details

property	value
status	complete
benchmark	isort-fold.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	hoca

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.539 seconds
cpu usage	337.984
user time	335.078
system time	2.9068
max virtual memory	3.787918E7
max residence set size	5686740.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 279 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 118 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 1418 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 475 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 473 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 157 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) FinalProof [FINISHED, 0 ms] (40) BOUNDS(1, n^2) (41) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxTRS (43) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (44) typed CpxTrs (45) OrderProof [LOWER BOUND(ID), 0 ms] (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 233 ms] (48) BEST (49) proven lower bound (50) LowerBoundPropagationProof [FINISHED, 0 ms] (51) BOUNDS(n^1, INF) (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 347 ms] (54) BOUNDS(1, INF) ---------------------------------------- (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: fold#3(insert_ord(x2), Nil) -> Nil fold#3(insert_ord(x6), Cons(x4, x2)) -> insert_ord#2(x6, x4, fold#3(insert_ord(x6), x2)) cond_insert_ord_x_ys_1(True, x3, x2, x1) -> Cons(x3, Cons(x2, x1)) cond_insert_ord_x_ys_1(False, x0, x5, x2) -> Cons(x5, insert_ord#2(leq, x0, x2)) insert_ord#2(leq, x2, Nil) -> Cons(x2, Nil) insert_ord#2(leq, x6, Cons(x4, x2)) -> cond_insert_ord_x_ys_1(leq#2(x6, x4), x6, x4, x2) leq#2(0, x8) -> True leq#2(S(x12), 0) -> False leq#2(S(x4), S(x2)) -> leq#2(x4, x2) main(x3) -> fold#3(insert_ord(leq), x3) 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: fold#3(insert_ord(x2), Nil) -> Nil [1] popout

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job log

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actions

all output return to Runtime Complexity: TRS Innermost