Derivational Complexity: TRS Innermost pair #487106346

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	n147.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	3.45474 seconds
cpu usage	10.6847
user time	10.0071
system time	0.67761
max virtual memory	1.8676744E7
max residence set size	2505028.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(n^1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 120 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 690 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 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(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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