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Runti Compl Full Rewri 10127 pair #381902328
details
property
value
status
timeout (wallclock)
benchmark
aprove10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
301.008447886 seconds
cpu usage
919.349461003
max memory
1.5606136832E10
stage attributes
unavailable
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 3645 ms] (12) BOUNDS(1, n^3) (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 ---------------------------------------- (0) Obligation: The Runtime Complexity (full) 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: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: lessE([], t, n) lessE(l, t, []) lessE(l, [], n) The defined contexts are: if([], x1, x2, x3, x4) le([], x1) if(x0, [], x2, x3, x4) length([]) append([], cons(x1, x2)) append(x0, cons(x1, [])) append([], x1) append(x0, []) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(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
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