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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313919
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.638 seconds
cpu usage
1140.52
user time
1126.25
system time
14.2702
max virtual memory
5.699992E7
max residence set size
1.5031712E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1140.10/291.55 WORST_CASE(Omega(n^1), O(n^3)) 1140.36/291.56 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1140.36/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1140.36/291.56 1140.36/291.56 1140.36/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1140.36/291.56 1140.36/291.56 (0) CpxTRS 1140.36/291.56 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1140.36/291.56 (2) CpxWeightedTrs 1140.36/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1140.36/291.56 (4) CpxTypedWeightedTrs 1140.36/291.56 (5) CompletionProof [UPPER BOUND(ID), 8 ms] 1140.36/291.56 (6) CpxTypedWeightedCompleteTrs 1140.36/291.56 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1140.36/291.56 (8) CpxRNTS 1140.36/291.56 (9) CompleteCoflocoProof [FINISHED, 1595 ms] 1140.36/291.56 (10) BOUNDS(1, n^3) 1140.36/291.56 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1140.36/291.56 (12) TRS for Loop Detection 1140.36/291.56 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1140.36/291.56 (14) BEST 1140.36/291.56 (15) proven lower bound 1140.36/291.56 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1140.36/291.56 (17) BOUNDS(n^1, INF) 1140.36/291.56 (18) TRS for Loop Detection 1140.36/291.56 1140.36/291.56 1140.36/291.56 ---------------------------------------- 1140.36/291.56 1140.36/291.56 (0) 1140.36/291.56 Obligation: 1140.36/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1140.36/291.56 1140.36/291.56 1140.36/291.56 The TRS R consists of the following rules: 1140.36/291.56 1140.36/291.56 minus(s(x), y) -> if(gt(s(x), y), x, y) 1140.36/291.56 if(true, x, y) -> s(minus(x, y)) 1140.36/291.56 if(false, x, y) -> 0 1140.36/291.56 gcd(x, y) -> if1(ge(x, y), x, y) 1140.36/291.56 if1(true, x, y) -> if2(gt(y, 0), x, y) 1140.36/291.56 if1(false, x, y) -> gcd(y, x) 1140.36/291.56 if2(true, x, y) -> gcd(minus(x, y), y) 1140.36/291.56 if2(false, x, y) -> x 1140.36/291.56 gt(0, y) -> false 1140.36/291.56 gt(s(x), 0) -> true 1140.36/291.56 gt(s(x), s(y)) -> gt(x, y) 1140.36/291.56 ge(x, 0) -> true 1140.36/291.56 ge(0, s(x)) -> false 1140.36/291.56 ge(s(x), s(y)) -> ge(x, y) 1140.36/291.56 1140.36/291.56 S is empty. 1140.36/291.56 Rewrite Strategy: INNERMOST 1140.36/291.56 ---------------------------------------- 1140.36/291.56 1140.36/291.56 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1140.36/291.56 Transformed relative TRS to weighted TRS 1140.36/291.56 ---------------------------------------- 1140.36/291.56 1140.36/291.56 (2) 1140.36/291.56 Obligation: 1140.36/291.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1140.36/291.56 1140.36/291.56 1140.36/291.56 The TRS R consists of the following rules: 1140.36/291.56 1140.36/291.56 minus(s(x), y) -> if(gt(s(x), y), x, y) [1] 1140.36/291.56 if(true, x, y) -> s(minus(x, y)) [1] 1140.36/291.56 if(false, x, y) -> 0 [1] 1140.36/291.56 gcd(x, y) -> if1(ge(x, y), x, y) [1] 1140.36/291.56 if1(true, x, y) -> if2(gt(y, 0), x, y) [1] 1140.36/291.56 if1(false, x, y) -> gcd(y, x) [1] 1140.36/291.56 if2(true, x, y) -> gcd(minus(x, y), y) [1] 1140.36/291.56 if2(false, x, y) -> x [1] 1140.36/291.56 gt(0, y) -> false [1] 1140.36/291.56 gt(s(x), 0) -> true [1] 1140.36/291.56 gt(s(x), s(y)) -> gt(x, y) [1] 1140.36/291.56 ge(x, 0) -> true [1] 1140.36/291.56 ge(0, s(x)) -> false [1] 1140.36/291.56 ge(s(x), s(y)) -> ge(x, y) [1] 1140.36/291.56 1140.36/291.56 Rewrite Strategy: INNERMOST 1140.36/291.56 ---------------------------------------- 1140.36/291.56 1140.36/291.56 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1140.36/291.56 Infered types. 1140.36/291.56 ---------------------------------------- 1140.36/291.56 1140.36/291.56 (4) 1140.36/291.56 Obligation: 1140.36/291.56 Runtime Complexity Weighted TRS with Types. 1140.36/291.56 The TRS R consists of the following rules: 1140.36/291.56 1140.36/291.56 minus(s(x), y) -> if(gt(s(x), y), x, y) [1] 1140.36/291.56 if(true, x, y) -> s(minus(x, y)) [1] 1140.36/291.56 if(false, x, y) -> 0 [1] 1140.36/291.56 gcd(x, y) -> if1(ge(x, y), x, y) [1] 1140.36/291.56 if1(true, x, y) -> if2(gt(y, 0), x, y) [1] 1140.36/291.56 if1(false, x, y) -> gcd(y, x) [1]
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