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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313796
details
property
value
status
complete
benchmark
overlap.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.526 seconds
cpu usage
327.694
user time
324.11
system time
3.58444
max virtual memory
1.9212468E7
max residence set size
5571144.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
327.54/291.46 WORST_CASE(Omega(n^1), O(n^2)) 327.54/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 327.54/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 327.54/291.47 327.54/291.47 327.54/291.47 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 327.54/291.47 327.54/291.47 (0) CpxRelTRS 327.54/291.47 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 204 ms] 327.54/291.47 (2) CpxRelTRS 327.54/291.47 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (4) CpxWeightedTrs 327.54/291.47 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (6) CpxTypedWeightedTrs 327.54/291.47 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (8) CpxTypedWeightedCompleteTrs 327.54/291.47 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (10) CpxTypedWeightedCompleteTrs 327.54/291.47 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (12) CpxRNTS 327.54/291.47 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (14) CpxRNTS 327.54/291.47 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (16) CpxRNTS 327.54/291.47 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (18) CpxRNTS 327.54/291.47 (19) IntTrsBoundProof [UPPER BOUND(ID), 171 ms] 327.54/291.47 (20) CpxRNTS 327.54/291.47 (21) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] 327.54/291.47 (22) CpxRNTS 327.54/291.47 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (24) CpxRNTS 327.54/291.47 (25) IntTrsBoundProof [UPPER BOUND(ID), 514 ms] 327.54/291.47 (26) CpxRNTS 327.54/291.47 (27) IntTrsBoundProof [UPPER BOUND(ID), 74 ms] 327.54/291.47 (28) CpxRNTS 327.54/291.47 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (30) CpxRNTS 327.54/291.47 (31) IntTrsBoundProof [UPPER BOUND(ID), 1220 ms] 327.54/291.47 (32) CpxRNTS 327.54/291.47 (33) IntTrsBoundProof [UPPER BOUND(ID), 433 ms] 327.54/291.47 (34) CpxRNTS 327.54/291.47 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (36) CpxRNTS 327.54/291.47 (37) IntTrsBoundProof [UPPER BOUND(ID), 1006 ms] 327.54/291.47 (38) CpxRNTS 327.54/291.47 (39) IntTrsBoundProof [UPPER BOUND(ID), 494 ms] 327.54/291.47 (40) CpxRNTS 327.54/291.47 (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (42) CpxRNTS 327.54/291.47 (43) IntTrsBoundProof [UPPER BOUND(ID), 146 ms] 327.54/291.47 (44) CpxRNTS 327.54/291.47 (45) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 327.54/291.47 (46) CpxRNTS 327.54/291.47 (47) FinalProof [FINISHED, 0 ms] 327.54/291.47 (48) BOUNDS(1, n^2) 327.54/291.47 (49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (50) CpxRelTRS 327.54/291.47 (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 327.54/291.47 (52) typed CpxTrs 327.54/291.47 (53) OrderProof [LOWER BOUND(ID), 0 ms] 327.54/291.47 (54) typed CpxTrs 327.54/291.47 (55) RewriteLemmaProof [LOWER BOUND(ID), 285 ms] 327.54/291.47 (56) typed CpxTrs 327.54/291.47 (57) RewriteLemmaProof [LOWER BOUND(ID), 23 ms] 327.54/291.47 (58) BEST 327.54/291.47 (59) proven lower bound 327.54/291.47 (60) LowerBoundPropagationProof [FINISHED, 0 ms] 327.54/291.47 (61) BOUNDS(n^1, INF) 327.54/291.47 (62) typed CpxTrs 327.54/291.47 (63) RewriteLemmaProof [LOWER BOUND(ID), 13 ms] 327.54/291.47 (64) BOUNDS(1, INF) 327.54/291.47 327.54/291.47 327.54/291.47 ---------------------------------------- 327.54/291.47 327.54/291.47 (0) 327.54/291.47 Obligation: 327.54/291.47 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 327.54/291.47 327.54/291.47 327.54/291.47 The TRS R consists of the following rules: 327.54/291.47 327.54/291.47 overlap(Cons(x, xs), ys) -> overlap[Ite][True][Ite](member(x, ys), Cons(x, xs), ys) 327.54/291.47 overlap(Nil, ys) -> False 327.54/291.47 member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x, x'), x', Cons(x, xs)) 327.54/291.47 member(x, Nil) -> False 327.54/291.47 notEmpty(Cons(x, xs)) -> True 327.54/291.47 notEmpty(Nil) -> False 327.54/291.47 goal(xs, ys) -> overlap(xs, ys) 327.54/291.47 327.54/291.47 The (relative) TRS S consists of the following rules: 327.54/291.47 327.54/291.47 !EQ(S(x), S(y)) -> !EQ(x, y) 327.54/291.47 !EQ(0, S(y)) -> False 327.54/291.47 !EQ(S(x), 0) -> False 327.54/291.47 !EQ(0, 0) -> True 327.54/291.47 overlap[Ite][True][Ite](False, Cons(x, xs), ys) -> overlap(xs, ys) 327.54/291.47 member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) 327.54/291.47 overlap[Ite][True][Ite](True, xs, ys) -> True
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
