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Runti Compl Inner Rewri 22807 pair #381904234
details
property
value
status
complete
benchmark
aprove10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
297.286720991 seconds
cpu usage
912.560691731
max memory
1.4942900224E10
stage attributes
key
value
output-size
41137
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
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^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 3646 ms] (10) BOUNDS(1, n^3) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: lessElements(l, t) -> lessE(l, t, 0) lessE(l, t, n) -> if(le(length(l), n), le(length(toList(t)), n), l, t, n) if(true, b, l, t, n) -> l if(false, true, l, t, n) -> t if(false, false, l, t, n) -> lessE(l, t, s(n)) length(nil) -> 0 length(cons(n, l)) -> s(length(l)) toList(leaf) -> nil toList(node(t1, n, t2)) -> append(toList(t1), cons(n, toList(t2))) append(nil, l2) -> l2 append(cons(n, l1), l2) -> cons(n, append(l1, l2)) le(s(n), 0) -> false le(0, m) -> true le(s(n), s(m)) -> le(n, m) a -> c a -> d S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: lessElements(l, t) -> lessE(l, t, 0) [1] lessE(l, t, n) -> if(le(length(l), n), le(length(toList(t)), n), l, t, n) [1] if(true, b, l, t, n) -> l [1] if(false, true, l, t, n) -> t [1] if(false, false, l, t, n) -> lessE(l, t, s(n)) [1] length(nil) -> 0 [1] length(cons(n, l)) -> s(length(l)) [1] toList(leaf) -> nil [1] toList(node(t1, n, t2)) -> append(toList(t1), cons(n, toList(t2))) [1] append(nil, l2) -> l2 [1] append(cons(n, l1), l2) -> cons(n, append(l1, l2)) [1] le(s(n), 0) -> false [1] le(0, m) -> true [1] le(s(n), s(m)) -> le(n, m) [1] a -> c [1] a -> d [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4)
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