details

property	value
status	complete
benchmark	thiemann38.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.566 seconds
cpu usage	1114.63
user time	1102.7
system time	11.9302
max virtual memory	3.7774652E7
max residence set size	9633024.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (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, 563 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 272 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 69 ms] (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: length(nil) -> 0 length(cons(x, l)) -> s(length(l)) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) head(cons(x, l)) -> x head(nil) -> undefined tail(nil) -> nil tail(cons(x, l)) -> l reverse(l) -> rev(0, l, nil, l) rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) if(false, x, l, accu, orig) -> accu 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^2). The TRS R consists of the following rules: length(nil) -> 0 [1] length(cons(x, l)) -> s(length(l)) [1] lt(x, 0) -> false [1] lt(0, s(y)) -> true [1] lt(s(x), s(y)) -> lt(x, y) [1] head(cons(x, l)) -> x [1] head(nil) -> undefined [1] tail(nil) -> nil [1] tail(cons(x, l)) -> l [1] reverse(l) -> rev(0, l, nil, l) [1] rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) [1] if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) [1] if(false, x, l, accu, orig) -> accu [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: length(nil) -> 0 [1] length(cons(x, l)) -> s(length(l)) [1] popout

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actions

all output return to Runtime Complexity: TRS Innermost