details

property	value
status	complete
benchmark	fold.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.14487 seconds
cpu usage	15.8041
user time	14.9069
system time	0.897237
max virtual memory	1.9176608E7
max residence set size	2838160.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (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, 213 ms] (10) BOUNDS(1, n^1) (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^1). The TRS R consists of the following rules: foldl(x, Cons(S(0), xs)) -> foldl(S(x), xs) foldl(S(0), Cons(x, xs)) -> foldl(S(x), xs) foldr(a, Cons(x, xs)) -> op(x, foldr(a, xs)) foldr(a, Nil) -> a foldl(a, Nil) -> a notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False op(x, S(0)) -> S(x) op(S(0), y) -> S(y) fold(a, xs) -> Cons(foldl(a, xs), Cons(foldr(a, xs), Nil)) 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^1). The TRS R consists of the following rules: foldl(x, Cons(S(0), xs)) -> foldl(S(x), xs) [1] foldl(S(0), Cons(x, xs)) -> foldl(S(x), xs) [1] foldr(a, Cons(x, xs)) -> op(x, foldr(a, xs)) [1] foldr(a, Nil) -> a [1] foldl(a, Nil) -> a [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] op(x, S(0)) -> S(x) [1] op(S(0), y) -> S(y) [1] fold(a, xs) -> Cons(foldl(a, xs), Cons(foldr(a, xs), Nil)) [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: foldl(x, Cons(S(0), xs)) -> foldl(S(x), xs) [1] foldl(S(0), Cons(x, xs)) -> foldl(S(x), xs) [1] foldr(a, Cons(x, xs)) -> op(x, foldr(a, xs)) [1] foldr(a, Nil) -> a [1] foldl(a, Nil) -> a [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] op(x, S(0)) -> S(x) [1] op(S(0), y) -> S(y) [1] fold(a, xs) -> Cons(foldl(a, xs), Cons(foldr(a, xs), Nil)) [1] The TRS has the following type information: foldl :: 0:S -> Cons:Nil -> 0:S Cons :: 0:S -> Cons:Nil -> Cons:Nil popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost