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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313840
details
property
value
status
complete
benchmark
cade10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.775 seconds
cpu usage
1113.06
user time
1099.4
system time
13.6614
max virtual memory
5.700232E7
max residence set size
1.3987876E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1112.86/291.69 WORST_CASE(Omega(n^1), O(n^2)) 1112.86/291.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1112.86/291.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1112.86/291.70 1112.86/291.70 1112.86/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1112.86/291.70 1112.86/291.70 (0) CpxTRS 1112.86/291.70 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.86/291.70 (2) CpxWeightedTrs 1112.86/291.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1112.86/291.70 (4) CpxTypedWeightedTrs 1112.86/291.70 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1112.86/291.70 (6) CpxTypedWeightedCompleteTrs 1112.86/291.70 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] 1112.86/291.70 (8) CpxRNTS 1112.86/291.70 (9) CompleteCoflocoProof [FINISHED, 570 ms] 1112.86/291.70 (10) BOUNDS(1, n^2) 1112.86/291.70 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1112.86/291.70 (12) TRS for Loop Detection 1112.86/291.70 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1112.86/291.70 (14) BEST 1112.86/291.70 (15) proven lower bound 1112.86/291.70 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1112.86/291.70 (17) BOUNDS(n^1, INF) 1112.86/291.70 (18) TRS for Loop Detection 1112.86/291.70 1112.86/291.70 1112.86/291.70 ---------------------------------------- 1112.86/291.70 1112.86/291.70 (0) 1112.86/291.70 Obligation: 1112.86/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1112.86/291.70 1112.86/291.70 1112.86/291.70 The TRS R consists of the following rules: 1112.86/291.70 1112.86/291.70 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) 1112.86/291.70 trunc(0) -> 0 1112.86/291.70 trunc(s(0)) -> 0 1112.86/291.70 trunc(s(s(x))) -> s(s(trunc(x))) 1112.86/291.70 gt(0, v) -> false 1112.86/291.70 gt(s(u), 0) -> true 1112.86/291.70 gt(s(u), s(v)) -> gt(u, v) 1112.86/291.70 1112.86/291.70 S is empty. 1112.86/291.70 Rewrite Strategy: INNERMOST 1112.86/291.70 ---------------------------------------- 1112.86/291.70 1112.86/291.70 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1112.86/291.70 Transformed relative TRS to weighted TRS 1112.86/291.70 ---------------------------------------- 1112.86/291.70 1112.86/291.70 (2) 1112.86/291.70 Obligation: 1112.86/291.70 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1112.86/291.70 1112.86/291.70 1112.86/291.70 The TRS R consists of the following rules: 1112.86/291.70 1112.86/291.70 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) [1] 1112.86/291.70 trunc(0) -> 0 [1] 1112.86/291.70 trunc(s(0)) -> 0 [1] 1112.86/291.70 trunc(s(s(x))) -> s(s(trunc(x))) [1] 1112.86/291.70 gt(0, v) -> false [1] 1112.86/291.70 gt(s(u), 0) -> true [1] 1112.86/291.70 gt(s(u), s(v)) -> gt(u, v) [1] 1112.86/291.70 1112.86/291.70 Rewrite Strategy: INNERMOST 1112.86/291.70 ---------------------------------------- 1112.86/291.70 1112.86/291.70 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1112.86/291.70 Infered types. 1112.86/291.70 ---------------------------------------- 1112.86/291.70 1112.86/291.70 (4) 1112.86/291.70 Obligation: 1112.86/291.70 Runtime Complexity Weighted TRS with Types. 1112.86/291.70 The TRS R consists of the following rules: 1112.86/291.70 1112.86/291.70 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) [1] 1112.86/291.70 trunc(0) -> 0 [1] 1112.86/291.70 trunc(s(0)) -> 0 [1] 1112.86/291.70 trunc(s(s(x))) -> s(s(trunc(x))) [1] 1112.86/291.70 gt(0, v) -> false [1] 1112.86/291.70 gt(s(u), 0) -> true [1] 1112.86/291.70 gt(s(u), s(v)) -> gt(u, v) [1] 1112.86/291.70 1112.86/291.70 The TRS has the following type information: 1112.86/291.70 f :: true:false -> s:0 -> s:0 -> f 1112.86/291.70 true :: true:false 1112.86/291.70 gt :: s:0 -> s:0 -> true:false 1112.86/291.70 trunc :: s:0 -> s:0 1112.86/291.70 s :: s:0 -> s:0 1112.86/291.70 0 :: s:0 1112.86/291.70 false :: true:false 1112.86/291.70 1112.86/291.70 Rewrite Strategy: INNERMOST 1112.86/291.70 ---------------------------------------- 1112.86/291.70
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