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Runtime Complexity: TRS pair #487111054
details
property
value
status
complete
benchmark
thiemann30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.545 seconds
cpu usage
310.107
user time
308.372
system time
1.73528
max virtual memory
1.8281488E7
max residence set size
5232452.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(nil) -> 0 min(add(n, x)) -> minIter(add(n, x), add(n, x), 0) minIter(nil, add(n, y), m) -> minIter(add(n, y), add(n, y), s(m)) minIter(add(n, x), y, m) -> if_min(le(n, m), x, y, m) if_min(true, x, y, m) -> m if_min(false, x, y, m) -> minIter(x, y, m) head(add(n, x)) -> n tail(add(n, x)) -> x tail(nil) -> nil null(nil) -> true null(add(n, x)) -> false rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(nil, nil) -> nil minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(nil) -> 0 min(add(n, x)) -> minIter(add(n, x), add(n, x), 0) minIter(nil, add(n, y), m) -> minIter(add(n, y), add(n, y), s(m)) minIter(add(n, x), y, m) -> if_min(le(n, m), x, y, m) if_min(true, x, y, m) -> m if_min(false, x, y, m) -> minIter(x, y, m) head(add(n, x)) -> n tail(add(n, x)) -> x tail(nil) -> nil null(nil) -> true null(add(n, x)) -> false rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(nil, nil) -> nil minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil))
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return to Runtime Complexity: TRS