Runti Compl Inner Rewri 22807 pair #381904828

details

property	value
status	complete
benchmark	Ex7_BLR02_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.005340815 seconds
cpu usage	330.839873772
max memory	5.767774208E9

stage attributes

key	value
output-size	16675
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (8) CdtProblem
    (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 60 ms]
    (12) CdtProblem
    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 38 ms]
    (14) CdtProblem
    (15) CdtKnowledgeProof [FINISHED, 0 ms]
    (16) BOUNDS(1, 1)
(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(18) TRS for Loop Detection
    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (20) BEST
        (21) proven lower bound
            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
            (23) BOUNDS(n^1, INF)
        (24) TRS for Loop Detection


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   from(X) -> cons(X, n__from(s(X)))
   head(cons(X, XS)) -> X
   2nd(cons(X, XS)) -> head(activate(XS))
   take(0, XS) -> nil
   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
   sel(0, cons(X, XS)) -> X
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
   from(X) -> n__from(X)
   take(X1, X2) -> n__take(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__take(X1, X2)) -> take(X1, X2)
   activate(X) -> X

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   head(cons(z0, z1)) -> z0
   2nd(cons(z0, z1)) -> head(activate(z1))
   take(0, z0) -> nil
   take(s(z0), cons(z1, z2)) -> cons(z1, n__take(z0, activate(z2)))
   take(z0, z1) -> n__take(z0, z1)
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   activate(n__from(z0)) -> from(z0)
   activate(n__take(z0, z1)) -> take(z0, z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   HEAD(cons(z0, z1)) -> c2
   2ND(cons(z0, z1)) -> c3(HEAD(activate(z1)), ACTIVATE(z1))
   TAKE(0, z0) -> c4
   TAKE(s(z0), cons(z1, z2)) -> c5(ACTIVATE(z2))
   TAKE(z0, z1) -> c6
   SEL(0, cons(z0, z1)) -> c7
   SEL(s(z0), cons(z1, z2)) -> c8(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__from(z0)) -> c9(FROM(z0))
   ACTIVATE(n__take(z0, z1)) -> c10(TAKE(z0, z1))
   ACTIVATE(z0) -> c11

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