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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313312
details
property
value
status
complete
benchmark
aprove05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.541 seconds
cpu usage
1106.19
user time
1092.72
system time
13.4749
max virtual memory
5.7202012E7
max residence set size
1.4893348E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1106.00/291.47 WORST_CASE(Omega(n^1), ?) 1106.00/291.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1106.00/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1106.00/291.48 1106.00/291.48 1106.00/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1106.00/291.48 1106.00/291.48 (0) CpxTRS 1106.00/291.48 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1106.00/291.48 (2) TRS for Loop Detection 1106.00/291.48 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1106.00/291.48 (4) BEST 1106.00/291.48 (5) proven lower bound 1106.00/291.48 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1106.00/291.48 (7) BOUNDS(n^1, INF) 1106.00/291.48 (8) TRS for Loop Detection 1106.00/291.48 1106.00/291.48 1106.00/291.48 ---------------------------------------- 1106.00/291.48 1106.00/291.48 (0) 1106.00/291.48 Obligation: 1106.00/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1106.00/291.48 1106.00/291.48 1106.00/291.48 The TRS R consists of the following rules: 1106.00/291.48 1106.00/291.48 prod(xs) -> prodIter(xs, s(0)) 1106.00/291.48 prodIter(xs, x) -> ifProd(isempty(xs), xs, x) 1106.00/291.48 ifProd(true, xs, x) -> x 1106.00/291.48 ifProd(false, xs, x) -> prodIter(tail(xs), times(x, head(xs))) 1106.00/291.48 plus(0, y) -> y 1106.00/291.48 plus(s(x), y) -> s(plus(x, y)) 1106.00/291.48 times(x, y) -> timesIter(x, y, 0, 0) 1106.00/291.48 timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u) 1106.00/291.48 ifTimes(true, x, y, z, u) -> z 1106.00/291.48 ifTimes(false, x, y, z, u) -> timesIter(x, y, plus(y, z), s(u)) 1106.00/291.48 isempty(nil) -> true 1106.00/291.48 isempty(cons(x, xs)) -> false 1106.00/291.48 head(nil) -> error 1106.00/291.48 head(cons(x, xs)) -> x 1106.00/291.48 tail(nil) -> nil 1106.00/291.48 tail(cons(x, xs)) -> xs 1106.00/291.48 ge(x, 0) -> true 1106.00/291.48 ge(0, s(y)) -> false 1106.00/291.48 ge(s(x), s(y)) -> ge(x, y) 1106.00/291.48 a -> b 1106.00/291.48 a -> c 1106.00/291.48 1106.00/291.48 S is empty. 1106.00/291.48 Rewrite Strategy: INNERMOST 1106.00/291.48 ---------------------------------------- 1106.00/291.48 1106.00/291.48 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1106.00/291.48 Transformed a relative TRS into a decreasing-loop problem. 1106.00/291.48 ---------------------------------------- 1106.00/291.48 1106.00/291.48 (2) 1106.00/291.48 Obligation: 1106.00/291.48 Analyzing the following TRS for decreasing loops: 1106.00/291.48 1106.00/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1106.00/291.48 1106.00/291.48 1106.00/291.48 The TRS R consists of the following rules: 1106.00/291.48 1106.00/291.48 prod(xs) -> prodIter(xs, s(0)) 1106.00/291.48 prodIter(xs, x) -> ifProd(isempty(xs), xs, x) 1106.00/291.48 ifProd(true, xs, x) -> x 1106.00/291.48 ifProd(false, xs, x) -> prodIter(tail(xs), times(x, head(xs))) 1106.00/291.48 plus(0, y) -> y 1106.00/291.48 plus(s(x), y) -> s(plus(x, y)) 1106.00/291.48 times(x, y) -> timesIter(x, y, 0, 0) 1106.00/291.48 timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u) 1106.00/291.48 ifTimes(true, x, y, z, u) -> z 1106.00/291.48 ifTimes(false, x, y, z, u) -> timesIter(x, y, plus(y, z), s(u)) 1106.00/291.48 isempty(nil) -> true 1106.00/291.48 isempty(cons(x, xs)) -> false 1106.00/291.48 head(nil) -> error 1106.00/291.48 head(cons(x, xs)) -> x 1106.00/291.48 tail(nil) -> nil 1106.00/291.48 tail(cons(x, xs)) -> xs 1106.00/291.48 ge(x, 0) -> true 1106.00/291.48 ge(0, s(y)) -> false 1106.00/291.48 ge(s(x), s(y)) -> ge(x, y) 1106.00/291.48 a -> b 1106.00/291.48 a -> c 1106.00/291.48 1106.00/291.48 S is empty. 1106.00/291.48 Rewrite Strategy: INNERMOST 1106.00/291.48 ---------------------------------------- 1106.00/291.48 1106.00/291.48 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1106.00/291.48 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1106.00/291.48 1106.00/291.48 The rewrite sequence 1106.00/291.48 1106.00/291.48 plus(s(x), y) ->^+ s(plus(x, y)) 1106.00/291.48 1106.00/291.48 gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
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