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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308470
details
property
value
status
complete
benchmark
aprove09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n128.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.579 seconds
cpu usage
312.859
user time
311.001
system time
1.85791
max virtual memory
1.8288376E7
max residence set size
5264280.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
312.75/291.54 WORST_CASE(Omega(n^1), ?) 312.75/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 312.75/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 312.75/291.55 312.75/291.55 312.75/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.75/291.55 312.75/291.55 (0) CpxTRS 312.75/291.55 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 312.75/291.55 (2) TRS for Loop Detection 312.75/291.55 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 312.75/291.55 (4) BEST 312.75/291.55 (5) proven lower bound 312.75/291.55 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 312.75/291.55 (7) BOUNDS(n^1, INF) 312.75/291.55 (8) TRS for Loop Detection 312.75/291.55 312.75/291.55 312.75/291.55 ---------------------------------------- 312.75/291.55 312.75/291.55 (0) 312.75/291.55 Obligation: 312.75/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.75/291.55 312.75/291.55 312.75/291.55 The TRS R consists of the following rules: 312.75/291.55 312.75/291.55 div(x, y) -> div2(x, y, 0) 312.75/291.55 div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) 312.75/291.55 if1(true, b, x, y, i, j) -> divZeroError 312.75/291.55 if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) 312.75/291.55 if2(true, x, y, i, j) -> div2(minus(x, y), y, j) 312.75/291.55 if2(false, x, y, i, j) -> i 312.75/291.55 inc(0) -> 0 312.75/291.55 inc(s(i)) -> s(inc(i)) 312.75/291.55 le(s(x), 0) -> false 312.75/291.55 le(0, y) -> true 312.75/291.55 le(s(x), s(y)) -> le(x, y) 312.75/291.55 minus(x, 0) -> x 312.75/291.55 minus(0, y) -> 0 312.75/291.55 minus(s(x), s(y)) -> minus(x, y) 312.75/291.55 plus(x, y) -> plusIter(x, y, 0) 312.75/291.55 plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 312.75/291.55 ifPlus(true, x, y, z) -> y 312.75/291.55 ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) 312.75/291.55 a -> c 312.75/291.55 a -> d 312.75/291.55 312.75/291.55 S is empty. 312.75/291.55 Rewrite Strategy: FULL 312.75/291.55 ---------------------------------------- 312.75/291.55 312.75/291.55 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 312.75/291.55 Transformed a relative TRS into a decreasing-loop problem. 312.75/291.55 ---------------------------------------- 312.75/291.55 312.75/291.55 (2) 312.75/291.55 Obligation: 312.75/291.55 Analyzing the following TRS for decreasing loops: 312.75/291.55 312.75/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.75/291.55 312.75/291.55 312.75/291.55 The TRS R consists of the following rules: 312.75/291.55 312.75/291.55 div(x, y) -> div2(x, y, 0) 312.75/291.55 div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) 312.75/291.55 if1(true, b, x, y, i, j) -> divZeroError 312.75/291.55 if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) 312.75/291.55 if2(true, x, y, i, j) -> div2(minus(x, y), y, j) 312.75/291.55 if2(false, x, y, i, j) -> i 312.75/291.55 inc(0) -> 0 312.75/291.55 inc(s(i)) -> s(inc(i)) 312.75/291.55 le(s(x), 0) -> false 312.75/291.55 le(0, y) -> true 312.75/291.55 le(s(x), s(y)) -> le(x, y) 312.75/291.55 minus(x, 0) -> x 312.75/291.55 minus(0, y) -> 0 312.75/291.55 minus(s(x), s(y)) -> minus(x, y) 312.75/291.55 plus(x, y) -> plusIter(x, y, 0) 312.75/291.55 plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 312.75/291.55 ifPlus(true, x, y, z) -> y 312.75/291.55 ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) 312.75/291.55 a -> c 312.75/291.55 a -> d 312.75/291.55 312.75/291.55 S is empty. 312.75/291.55 Rewrite Strategy: FULL 312.75/291.55 ---------------------------------------- 312.75/291.55 312.75/291.55 (3) DecreasingLoopProof (LOWER BOUND(ID)) 312.75/291.55 The following loop(s) give(s) rise to the lower bound Omega(n^1): 312.75/291.55 312.75/291.55 The rewrite sequence 312.75/291.55 312.75/291.55 le(s(x), s(y)) ->^+ le(x, y) 312.75/291.55 312.75/291.55 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 312.75/291.55 312.75/291.55 The pumping substitution is [x / s(x), y / s(y)].
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