))
   4(1(0(1(x1)))) -> 4(1(3(0(2(1(x1))))))
   4(1(1(1(x1)))) -> 4(1(3(1(3(1(x1))))))
   4(3(0(1(x1)))) -> 0(2(1(3(4(x1)))))
   4(3(0(1(x1)))) -> 0(2(4(1(3(x1)))))
   4(3(0(1(x1)))) -> 0(4(2(1(3(x1)))))
   4(3(0(1(x1)))) -> 3(0(4(2(1(x1)))))
   4(3(0(1(x1)))) -> 3(4(0(2(1(x1)))))
   4(3(0(1(x1)))) -> 4(0(2(1(3(x1)))))
   4(3(0(1(x1)))) -> 4(3(0(2(1(x1)))))
   4(3(0(1(x1)))) -> 0(2(1(3(3(4(x1))))))
   4(3(0(1(x1)))) -> 0(2(1(3(4(3(x1))))))
   4(3(0(1(x1)))) -> 0(2(4(1(3(3(x1))))))
   4(3(0(1(x1)))) -> 0(4(2(2(1(3(x1))))))
   4(3(0(1(x1)))) -> 0(4(5(2(1(3(x1))))))
   4(3(0(1(x1)))) -> 1(0(2(1(3(4(x1))))))
   4(3(0(1(x1)))) -> 1(0(2(4(1(3(x1))))))
   4(3(0(1(x1)))) -> 1(0(4(2(1(3(x1))))))
   4(3(0(1(x1)))) -> 1(3(0(4(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(0(4(5(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(1(0(4(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(3(4(0(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(4(0(2(1(3(x1))))))
   4(3(0(1(x1)))) -> 3(4(0(2(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(4(0(5(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(4(1(0(2(1(x1))))))
   4(3(0(1(x1)))) -> 3(4(3(0(2(1(x1))))))
   4(3(0(1(x1)))) -> 4(3(0(2(1(3(x1))))))
   4(3(0(1(x1)))) -> 4(3(0(5(2(1(x1))))))
   4(3(0(1(x1)))) -> 4(3(1(0(2(1(x1))))))
   4(3(0(1(x1)))) -> 4(3(3(0(2(1(x1))))))
   4(5(1(1(x1)))) -> 4(5(2(1(1(x1)))))
   4(5(1(1(x1)))) -> 4(2(5(2(1(1(x1))))))
   4(5(1(1(x1)))) -> 4(5(2(1(3(1(x1))))))
   4(5(1(1(x1)))) -> 4(5(2(2(1(1(x1))))))
   4(5(1(1(x1)))) -> 4(5(5(2(1(1(x1))))))
   0(0(1(0(1(x1))))) -> 0(0(1(0(2(1(x1))))))
   0(0(3(1(1(x1))))) -> 2(1(3(1(0(0(x1))))))
   0(0(5(1(1(x1))))) -> 5(0(0(2(1(1(x1))))))
   0(4(1(0(1(x1))))) -> 2(1(0(4(0(1(x1))))))
   0(4(3(0(1(x1))))) -> 0(0(2(1(3(4(x1))))))
   0(4(3(0(1(x1))))) -> 0(4(3(0(2(1(x1))))))
   0(4(3(0(1(x1))))) -> 2(3(1(0(4(0(x1))))))
   0(4(3(1(1(x1))))) -> 2(1(4(1(3(0(x1))))))
   0(4(3(1(1(x1))))) -> 4(2(0(3(1(1(x1))))))
   0(4(5(1(1(x1))))) -> 4(0(1(5(2(1(x1))))))
   0(4(5(1(1(x1))))) -> 5(2(1(4(0(1(x1))))))
   4(0(3(0(1(x1))))) -> 0(0(4(2(1(3(x1))))))
   4(0(3(0(1(x1))))) -> 2(0(4(0(1(3(x1))))))
   4(0(3(0(1(x1))))) -> 2(0(4(0(3(1(x1))))))
   4(1(0(1(1(x1))))) -> 1(0(4(2(1(1(x1))))))
   4(1(1(0(1(x1))))) -> 4(1(0(2(1(1(x1))))))
   4(1(2(0(1(x1))))) -> 0(4(2(1(3(1(x1))))))
   4(1(2(0(1(x1))))) -> 1(0(2(4(1(3(x1))))))

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