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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313836
details
property
value
status
complete
benchmark
cade14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.642 seconds
cpu usage
1117.85
user time
1107.93
system time
9.91101
max virtual memory
5.6408728E7
max residence set size
1.0446244E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1117.53/291.56 WORST_CASE(Omega(n^1), O(n^2)) 1117.53/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1117.53/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1117.53/291.57 1117.53/291.57 1117.53/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1117.53/291.57 1117.53/291.57 (0) CpxTRS 1117.53/291.57 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1117.53/291.57 (2) CpxWeightedTrs 1117.53/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1117.53/291.57 (4) CpxTypedWeightedTrs 1117.53/291.57 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1117.53/291.57 (6) CpxTypedWeightedCompleteTrs 1117.53/291.57 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1117.53/291.57 (8) CpxRNTS 1117.53/291.57 (9) CompleteCoflocoProof [FINISHED, 544 ms] 1117.53/291.57 (10) BOUNDS(1, n^2) 1117.53/291.57 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1117.53/291.57 (12) TRS for Loop Detection 1117.53/291.57 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1117.53/291.57 (14) BEST 1117.53/291.57 (15) proven lower bound 1117.53/291.57 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1117.53/291.57 (17) BOUNDS(n^1, INF) 1117.53/291.57 (18) TRS for Loop Detection 1117.53/291.57 1117.53/291.57 1117.53/291.57 ---------------------------------------- 1117.72/291.58 1117.72/291.58 (0) 1117.72/291.58 Obligation: 1117.72/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1117.72/291.58 1117.72/291.58 1117.72/291.58 The TRS R consists of the following rules: 1117.72/291.58 1117.72/291.58 diff(x, y) -> cond1(equal(x, y), x, y) 1117.72/291.58 cond1(true, x, y) -> 0 1117.72/291.58 cond1(false, x, y) -> cond2(gt(x, y), x, y) 1117.72/291.58 cond2(true, x, y) -> s(diff(x, s(y))) 1117.72/291.58 cond2(false, x, y) -> s(diff(s(x), y)) 1117.72/291.58 gt(0, v) -> false 1117.72/291.58 gt(s(u), 0) -> true 1117.72/291.58 gt(s(u), s(v)) -> gt(u, v) 1117.72/291.58 equal(0, 0) -> true 1117.72/291.58 equal(s(x), 0) -> false 1117.72/291.58 equal(0, s(y)) -> false 1117.72/291.58 equal(s(x), s(y)) -> equal(x, y) 1117.72/291.58 1117.72/291.58 S is empty. 1117.72/291.58 Rewrite Strategy: INNERMOST 1117.72/291.58 ---------------------------------------- 1117.72/291.58 1117.72/291.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1117.72/291.58 Transformed relative TRS to weighted TRS 1117.72/291.58 ---------------------------------------- 1117.72/291.58 1117.72/291.58 (2) 1117.72/291.58 Obligation: 1117.72/291.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1117.72/291.58 1117.72/291.58 1117.72/291.58 The TRS R consists of the following rules: 1117.72/291.58 1117.72/291.58 diff(x, y) -> cond1(equal(x, y), x, y) [1] 1117.72/291.58 cond1(true, x, y) -> 0 [1] 1117.72/291.58 cond1(false, x, y) -> cond2(gt(x, y), x, y) [1] 1117.72/291.58 cond2(true, x, y) -> s(diff(x, s(y))) [1] 1117.72/291.58 cond2(false, x, y) -> s(diff(s(x), y)) [1] 1117.72/291.58 gt(0, v) -> false [1] 1117.72/291.58 gt(s(u), 0) -> true [1] 1117.72/291.58 gt(s(u), s(v)) -> gt(u, v) [1] 1117.72/291.58 equal(0, 0) -> true [1] 1117.72/291.58 equal(s(x), 0) -> false [1] 1117.72/291.58 equal(0, s(y)) -> false [1] 1117.72/291.58 equal(s(x), s(y)) -> equal(x, y) [1] 1117.72/291.58 1117.72/291.58 Rewrite Strategy: INNERMOST 1117.72/291.58 ---------------------------------------- 1117.72/291.58 1117.72/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1117.72/291.58 Infered types. 1117.72/291.58 ---------------------------------------- 1117.72/291.58 1117.72/291.58 (4) 1117.72/291.58 Obligation: 1117.72/291.58 Runtime Complexity Weighted TRS with Types. 1117.72/291.58 The TRS R consists of the following rules: 1117.72/291.58 1117.72/291.58 diff(x, y) -> cond1(equal(x, y), x, y) [1] 1117.72/291.58 cond1(true, x, y) -> 0 [1] 1117.72/291.58 cond1(false, x, y) -> cond2(gt(x, y), x, y) [1] 1117.72/291.58 cond2(true, x, y) -> s(diff(x, s(y))) [1] 1117.72/291.58 cond2(false, x, y) -> s(diff(s(x), y)) [1] 1117.72/291.58 gt(0, v) -> false [1] 1117.72/291.58 gt(s(u), 0) -> true [1] 1117.72/291.58 gt(s(u), s(v)) -> gt(u, v) [1] 1117.72/291.58 equal(0, 0) -> true [1] 1117.72/291.58 equal(s(x), 0) -> false [1]
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