details

property	value
status	complete
benchmark	selsort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	293.276082039 seconds
cpu usage	1133.24956684
max memory	1.5275810816E10

stage attributes

key	value
output-size	51855
starexec-result	WORST_CASE(Omega(n^2), O(n^3))

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^2), O(n^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). (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, 6195 ms] (10) BOUNDS(1, n^3) (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), 318 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), 86 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 52 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (28) proven lower bound (29) LowerBoundPropagationProof [FINISHED, 0 ms] (30) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(Y)) -> false eq(s(X), 0) -> false eq(s(X), s(Y)) -> eq(X, Y) le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) min(cons(0, nil)) -> 0 min(cons(s(N), nil)) -> s(N) min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L))) ifmin(true, cons(N, cons(M, L))) -> min(cons(N, L)) ifmin(false, cons(N, cons(M, L))) -> min(cons(M, L)) replace(N, M, nil) -> nil replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L)) ifrepl(true, N, M, cons(K, L)) -> cons(M, L) ifrepl(false, N, M, cons(K, L)) -> cons(K, replace(N, M, L)) selsort(nil) -> nil selsort(cons(N, L)) -> ifselsort(eq(N, min(cons(N, L))), cons(N, L)) ifselsort(true, cons(N, L)) -> cons(N, selsort(L)) ifselsort(false, cons(N, L)) -> cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) 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^3). The TRS R consists of the following rules: eq(0, 0) -> true [1] eq(0, s(Y)) -> false [1] eq(s(X), 0) -> false [1] eq(s(X), s(Y)) -> eq(X, Y) [1] le(0, Y) -> true [1] le(s(X), 0) -> false [1] le(s(X), s(Y)) -> le(X, Y) [1] min(cons(0, nil)) -> 0 [1] min(cons(s(N), nil)) -> s(N) [1] popout

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job log

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actions

all output return to Runti Compl Inner Rewri 22807