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Runti Compl Inner Rewri 22807 pair #381904384
details
property
value
status
complete
benchmark
aprove01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.983221054 seconds
cpu usage
1139.29016873
max memory
1.5508238336E10
stage attributes
key
value
output-size
6123
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0) gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(xs) -> sum2(xs, 0) sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y) ifsum(true, b, xs, y) -> y ifsum(false, b, xs, y) -> ifsum2(b, xs, y) ifsum2(true, xs, y) -> sum2(tail(xs), y) ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y)) isNil(nil) -> true isNil(cons(x, xs)) -> false tail(nil) -> nil tail(cons(x, xs)) -> xs head(cons(x, xs)) -> x head(nil) -> error isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) p(0) -> s(s(0)) p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) a -> c a -> d S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: times(x, y) -> sum(generate(x, y)) generate(x, y) -> gen(x, y, 0) gen(x, y, z) -> if(ge(z, x), x, y, z) if(true, x, y, z) -> nil if(false, x, y, z) -> cons(y, gen(x, y, s(z))) sum(xs) -> sum2(xs, 0) sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y) ifsum(true, b, xs, y) -> y ifsum(false, b, xs, y) -> ifsum2(b, xs, y) ifsum2(true, xs, y) -> sum2(tail(xs), y) ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y)) isNil(nil) -> true isNil(cons(x, xs)) -> false tail(nil) -> nil tail(cons(x, xs)) -> xs head(cons(x, xs)) -> x head(nil) -> error isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) p(0) -> s(s(0))
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