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Runtime Complexity: TRS Innermost pair #487112776
details
property
value
status
complete
benchmark
2.20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.75304 seconds
cpu usage
15.5857
user time
14.1278
system time
1.45788
max virtual memory
1.8778052E7
max residence set size
4003104.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (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, 34 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 746 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: sum(0) -> 0 sum(s(x)) -> +(sqr(s(x)), sum(x)) sqr(x) -> *(x, x) sum(s(x)) -> +(*(s(x), s(x)), sum(x)) 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^1). The TRS R consists of the following rules: sum(0) -> 0 [1] sum(s(x)) -> +(sqr(s(x)), sum(x)) [1] sqr(x) -> *(x, x) [1] sum(s(x)) -> +(*(s(x), s(x)), sum(x)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: sum(0) -> 0 [1] sum(s(x)) -> +(sqr(s(x)), sum(x)) [1] sqr(x) -> *(x, x) [1] sum(s(x)) -> +(*(s(x), s(x)), sum(x)) [1] The TRS has the following type information: sum :: 0:s:+ -> 0:s:+ 0 :: 0:s:+ s :: 0:s:+ -> 0:s:+ + :: * -> 0:s:+ -> 0:s:+ sqr :: 0:s:+ -> * * :: 0:s:+ -> 0:s:+ -> * Rewrite Strategy: INNERMOST ---------------------------------------- (5) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: sum(v0) -> null_sum [0] And the following fresh constants: null_sum, const
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