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Runtime Complexity: TRS Innermost pair #487111656
details
property
value
status
complete
benchmark
dyade.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.585 seconds
cpu usage
365.612
user time
361.89
system time
3.72141
max virtual memory
3.7652148E7
max residence set size
5623384.0
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/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 357 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 1350 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 2 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 209 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 61 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 161 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 2040 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 328 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 553 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 83 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 879 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 597 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (56) CpxRNTS (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 1157 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 177 ms] (62) CpxRNTS (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 1436 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 174 ms] (68) CpxRNTS (69) FinalProof [FINISHED, 0 ms] (70) BOUNDS(1, n^2) (71) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (72) TRS for Loop Detection (73) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (74) BEST (75) proven lower bound (76) LowerBoundPropagationProof [FINISHED, 0 ms] (77) BOUNDS(n^1, INF) (78) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: *(@x, @y) -> #mult(@x, @y) dyade(@l1, @l2) -> dyade#1(@l1, @l2) dyade#1(::(@x, @xs), @l2) -> ::(mult(@x, @l2), dyade(@xs, @l2))
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