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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313917
details
property
value
status
complete
benchmark
mod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.654 seconds
cpu usage
1113.18
user time
1100.06
system time
13.1258
max virtual memory
3.777988E7
max residence set size
1.5124056E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1112.94/291.55 WORST_CASE(Omega(n^1), O(n^3)) 1112.94/291.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1112.94/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1112.94/291.57 1112.94/291.57 1112.94/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1112.94/291.57 1112.94/291.57 (0) CpxTRS 1112.94/291.57 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.94/291.57 (2) CpxWeightedTrs 1112.94/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.94/291.57 (4) CpxTypedWeightedTrs 1112.94/291.57 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1112.94/291.57 (6) CpxTypedWeightedCompleteTrs 1112.94/291.57 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1112.94/291.57 (8) CpxRNTS 1112.94/291.57 (9) CompleteCoflocoProof [FINISHED, 515 ms] 1112.94/291.57 (10) BOUNDS(1, n^3) 1112.94/291.57 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1112.94/291.57 (12) TRS for Loop Detection 1112.94/291.57 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1112.94/291.57 (14) BEST 1112.94/291.57 (15) proven lower bound 1112.94/291.57 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1112.94/291.57 (17) BOUNDS(n^1, INF) 1112.94/291.57 (18) TRS for Loop Detection 1112.94/291.57 1112.94/291.57 1112.94/291.57 ---------------------------------------- 1112.94/291.57 1112.94/291.57 (0) 1112.94/291.57 Obligation: 1112.94/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1112.94/291.57 1112.94/291.57 1112.94/291.57 The TRS R consists of the following rules: 1112.94/291.57 1112.94/291.57 minus(0, y) -> 0 1112.94/291.57 minus(s(x), y) -> if(gt(s(x), y), x, y) 1112.94/291.57 if(true, x, y) -> s(minus(x, y)) 1112.94/291.57 if(false, x, y) -> 0 1112.94/291.57 mod(x, 0) -> 0 1112.94/291.57 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 1112.94/291.57 if1(true, x, y) -> x 1112.94/291.57 if1(false, x, y) -> mod(minus(x, y), y) 1112.94/291.57 gt(0, y) -> false 1112.94/291.57 gt(s(x), 0) -> true 1112.94/291.57 gt(s(x), s(y)) -> gt(x, y) 1112.94/291.57 lt(x, 0) -> false 1112.94/291.57 lt(0, s(x)) -> true 1112.94/291.57 lt(s(x), s(y)) -> lt(x, y) 1112.94/291.57 1112.94/291.57 S is empty. 1112.94/291.57 Rewrite Strategy: INNERMOST 1112.94/291.57 ---------------------------------------- 1112.94/291.57 1112.94/291.57 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1112.94/291.57 Transformed relative TRS to weighted TRS 1112.94/291.57 ---------------------------------------- 1112.94/291.57 1112.94/291.57 (2) 1112.94/291.57 Obligation: 1112.94/291.57 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1112.94/291.57 1112.94/291.57 1112.94/291.57 The TRS R consists of the following rules: 1112.94/291.57 1112.94/291.57 minus(0, y) -> 0 [1] 1112.94/291.57 minus(s(x), y) -> if(gt(s(x), y), x, y) [1] 1112.94/291.57 if(true, x, y) -> s(minus(x, y)) [1] 1112.94/291.57 if(false, x, y) -> 0 [1] 1112.94/291.57 mod(x, 0) -> 0 [1] 1112.94/291.57 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) [1] 1112.94/291.57 if1(true, x, y) -> x [1] 1112.94/291.57 if1(false, x, y) -> mod(minus(x, y), y) [1] 1112.94/291.57 gt(0, y) -> false [1] 1112.94/291.57 gt(s(x), 0) -> true [1] 1112.94/291.57 gt(s(x), s(y)) -> gt(x, y) [1] 1112.94/291.57 lt(x, 0) -> false [1] 1112.94/291.57 lt(0, s(x)) -> true [1] 1112.94/291.57 lt(s(x), s(y)) -> lt(x, y) [1] 1112.94/291.57 1112.94/291.57 Rewrite Strategy: INNERMOST 1112.94/291.57 ---------------------------------------- 1112.94/291.57 1112.94/291.57 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1112.94/291.57 Infered types. 1112.94/291.57 ---------------------------------------- 1112.94/291.57 1112.94/291.57 (4) 1112.94/291.57 Obligation: 1112.94/291.57 Runtime Complexity Weighted TRS with Types. 1112.94/291.57 The TRS R consists of the following rules: 1112.94/291.57 1112.94/291.57 minus(0, y) -> 0 [1] 1112.94/291.57 minus(s(x), y) -> if(gt(s(x), y), x, y) [1] 1112.94/291.57 if(true, x, y) -> s(minus(x, y)) [1] 1112.94/291.57 if(false, x, y) -> 0 [1] 1112.94/291.57 mod(x, 0) -> 0 [1] 1112.94/291.57 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) [1]
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