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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313918
details
property
value
status
complete
benchmark
divhard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.61 seconds
cpu usage
1135.43
user time
1121.99
system time
13.4371
max virtual memory
3.7842016E7
max residence set size
1.3554116E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1134.97/291.49 WORST_CASE(Omega(n^1), O(n^3)) 1134.97/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1134.97/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1134.97/291.53 1134.97/291.53 1134.97/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1134.97/291.53 1134.97/291.53 (0) CpxTRS 1134.97/291.53 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1134.97/291.53 (2) CpxWeightedTrs 1134.97/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1134.97/291.53 (4) CpxTypedWeightedTrs 1134.97/291.53 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1134.97/291.53 (6) CpxTypedWeightedCompleteTrs 1134.97/291.53 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1134.97/291.53 (8) CpxRNTS 1134.97/291.53 (9) CompleteCoflocoProof [FINISHED, 616 ms] 1134.97/291.53 (10) BOUNDS(1, n^3) 1134.97/291.53 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1134.97/291.53 (12) TRS for Loop Detection 1134.97/291.53 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1134.97/291.53 (14) BEST 1134.97/291.53 (15) proven lower bound 1134.97/291.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1134.97/291.53 (17) BOUNDS(n^1, INF) 1134.97/291.53 (18) TRS for Loop Detection 1134.97/291.53 1134.97/291.53 1134.97/291.53 ---------------------------------------- 1134.97/291.53 1134.97/291.53 (0) 1134.97/291.53 Obligation: 1134.97/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1134.97/291.53 1134.97/291.53 1134.97/291.53 The TRS R consists of the following rules: 1134.97/291.53 1134.97/291.53 minus(x, y) -> if(gt(x, y), x, y) 1134.97/291.53 if(true, x, y) -> s(minus(p(x), y)) 1134.97/291.53 if(false, x, y) -> 0 1134.97/291.53 p(0) -> 0 1134.97/291.53 p(s(x)) -> x 1134.97/291.53 ge(x, 0) -> true 1134.97/291.53 ge(0, s(x)) -> false 1134.97/291.53 ge(s(x), s(y)) -> ge(x, y) 1134.97/291.53 gt(0, y) -> false 1134.97/291.53 gt(s(x), 0) -> true 1134.97/291.53 gt(s(x), s(y)) -> gt(x, y) 1134.97/291.53 div(x, y) -> if1(ge(x, y), x, y) 1134.97/291.53 if1(true, x, y) -> if2(gt(y, 0), x, y) 1134.97/291.53 if1(false, x, y) -> 0 1134.97/291.53 if2(true, x, y) -> s(div(minus(x, y), y)) 1134.97/291.53 if2(false, x, y) -> 0 1134.97/291.53 1134.97/291.53 S is empty. 1134.97/291.53 Rewrite Strategy: INNERMOST 1134.97/291.53 ---------------------------------------- 1134.97/291.53 1134.97/291.53 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1134.97/291.53 Transformed relative TRS to weighted TRS 1134.97/291.53 ---------------------------------------- 1134.97/291.53 1134.97/291.53 (2) 1134.97/291.53 Obligation: 1134.97/291.53 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1134.97/291.53 1134.97/291.53 1134.97/291.53 The TRS R consists of the following rules: 1134.97/291.53 1134.97/291.53 minus(x, y) -> if(gt(x, y), x, y) [1] 1134.97/291.53 if(true, x, y) -> s(minus(p(x), y)) [1] 1134.97/291.53 if(false, x, y) -> 0 [1] 1134.97/291.53 p(0) -> 0 [1] 1134.97/291.53 p(s(x)) -> x [1] 1134.97/291.53 ge(x, 0) -> true [1] 1134.97/291.53 ge(0, s(x)) -> false [1] 1134.97/291.53 ge(s(x), s(y)) -> ge(x, y) [1] 1134.97/291.53 gt(0, y) -> false [1] 1134.97/291.53 gt(s(x), 0) -> true [1] 1134.97/291.53 gt(s(x), s(y)) -> gt(x, y) [1] 1134.97/291.53 div(x, y) -> if1(ge(x, y), x, y) [1] 1134.97/291.53 if1(true, x, y) -> if2(gt(y, 0), x, y) [1] 1134.97/291.53 if1(false, x, y) -> 0 [1] 1134.97/291.53 if2(true, x, y) -> s(div(minus(x, y), y)) [1] 1134.97/291.53 if2(false, x, y) -> 0 [1] 1134.97/291.53 1134.97/291.53 Rewrite Strategy: INNERMOST 1134.97/291.53 ---------------------------------------- 1134.97/291.53 1134.97/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1134.97/291.53 Infered types. 1134.97/291.53 ---------------------------------------- 1134.97/291.53 1134.97/291.53 (4) 1134.97/291.53 Obligation: 1134.97/291.53 Runtime Complexity Weighted TRS with Types. 1134.97/291.53 The TRS R consists of the following rules: 1134.97/291.53 1134.97/291.53 minus(x, y) -> if(gt(x, y), x, y) [1] 1134.97/291.53 if(true, x, y) -> s(minus(p(x), y)) [1]
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