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Runti Compl Inner Rewri 22807 pair #381905177
details
property
value
status
complete
benchmark
LISTUTILITIES_nosorts_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.57661294937 seconds
cpu usage
14.479891843
max memory
3.638452224E9
stage attributes
key
value
output-size
17820
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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)), 46 ms] (12) CdtProblem (13) CdtKnowledgeProof [FINISHED, 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 150 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: U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X)) U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) afterNth(N, XS) -> snd(splitAt(N, XS)) and(tt, X) -> activate(X) fst(pair(X, Y)) -> X head(cons(N, XS)) -> N natsFrom(N) -> cons(N, n__natsFrom(s(N))) sel(N, XS) -> head(afterNth(N, XS)) snd(pair(X, Y)) -> Y splitAt(0, XS) -> pair(nil, XS) splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, activate(XS)) tail(cons(N, XS)) -> activate(XS) take(N, XS) -> fst(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: U11(tt, z0, z1, z2) -> U12(splitAt(activate(z0), activate(z2)), activate(z1)) U12(pair(z0, z1), z2) -> pair(cons(activate(z2), z0), z1) afterNth(z0, z1) -> snd(splitAt(z0, z1)) and(tt, z0) -> activate(z0) fst(pair(z0, z1)) -> z0 head(cons(z0, z1)) -> z0 natsFrom(z0) -> cons(z0, n__natsFrom(s(z0))) natsFrom(z0) -> n__natsFrom(z0) sel(z0, z1) -> head(afterNth(z0, z1)) snd(pair(z0, z1)) -> z1 splitAt(0, z0) -> pair(nil, z0) splitAt(s(z0), cons(z1, z2)) -> U11(tt, z0, z1, activate(z2)) tail(cons(z0, z1)) -> activate(z1) take(z0, z1) -> fst(splitAt(z0, z1)) activate(n__natsFrom(z0)) -> natsFrom(z0) activate(z0) -> z0 Tuples: U11'(tt, z0, z1, z2) -> c(U12'(splitAt(activate(z0), activate(z2)), activate(z1)), SPLITAT(activate(z0), activate(z2)), ACTIVATE(z0), ACTIVATE(z2), ACTIVATE(z1)) U12'(pair(z0, z1), z2) -> c1(ACTIVATE(z2)) AFTERNTH(z0, z1) -> c2(SND(splitAt(z0, z1)), SPLITAT(z0, z1)) AND(tt, z0) -> c3(ACTIVATE(z0)) FST(pair(z0, z1)) -> c4 HEAD(cons(z0, z1)) -> c5
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