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Runti Compl Inner Rewri 22807 pair #381904325
details
property
value
status
complete
benchmark
minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.373358011 seconds
cpu usage
1122.5970632
max memory
1.5191683072E10
stage attributes
key
value
output-size
5238
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) minsort(nil) -> nil minsort(cons(x, xs)) -> cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs)))) min(nil) -> 0 min(cons(x, nil)) -> x min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs) if1(true, x, y, xs) -> min(cons(x, xs)) if1(false, x, y, xs) -> min(cons(y, xs)) rm(x, nil) -> nil rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) if2(true, x, y, xs) -> rm(x, xs) if2(false, x, y, xs) -> cons(y, rm(x, xs)) 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) minsort(nil) -> nil minsort(cons(x, xs)) -> cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs)))) min(nil) -> 0 min(cons(x, nil)) -> x min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs) if1(true, x, y, xs) -> min(cons(x, xs)) if1(false, x, y, xs) -> min(cons(y, xs)) rm(x, nil) -> nil rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) if2(true, x, y, xs) -> rm(x, xs) if2(false, x, y, xs) -> cons(y, rm(x, xs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence le(s(x), s(y)) ->^+ le(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position [].
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