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	n140.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.741 seconds
cpu usage	1110.11
user time	1103.39
system time	6.72215
max virtual memory	3.8043872E7
max residence set size	6216356.0

stage attributes

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

output

WORST_CASE(Omega(n^2), O(n^3)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 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), 4 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 331 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 178 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 321 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 137 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 436 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 204 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 696 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 173 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 1219 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 375 ms] (44) CpxRNTS (45) FinalProof [FINISHED, 0 ms] (46) BOUNDS(1, n^3) (47) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTRS (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (50) typed CpxTrs (51) OrderProof [LOWER BOUND(ID), 0 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 262 ms] (54) BEST (55) proven lower bound (56) LowerBoundPropagationProof [FINISHED, 0 ms] (57) BOUNDS(n^1, INF) (58) typed CpxTrs (59) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] (60) typed CpxTrs (61) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] (62) typed CpxTrs (63) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] (64) proven lower bound (65) LowerBoundPropagationProof [FINISHED, 0 ms] (66) 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) 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