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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313371
details
property
value
status
complete
benchmark
mergesort.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.836 seconds
cpu usage
1047.4
user time
1030.31
system time
17.09
max virtual memory
3.837232E7
max residence set size
1.5165392E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1047.16/291.75 WORST_CASE(Omega(n^1), ?) 1047.16/291.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1047.16/291.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1047.16/291.76 1047.16/291.76 1047.16/291.76 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1047.16/291.76 1047.16/291.76 (0) CpxRelTRS 1047.16/291.76 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 209 ms] 1047.16/291.76 (2) CpxRelTRS 1047.16/291.76 (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1047.16/291.76 (4) TRS for Loop Detection 1047.16/291.76 (5) DecreasingLoopProof [LOWER BOUND(ID), 137 ms] 1047.16/291.76 (6) BEST 1047.16/291.76 (7) proven lower bound 1047.16/291.76 (8) LowerBoundPropagationProof [FINISHED, 0 ms] 1047.16/291.76 (9) BOUNDS(n^1, INF) 1047.16/291.76 (10) TRS for Loop Detection 1047.16/291.76 1047.16/291.76 1047.16/291.76 ---------------------------------------- 1047.16/291.76 1047.16/291.76 (0) 1047.16/291.76 Obligation: 1047.16/291.76 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1047.16/291.76 1047.16/291.76 1047.16/291.76 The TRS R consists of the following rules: 1047.16/291.76 1047.16/291.76 #less(@x, @y) -> #cklt(#compare(@x, @y)) 1047.16/291.76 merge(@l1, @l2) -> merge#1(@l1, @l2) 1047.16/291.76 merge#1(::(@x, @xs), @l2) -> merge#2(@l2, @x, @xs) 1047.16/291.76 merge#1(nil, @l2) -> @l2 1047.16/291.76 merge#2(::(@y, @ys), @x, @xs) -> merge#3(#less(@x, @y), @x, @xs, @y, @ys) 1047.16/291.76 merge#2(nil, @x, @xs) -> ::(@x, @xs) 1047.16/291.76 merge#3(#false, @x, @xs, @y, @ys) -> ::(@y, merge(::(@x, @xs), @ys)) 1047.16/291.76 merge#3(#true, @x, @xs, @y, @ys) -> ::(@x, merge(@xs, ::(@y, @ys))) 1047.16/291.76 mergesort(@l) -> mergesort#1(@l) 1047.16/291.76 mergesort#1(::(@x1, @xs)) -> mergesort#2(@xs, @x1) 1047.16/291.76 mergesort#1(nil) -> nil 1047.16/291.76 mergesort#2(::(@x2, @xs'), @x1) -> mergesort#3(msplit(::(@x1, ::(@x2, @xs')))) 1047.16/291.76 mergesort#2(nil, @x1) -> ::(@x1, nil) 1047.16/291.76 mergesort#3(tuple#2(@l1, @l2)) -> merge(mergesort(@l1), mergesort(@l2)) 1047.16/291.76 msplit(@l) -> msplit#1(@l) 1047.16/291.76 msplit#1(::(@x1, @xs)) -> msplit#2(@xs, @x1) 1047.16/291.76 msplit#1(nil) -> tuple#2(nil, nil) 1047.16/291.76 msplit#2(::(@x2, @xs'), @x1) -> msplit#3(msplit(@xs'), @x1, @x2) 1047.16/291.76 msplit#2(nil, @x1) -> tuple#2(::(@x1, nil), nil) 1047.16/291.76 msplit#3(tuple#2(@l1, @l2), @x1, @x2) -> tuple#2(::(@x1, @l1), ::(@x2, @l2)) 1047.16/291.76 1047.16/291.76 The (relative) TRS S consists of the following rules: 1047.16/291.76 1047.16/291.76 #cklt(#EQ) -> #false 1047.16/291.76 #cklt(#GT) -> #false 1047.16/291.76 #cklt(#LT) -> #true 1047.16/291.76 #compare(#0, #0) -> #EQ 1047.16/291.76 #compare(#0, #neg(@y)) -> #GT 1047.16/291.76 #compare(#0, #pos(@y)) -> #LT 1047.16/291.76 #compare(#0, #s(@y)) -> #LT 1047.16/291.76 #compare(#neg(@x), #0) -> #LT 1047.16/291.76 #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x) 1047.16/291.76 #compare(#neg(@x), #pos(@y)) -> #LT 1047.16/291.76 #compare(#pos(@x), #0) -> #GT 1047.16/291.76 #compare(#pos(@x), #neg(@y)) -> #GT 1047.16/291.76 #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y) 1047.16/291.76 #compare(#s(@x), #0) -> #GT 1047.16/291.76 #compare(#s(@x), #s(@y)) -> #compare(@x, @y) 1047.16/291.76 1047.16/291.76 Rewrite Strategy: INNERMOST 1047.16/291.76 ---------------------------------------- 1047.16/291.76 1047.16/291.76 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 1047.16/291.76 proved termination of relative rules 1047.16/291.76 ---------------------------------------- 1047.16/291.76 1047.16/291.76 (2) 1047.16/291.76 Obligation: 1047.16/291.76 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1047.16/291.76 1047.16/291.76 1047.16/291.76 The TRS R consists of the following rules: 1047.16/291.76 1047.16/291.76 #less(@x, @y) -> #cklt(#compare(@x, @y)) 1047.16/291.76 merge(@l1, @l2) -> merge#1(@l1, @l2) 1047.16/291.76 merge#1(::(@x, @xs), @l2) -> merge#2(@l2, @x, @xs) 1047.16/291.76 merge#1(nil, @l2) -> @l2 1047.16/291.76 merge#2(::(@y, @ys), @x, @xs) -> merge#3(#less(@x, @y), @x, @xs, @y, @ys) 1047.16/291.76 merge#2(nil, @x, @xs) -> ::(@x, @xs) 1047.16/291.76 merge#3(#false, @x, @xs, @y, @ys) -> ::(@y, merge(::(@x, @xs), @ys)) 1047.16/291.76 merge#3(#true, @x, @xs, @y, @ys) -> ::(@x, merge(@xs, ::(@y, @ys))) 1047.16/291.76 mergesort(@l) -> mergesort#1(@l) 1047.16/291.76 mergesort#1(::(@x1, @xs)) -> mergesort#2(@xs, @x1) 1047.16/291.76 mergesort#1(nil) -> nil 1047.16/291.76 mergesort#2(::(@x2, @xs'), @x1) -> mergesort#3(msplit(::(@x1, ::(@x2, @xs')))) 1047.16/291.76 mergesort#2(nil, @x1) -> ::(@x1, nil) 1047.16/291.76 mergesort#3(tuple#2(@l1, @l2)) -> merge(mergesort(@l1), mergesort(@l2)) 1047.16/291.76 msplit(@l) -> msplit#1(@l) 1047.16/291.76 msplit#1(::(@x1, @xs)) -> msplit#2(@xs, @x1) 1047.16/291.76 msplit#1(nil) -> tuple#2(nil, nil) 1047.16/291.76 msplit#2(::(@x2, @xs'), @x1) -> msplit#3(msplit(@xs'), @x1, @x2)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40