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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308465
details
property
value
status
complete
benchmark
aprove04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.615 seconds
cpu usage
305.731
user time
303.847
system time
1.88472
max virtual memory
1.828134E7
max residence set size
5314052.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
305.58/291.54 WORST_CASE(Omega(n^1), ?) 305.58/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 305.58/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 305.58/291.58 305.58/291.58 305.58/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.58/291.58 305.58/291.58 (0) CpxTRS 305.58/291.58 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 305.58/291.58 (2) TRS for Loop Detection 305.58/291.58 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 305.58/291.58 (4) BEST 305.58/291.58 (5) proven lower bound 305.58/291.58 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 305.58/291.58 (7) BOUNDS(n^1, INF) 305.58/291.58 (8) TRS for Loop Detection 305.58/291.58 305.58/291.58 305.58/291.58 ---------------------------------------- 305.58/291.58 305.58/291.58 (0) 305.58/291.58 Obligation: 305.58/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.58/291.58 305.58/291.58 305.58/291.58 The TRS R consists of the following rules: 305.58/291.58 305.58/291.58 lcm(x, y) -> lcmIter(x, y, 0, times(x, y)) 305.58/291.58 lcmIter(x, y, z, u) -> if(or(ge(0, x), ge(z, u)), x, y, z, u) 305.58/291.58 if(true, x, y, z, u) -> z 305.58/291.58 if(false, x, y, z, u) -> if2(divisible(z, y), x, y, z, u) 305.58/291.58 if2(true, x, y, z, u) -> z 305.58/291.58 if2(false, x, y, z, u) -> lcmIter(x, y, plus(x, z), u) 305.58/291.58 plus(0, y) -> y 305.58/291.58 plus(s(x), y) -> s(plus(x, y)) 305.58/291.58 times(x, y) -> ifTimes(ge(0, x), x, y) 305.58/291.58 ifTimes(true, x, y) -> 0 305.58/291.58 ifTimes(false, x, y) -> plus(y, times(y, p(x))) 305.58/291.58 p(s(x)) -> x 305.58/291.58 p(0) -> s(s(0)) 305.58/291.58 ge(x, 0) -> true 305.58/291.58 ge(0, s(y)) -> false 305.58/291.58 ge(s(x), s(y)) -> ge(x, y) 305.58/291.58 or(true, y) -> true 305.58/291.58 or(false, y) -> y 305.58/291.58 divisible(0, s(y)) -> true 305.58/291.58 divisible(s(x), s(y)) -> div(s(x), s(y), s(y)) 305.58/291.58 div(x, y, 0) -> divisible(x, y) 305.58/291.58 div(0, y, s(z)) -> false 305.58/291.58 div(s(x), y, s(z)) -> div(x, y, z) 305.58/291.58 a -> b 305.58/291.58 a -> c 305.58/291.58 305.58/291.58 S is empty. 305.58/291.58 Rewrite Strategy: FULL 305.58/291.58 ---------------------------------------- 305.58/291.58 305.58/291.58 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 305.58/291.58 Transformed a relative TRS into a decreasing-loop problem. 305.58/291.58 ---------------------------------------- 305.58/291.58 305.58/291.58 (2) 305.58/291.58 Obligation: 305.58/291.58 Analyzing the following TRS for decreasing loops: 305.58/291.58 305.58/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.58/291.58 305.58/291.58 305.58/291.58 The TRS R consists of the following rules: 305.58/291.58 305.58/291.58 lcm(x, y) -> lcmIter(x, y, 0, times(x, y)) 305.58/291.58 lcmIter(x, y, z, u) -> if(or(ge(0, x), ge(z, u)), x, y, z, u) 305.58/291.58 if(true, x, y, z, u) -> z 305.58/291.58 if(false, x, y, z, u) -> if2(divisible(z, y), x, y, z, u) 305.58/291.58 if2(true, x, y, z, u) -> z 305.58/291.58 if2(false, x, y, z, u) -> lcmIter(x, y, plus(x, z), u) 305.58/291.58 plus(0, y) -> y 305.58/291.58 plus(s(x), y) -> s(plus(x, y)) 305.58/291.58 times(x, y) -> ifTimes(ge(0, x), x, y) 305.58/291.58 ifTimes(true, x, y) -> 0 305.58/291.58 ifTimes(false, x, y) -> plus(y, times(y, p(x))) 305.58/291.58 p(s(x)) -> x 305.58/291.58 p(0) -> s(s(0)) 305.58/291.58 ge(x, 0) -> true 305.58/291.58 ge(0, s(y)) -> false 305.58/291.58 ge(s(x), s(y)) -> ge(x, y) 305.58/291.58 or(true, y) -> true 305.58/291.58 or(false, y) -> y 305.58/291.58 divisible(0, s(y)) -> true 305.58/291.58 divisible(s(x), s(y)) -> div(s(x), s(y), s(y)) 305.58/291.58 div(x, y, 0) -> divisible(x, y) 305.58/291.58 div(0, y, s(z)) -> false 305.58/291.58 div(s(x), y, s(z)) -> div(x, y, z) 305.58/291.58 a -> b 305.58/291.58 a -> c 305.58/291.58 305.58/291.58 S is empty. 305.58/291.58 Rewrite Strategy: FULL 305.58/291.58 ---------------------------------------- 305.58/291.58
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