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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313740
details
property
value
status
complete
benchmark
otto13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n155.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.592 seconds
cpu usage
1042.92
user time
1027.91
system time
15.0074
max virtual memory
3.7910756E7
max residence set size
1.5015516E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1042.55/291.49 WORST_CASE(Omega(n^1), O(n^2)) 1042.55/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1042.55/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1042.55/291.51 1042.55/291.51 1042.55/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1042.55/291.51 1042.55/291.51 (0) CpxTRS 1042.55/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1042.55/291.51 (2) CpxWeightedTrs 1042.55/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1042.55/291.51 (4) CpxTypedWeightedTrs 1042.55/291.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1042.55/291.51 (6) CpxTypedWeightedCompleteTrs 1042.55/291.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1042.55/291.51 (8) CpxRNTS 1042.55/291.51 (9) CompleteCoflocoProof [FINISHED, 1184 ms] 1042.55/291.51 (10) BOUNDS(1, n^2) 1042.55/291.51 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1042.55/291.51 (12) TRS for Loop Detection 1042.55/291.51 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1042.55/291.51 (14) BEST 1042.55/291.51 (15) proven lower bound 1042.55/291.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1042.55/291.51 (17) BOUNDS(n^1, INF) 1042.55/291.51 (18) TRS for Loop Detection 1042.55/291.51 1042.55/291.51 1042.55/291.51 ---------------------------------------- 1042.55/291.51 1042.55/291.51 (0) 1042.55/291.51 Obligation: 1042.55/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1042.55/291.51 1042.55/291.51 1042.55/291.51 The TRS R consists of the following rules: 1042.55/291.51 1042.55/291.51 le(0, y, z) -> greater(y, z) 1042.55/291.51 le(s(x), 0, z) -> false 1042.55/291.51 le(s(x), s(y), 0) -> false 1042.55/291.51 le(s(x), s(y), s(z)) -> le(x, y, z) 1042.55/291.51 greater(x, 0) -> first 1042.55/291.51 greater(0, s(y)) -> second 1042.55/291.51 greater(s(x), s(y)) -> greater(x, y) 1042.55/291.51 double(0) -> 0 1042.55/291.51 double(s(x)) -> s(s(double(x))) 1042.55/291.51 triple(x) -> if(le(x, x, double(x)), x, 0, 0) 1042.55/291.51 if(false, x, y, z) -> true 1042.55/291.51 if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) 1042.55/291.51 if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) 1042.55/291.51 1042.55/291.51 S is empty. 1042.55/291.51 Rewrite Strategy: INNERMOST 1042.55/291.51 ---------------------------------------- 1042.55/291.51 1042.55/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1042.55/291.51 Transformed relative TRS to weighted TRS 1042.55/291.51 ---------------------------------------- 1042.55/291.51 1042.55/291.51 (2) 1042.55/291.51 Obligation: 1042.55/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1042.55/291.51 1042.55/291.51 1042.55/291.51 The TRS R consists of the following rules: 1042.55/291.51 1042.55/291.51 le(0, y, z) -> greater(y, z) [1] 1042.55/291.51 le(s(x), 0, z) -> false [1] 1042.55/291.51 le(s(x), s(y), 0) -> false [1] 1042.55/291.51 le(s(x), s(y), s(z)) -> le(x, y, z) [1] 1042.55/291.51 greater(x, 0) -> first [1] 1042.55/291.51 greater(0, s(y)) -> second [1] 1042.55/291.51 greater(s(x), s(y)) -> greater(x, y) [1] 1042.55/291.51 double(0) -> 0 [1] 1042.55/291.51 double(s(x)) -> s(s(double(x))) [1] 1042.55/291.51 triple(x) -> if(le(x, x, double(x)), x, 0, 0) [1] 1042.55/291.51 if(false, x, y, z) -> true [1] 1042.55/291.51 if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) [1] 1042.55/291.51 if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) [1] 1042.55/291.51 1042.55/291.51 Rewrite Strategy: INNERMOST 1042.55/291.51 ---------------------------------------- 1042.55/291.51 1042.55/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1042.55/291.51 Infered types. 1042.55/291.51 ---------------------------------------- 1042.55/291.51 1042.55/291.51 (4) 1042.55/291.51 Obligation: 1042.55/291.51 Runtime Complexity Weighted TRS with Types. 1042.55/291.51 The TRS R consists of the following rules: 1042.55/291.51 1042.55/291.51 le(0, y, z) -> greater(y, z) [1] 1042.55/291.51 le(s(x), 0, z) -> false [1] 1042.55/291.51 le(s(x), s(y), 0) -> false [1] 1042.55/291.51 le(s(x), s(y), s(z)) -> le(x, y, z) [1] 1042.55/291.51 greater(x, 0) -> first [1] 1042.55/291.51 greater(0, s(y)) -> second [1] 1042.55/291.51 greater(s(x), s(y)) -> greater(x, y) [1] 1042.55/291.51 double(0) -> 0 [1]
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