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Runti Compl Full Rewri 10127 pair #381903625
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
n040.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.450803041 seconds
cpu usage
302.349297799
max memory
5.430530048E9
stage attributes
key
value
output-size
5310
starexec-result
WORST_CASE(Omega(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), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 302 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 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: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 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: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence U11(tt, s(N1_0), X, cons(X2_0, XS3_0)) ->^+ U12(U11(tt, N1_0, X2_0, XS3_0), activate(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [N1_0 / s(N1_0), XS3_0 / cons(X2_0, XS3_0)]. The result substitution is [X / X2_0].
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