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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307758
details
property
value
status
complete
benchmark
thiemann18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n068.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.568 seconds
cpu usage
310.782
user time
308.814
system time
1.96772
max virtual memory
1.8281316E7
max residence set size
5190764.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
310.67/291.53 WORST_CASE(Omega(n^1), ?) 310.73/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 310.73/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 310.73/291.54 310.73/291.54 310.73/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.73/291.54 310.73/291.54 (0) CpxTRS 310.73/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 310.73/291.54 (2) TRS for Loop Detection 310.73/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 310.73/291.54 (4) BEST 310.73/291.54 (5) proven lower bound 310.73/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 310.73/291.54 (7) BOUNDS(n^1, INF) 310.73/291.54 (8) TRS for Loop Detection 310.73/291.54 310.73/291.54 310.73/291.54 ---------------------------------------- 310.73/291.54 310.73/291.54 (0) 310.73/291.54 Obligation: 310.73/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.73/291.54 310.73/291.54 310.73/291.54 The TRS R consists of the following rules: 310.73/291.54 310.73/291.54 eq(0, 0) -> true 310.73/291.54 eq(0, s(m)) -> false 310.73/291.54 eq(s(n), 0) -> false 310.73/291.54 eq(s(n), s(m)) -> eq(n, m) 310.73/291.54 le(0, m) -> true 310.73/291.54 le(s(n), 0) -> false 310.73/291.54 le(s(n), s(m)) -> le(n, m) 310.73/291.54 min(cons(x, nil)) -> x 310.73/291.54 min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x))) 310.73/291.54 if_min(true, cons(n, cons(m, x))) -> min(cons(n, x)) 310.73/291.54 if_min(false, cons(n, cons(m, x))) -> min(cons(m, x)) 310.73/291.54 replace(n, m, nil) -> nil 310.73/291.54 replace(n, m, cons(k, x)) -> if_replace(eq(n, k), n, m, cons(k, x)) 310.73/291.54 if_replace(true, n, m, cons(k, x)) -> cons(m, x) 310.73/291.54 if_replace(false, n, m, cons(k, x)) -> cons(k, replace(n, m, x)) 310.73/291.54 empty(nil) -> true 310.73/291.54 empty(cons(n, x)) -> false 310.73/291.54 head(cons(n, x)) -> n 310.73/291.54 tail(nil) -> nil 310.73/291.54 tail(cons(n, x)) -> x 310.73/291.54 sort(x) -> sortIter(x, nil) 310.73/291.54 sortIter(x, y) -> if(empty(x), x, y, append(y, cons(min(x), nil))) 310.73/291.54 if(true, x, y, z) -> y 310.73/291.54 if(false, x, y, z) -> sortIter(replace(min(x), head(x), tail(x)), z) 310.73/291.54 310.73/291.54 S is empty. 310.73/291.54 Rewrite Strategy: FULL 310.73/291.54 ---------------------------------------- 310.73/291.54 310.73/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 310.73/291.54 Transformed a relative TRS into a decreasing-loop problem. 310.73/291.54 ---------------------------------------- 310.73/291.54 310.73/291.54 (2) 310.73/291.54 Obligation: 310.73/291.54 Analyzing the following TRS for decreasing loops: 310.73/291.54 310.73/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.73/291.54 310.73/291.54 310.73/291.54 The TRS R consists of the following rules: 310.73/291.54 310.73/291.54 eq(0, 0) -> true 310.73/291.54 eq(0, s(m)) -> false 310.73/291.54 eq(s(n), 0) -> false 310.73/291.54 eq(s(n), s(m)) -> eq(n, m) 310.73/291.54 le(0, m) -> true 310.73/291.54 le(s(n), 0) -> false 310.73/291.54 le(s(n), s(m)) -> le(n, m) 310.73/291.54 min(cons(x, nil)) -> x 310.73/291.54 min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x))) 310.73/291.54 if_min(true, cons(n, cons(m, x))) -> min(cons(n, x)) 310.73/291.54 if_min(false, cons(n, cons(m, x))) -> min(cons(m, x)) 310.73/291.54 replace(n, m, nil) -> nil 310.73/291.54 replace(n, m, cons(k, x)) -> if_replace(eq(n, k), n, m, cons(k, x)) 310.73/291.54 if_replace(true, n, m, cons(k, x)) -> cons(m, x) 310.73/291.54 if_replace(false, n, m, cons(k, x)) -> cons(k, replace(n, m, x)) 310.73/291.54 empty(nil) -> true 310.73/291.54 empty(cons(n, x)) -> false 310.73/291.54 head(cons(n, x)) -> n 310.73/291.54 tail(nil) -> nil 310.73/291.54 tail(cons(n, x)) -> x 310.73/291.54 sort(x) -> sortIter(x, nil) 310.73/291.54 sortIter(x, y) -> if(empty(x), x, y, append(y, cons(min(x), nil))) 310.73/291.54 if(true, x, y, z) -> y 310.73/291.54 if(false, x, y, z) -> sortIter(replace(min(x), head(x), tail(x)), z) 310.73/291.54 310.73/291.54 S is empty. 310.73/291.54 Rewrite Strategy: FULL 310.73/291.54 ---------------------------------------- 310.73/291.54 310.73/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 310.73/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1):
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