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Runtime Complexity: TRS Innermost pair #487111686
details
property
value
status
complete
benchmark
thiemann15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.524 seconds
cpu usage
1003.29
user time
997.975
system time
5.31425
max virtual memory
3.8239692E7
max residence set size
5720448.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) InliningProof [UPPER BOUND(ID), 69 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 279 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 47 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 198 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 1193 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 590 ms] (46) CpxRNTS (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 28 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) FinalProof [FINISHED, 0 ms] (54) BOUNDS(1, n^2) (55) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxTRS (57) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (58) typed CpxTrs (59) OrderProof [LOWER BOUND(ID), 0 ms] (60) typed CpxTrs (61) RewriteLemmaProof [LOWER BOUND(ID), 297 ms] (62) BEST (63) proven lower bound (64) LowerBoundPropagationProof [FINISHED, 0 ms] (65) BOUNDS(n^1, INF) (66) typed CpxTrs (67) RewriteLemmaProof [LOWER BOUND(ID), 39 ms] (68) typed CpxTrs ---------------------------------------- (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: half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) inc(0) -> 0 inc(s(x)) -> s(inc(x)) zero(0) -> true zero(s(x)) -> false p(0) -> 0 p(s(x)) -> x bits(x) -> bitIter(x, 0) bitIter(x, y) -> if(zero(x), x, inc(y)) if(true, x, y) -> p(y) if(false, x, y) -> bitIter(half(x), y)
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