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Runtime Complexity: TRS Innermost pair #487112756
details
property
value
status
complete
benchmark
div_notCeTermin.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
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.702 seconds
cpu usage
1139.24
user time
1130.14
system time
9.09708
max virtual memory
5.6802676E7
max residence set size
5757380.0
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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1865 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 403 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 153 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (26) 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: ge(0, 0) -> true ge(s(x), 0) -> ge(x, 0) ge(0, s(0)) -> false ge(0, s(s(x))) -> ge(0, s(x)) ge(s(x), s(y)) -> ge(x, y) minus(0, 0) -> 0 minus(0, s(x)) -> minus(0, x) minus(s(x), 0) -> s(minus(x, 0)) minus(s(x), s(y)) -> minus(x, y) plus(0, 0) -> 0 plus(0, s(x)) -> s(plus(0, x)) plus(s(x), y) -> s(plus(x, y)) div(x, y) -> ify(ge(y, s(0)), x, y) ify(false, x, y) -> divByZeroError ify(true, x, y) -> if(ge(x, y), x, y) if(false, x, y) -> 0 if(true, x, y) -> s(div(minus(x, y), y)) 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^2). The TRS R consists of the following rules: ge(0, 0) -> true [1] ge(s(x), 0) -> ge(x, 0) [1] ge(0, s(0)) -> false [1] ge(0, s(s(x))) -> ge(0, s(x)) [1] ge(s(x), s(y)) -> ge(x, y) [1] minus(0, 0) -> 0 [1] minus(0, s(x)) -> minus(0, x) [1] minus(s(x), 0) -> s(minus(x, 0)) [1] minus(s(x), s(y)) -> minus(x, y) [1] plus(0, 0) -> 0 [1] plus(0, s(x)) -> s(plus(0, x)) [1] plus(s(x), y) -> s(plus(x, y)) [1] div(x, y) -> ify(ge(y, s(0)), x, y) [1] ify(false, x, y) -> divByZeroError [1] ify(true, x, y) -> if(ge(x, y), x, y) [1] if(false, x, y) -> 0 [1] if(true, x, y) -> s(div(minus(x, y), y)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
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