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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313846
details
property
value
status
complete
benchmark
cade08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n165.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.548 seconds
cpu usage
1115.87
user time
1102.67
system time
13.1998
max virtual memory
5.7304612E7
max residence set size
1.5109848E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1115.63/291.46 WORST_CASE(Omega(n^1), O(n^2)) 1115.63/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1115.63/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.63/291.47 1115.63/291.47 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.47 1115.63/291.47 (0) CpxTRS 1115.63/291.47 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.63/291.47 (2) CpxWeightedTrs 1115.63/291.47 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.63/291.47 (4) CpxTypedWeightedTrs 1115.63/291.47 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1115.63/291.47 (6) CpxTypedWeightedCompleteTrs 1115.63/291.47 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1115.63/291.47 (8) CpxRNTS 1115.63/291.47 (9) CompleteCoflocoProof [FINISHED, 1980 ms] 1115.63/291.47 (10) BOUNDS(1, n^2) 1115.63/291.47 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1115.63/291.47 (12) TRS for Loop Detection 1115.63/291.47 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1115.63/291.47 (14) BEST 1115.63/291.47 (15) proven lower bound 1115.63/291.47 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.63/291.47 (17) BOUNDS(n^1, INF) 1115.63/291.47 (18) TRS for Loop Detection 1115.63/291.47 1115.63/291.47 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (0) 1115.63/291.47 Obligation: 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.47 1115.63/291.47 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1115.63/291.47 gt(0, v) -> false 1115.63/291.47 gt(s(u), 0) -> true 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) 1115.63/291.47 and(x, true) -> x 1115.63/291.47 and(x, false) -> false 1115.63/291.47 1115.63/291.47 S is empty. 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1115.63/291.47 Transformed relative TRS to weighted TRS 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (2) 1115.63/291.47 Obligation: 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1115.63/291.47 1115.63/291.47 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) [1] 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) [1] 1115.63/291.47 gt(0, v) -> false [1] 1115.63/291.47 gt(s(u), 0) -> true [1] 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) [1] 1115.63/291.47 and(x, true) -> x [1] 1115.63/291.47 and(x, false) -> false [1] 1115.63/291.47 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.63/291.47 Infered types. 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (4) 1115.63/291.47 Obligation: 1115.63/291.47 Runtime Complexity Weighted TRS with Types. 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) [1] 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) [1] 1115.63/291.47 gt(0, v) -> false [1] 1115.63/291.47 gt(s(u), 0) -> true [1] 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) [1] 1115.63/291.47 and(x, true) -> x [1] 1115.63/291.47 and(x, false) -> false [1] 1115.63/291.47 1115.63/291.47 The TRS has the following type information: 1115.63/291.47 f :: true:false -> s:0 -> s:0 -> s:0 -> f 1115.63/291.47 true :: true:false 1115.63/291.47 and :: true:false -> true:false -> true:false 1115.63/291.47 gt :: s:0 -> s:0 -> true:false 1115.63/291.47 s :: s:0 -> s:0 1115.63/291.47 0 :: s:0 1115.63/291.47 false :: true:false 1115.63/291.47 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47
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