Runti Compl Inner Rewri 22807 pair #381905163

details

property	value
status	complete
benchmark	Ex1_Luc02b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.954896927 seconds
cpu usage	332.190089339
max memory	5.792137216E9

stage attributes

key	value
output-size	13121
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 58 ms]
    (8) CdtProblem
    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 35 ms]
    (10) CdtProblem
    (11) CdtKnowledgeProof [FINISHED, 0 ms]
    (12) BOUNDS(1, 1)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) 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)))
   first(0, Z) -> nil
   first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
   sel(0, cons(X, Z)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
   from(X) -> n__from(X)
   first(X1, X2) -> n__first(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__first(X1, X2)) -> first(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)
   first(0, z0) -> nil
   first(s(z0), cons(z1, z2)) -> cons(z1, n__first(z0, activate(z2)))
   first(z0, z1) -> n__first(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__first(z0, z1)) -> first(z0, z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   FIRST(0, z0) -> c2
   FIRST(s(z0), cons(z1, z2)) -> c3(ACTIVATE(z2))
   FIRST(z0, z1) -> c4
   SEL(0, cons(z0, z1)) -> c5
   SEL(s(z0), cons(z1, z2)) -> c6(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__from(z0)) -> c7(FROM(z0))
   ACTIVATE(n__first(z0, z1)) -> c8(FIRST(z0, z1))
   ACTIVATE(z0) -> c9
S tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   FIRST(0, z0) -> c2
   FIRST(s(z0), cons(z1, z2)) -> c3(ACTIVATE(z2))
   FIRST(z0, z1) -> c4
   SEL(0, cons(z0, z1)) -> c5
   SEL(s(z0), cons(z1, z2)) -> c6(SEL(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__from(z0)) -> c7(FROM(z0))
   ACTIVATE(n__first(z0, z1)) -> c8(FIRST(z0, z1))

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