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Runti Compl Inner Rewri 22807 pair #381905237
details
property
value
status
complete
benchmark
ExSec4_2_DLMMU04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.15143013 seconds
cpu usage
12.250040767
max memory
3.209576448E9
stage attributes
key
value
output-size
15337
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (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)), 35 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: natsFrom(N) -> cons(N, n__natsFrom(s(N))) fst(pair(XS, YS)) -> XS snd(pair(XS, YS)) -> YS splitAt(0, XS) -> pair(nil, XS) splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS)) u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS) head(cons(N, XS)) -> N tail(cons(N, XS)) -> activate(XS) sel(N, XS) -> head(afterNth(N, XS)) take(N, XS) -> fst(splitAt(N, XS)) afterNth(N, XS) -> snd(splitAt(N, XS)) natsFrom(X) -> n__natsFrom(X) activate(n__natsFrom(X)) -> natsFrom(X) 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: natsFrom(z0) -> cons(z0, n__natsFrom(s(z0))) natsFrom(z0) -> n__natsFrom(z0) fst(pair(z0, z1)) -> z0 snd(pair(z0, z1)) -> z1 splitAt(0, z0) -> pair(nil, z0) splitAt(s(z0), cons(z1, z2)) -> u(splitAt(z0, activate(z2)), z0, z1, activate(z2)) u(pair(z0, z1), z2, z3, z4) -> pair(cons(activate(z3), z0), z1) head(cons(z0, z1)) -> z0 tail(cons(z0, z1)) -> activate(z1) sel(z0, z1) -> head(afterNth(z0, z1)) take(z0, z1) -> fst(splitAt(z0, z1)) afterNth(z0, z1) -> snd(splitAt(z0, z1)) activate(n__natsFrom(z0)) -> natsFrom(z0) activate(z0) -> z0 Tuples: NATSFROM(z0) -> c NATSFROM(z0) -> c1 FST(pair(z0, z1)) -> c2 SND(pair(z0, z1)) -> c3 SPLITAT(0, z0) -> c4 SPLITAT(s(z0), cons(z1, z2)) -> c5(U(splitAt(z0, activate(z2)), z0, z1, activate(z2)), SPLITAT(z0, activate(z2)), ACTIVATE(z2), ACTIVATE(z2)) U(pair(z0, z1), z2, z3, z4) -> c6(ACTIVATE(z3)) HEAD(cons(z0, z1)) -> c7 TAIL(cons(z0, z1)) -> c8(ACTIVATE(z1)) SEL(z0, z1) -> c9(HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
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