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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313305
details
property
value
status
complete
benchmark
aprove02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n132.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.69 seconds
cpu usage
1122.39
user time
1112.64
system time
9.74515
max virtual memory
3.799608E7
max residence set size
6495656.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^5))
output
1121.53/291.46 WORST_CASE(Omega(n^1), O(n^5)) 1121.85/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1121.85/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1121.85/291.51 1121.85/291.51 1121.85/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1121.85/291.51 1121.85/291.51 (0) CpxTRS 1121.85/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1121.85/291.51 (2) CpxWeightedTrs 1121.85/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1121.85/291.51 (4) CpxTypedWeightedTrs 1121.85/291.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1121.85/291.51 (6) CpxTypedWeightedCompleteTrs 1121.85/291.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] 1121.85/291.51 (8) CpxRNTS 1121.85/291.51 (9) CompleteCoflocoProof [FINISHED, 52.6 s] 1121.85/291.51 (10) BOUNDS(1, n^5) 1121.85/291.51 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1121.85/291.51 (12) TRS for Loop Detection 1121.85/291.51 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1121.85/291.51 (14) BEST 1121.85/291.51 (15) proven lower bound 1121.85/291.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1121.85/291.51 (17) BOUNDS(n^1, INF) 1121.85/291.51 (18) TRS for Loop Detection 1121.85/291.51 1121.85/291.51 1121.85/291.51 ---------------------------------------- 1121.85/291.51 1121.85/291.51 (0) 1121.85/291.51 Obligation: 1121.85/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1121.85/291.51 1121.85/291.51 1121.85/291.51 The TRS R consists of the following rules: 1121.85/291.51 1121.85/291.51 plus(x, y) -> ifPlus(isZero(x), x, inc(y)) 1121.85/291.51 ifPlus(true, x, y) -> p(y) 1121.85/291.51 ifPlus(false, x, y) -> plus(p(x), y) 1121.85/291.51 times(x, y) -> timesIter(0, x, y, 0) 1121.85/291.51 timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) 1121.85/291.51 ifTimes(true, i, x, y, z) -> z 1121.85/291.51 ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) 1121.85/291.51 isZero(0) -> true 1121.85/291.51 isZero(s(0)) -> false 1121.85/291.51 isZero(s(s(x))) -> isZero(s(x)) 1121.85/291.51 inc(0) -> s(0) 1121.85/291.51 inc(s(x)) -> s(inc(x)) 1121.85/291.51 inc(x) -> s(x) 1121.85/291.51 p(0) -> 0 1121.85/291.51 p(s(x)) -> x 1121.85/291.51 p(s(s(x))) -> s(p(s(x))) 1121.85/291.51 ge(x, 0) -> true 1121.85/291.51 ge(0, s(y)) -> false 1121.85/291.51 ge(s(x), s(y)) -> ge(x, y) 1121.85/291.51 f0(0, y, x) -> f1(x, y, x) 1121.85/291.51 f1(x, y, z) -> f2(x, y, z) 1121.85/291.51 f2(x, 1, z) -> f0(x, z, z) 1121.85/291.51 f0(x, y, z) -> d 1121.85/291.51 f1(x, y, z) -> c 1121.85/291.51 1121.85/291.51 S is empty. 1121.85/291.51 Rewrite Strategy: INNERMOST 1121.85/291.51 ---------------------------------------- 1121.85/291.51 1121.85/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1121.85/291.51 Transformed relative TRS to weighted TRS 1121.85/291.51 ---------------------------------------- 1121.85/291.51 1121.85/291.51 (2) 1121.85/291.51 Obligation: 1121.85/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^5). 1121.85/291.51 1121.85/291.51 1121.85/291.51 The TRS R consists of the following rules: 1121.85/291.51 1121.85/291.51 plus(x, y) -> ifPlus(isZero(x), x, inc(y)) [1] 1121.85/291.51 ifPlus(true, x, y) -> p(y) [1] 1121.85/291.51 ifPlus(false, x, y) -> plus(p(x), y) [1] 1121.85/291.51 times(x, y) -> timesIter(0, x, y, 0) [1] 1121.85/291.51 timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) [1] 1121.85/291.51 ifTimes(true, i, x, y, z) -> z [1] 1121.85/291.51 ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) [1] 1121.85/291.51 isZero(0) -> true [1] 1121.85/291.51 isZero(s(0)) -> false [1] 1121.85/291.51 isZero(s(s(x))) -> isZero(s(x)) [1] 1121.85/291.51 inc(0) -> s(0) [1] 1121.85/291.51 inc(s(x)) -> s(inc(x)) [1] 1121.85/291.51 inc(x) -> s(x) [1] 1121.85/291.51 p(0) -> 0 [1] 1121.85/291.51 p(s(x)) -> x [1] 1121.85/291.51 p(s(s(x))) -> s(p(s(x))) [1] 1121.85/291.51 ge(x, 0) -> true [1] 1121.85/291.51 ge(0, s(y)) -> false [1] 1121.85/291.51 ge(s(x), s(y)) -> ge(x, y) [1] 1121.85/291.51 f0(0, y, x) -> f1(x, y, x) [1] 1121.85/291.51 f1(x, y, z) -> f2(x, y, z) [1] 1121.85/291.51 f2(x, 1, z) -> f0(x, z, z) [1] 1121.85/291.51 f0(x, y, z) -> d [1]
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