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	n077.star.cs.uiowa.edu
space	hoca

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.491764069 seconds
cpu usage	333.525666876
max memory	5.63040256E9

stage attributes

key	value
output-size	43733
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 382 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 128 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 1860 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 638 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 645 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), 116 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) FinalProof [FINISHED, 0 ms] (40) BOUNDS(1, n^2) (41) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (42) TRS for Loop Detection (43) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (44) BEST (45) proven lower bound (46) LowerBoundPropagationProof [FINISHED, 0 ms] (47) BOUNDS(n^1, INF) (48) TRS for Loop Detection ---------------------------------------- (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 Runti Compl Inner Rewri 22807