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Runti Compl Inner Rewri 22807 pair #381904875
details
property
value
status
complete
benchmark
quicksortPtime.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
7.31058096886 seconds
cpu usage
30.660990447
max memory
1.75407104E8
stage attributes
key
value
output-size
114605
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: app(Cons(x,xs),ys) -> Cons(x,app(xs,ys)) app(Nil(),ys) -> ys notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() part(x,Nil(),xs1,xs2) -> app(xs1,xs2) part(x',Cons(x,xs),xs1,xs2) -> part[Ite](>(x',x),x',Cons(x,xs),xs1,xs2) qs(x',Cons(x,xs)) -> app(Cons(x,Nil()),Cons(x',quicksort(xs))) quicksort(Cons(x,Cons(x',xs))) -> qs(x,part(x,Cons(x',xs),Nil(),Nil())) quicksort(Cons(x,Nil())) -> Cons(x,Nil()) quicksort(Nil()) -> Nil() - Weak TRS: <(x,0()) -> False() <(0(),S(y)) -> True() <(S(x),S(y)) -> <(x,y) >(0(),y) -> False() >(S(x),0()) -> True() >(S(x),S(y)) -> >(x,y) part[False][Ite](False(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,xs1,xs2) part[False][Ite](True(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,xs1,Cons(x,xs2)) part[Ite](False(),x',Cons(x,xs),xs1,xs2) -> part[False][Ite](<(x',x),x',Cons(x,xs),xs1,xs2) part[Ite](True(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,Cons(x,xs1),xs2) - Signature: {</2,>/2,app/2,notEmpty/1,part/4,part[False][Ite]/5,part[Ite]/5,qs/2,quicksort/1} / {0/0,Cons/2,False/0 ,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<,>,app,notEmpty,part,part[False][Ite],part[Ite],qs ,quicksort} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(Cons(x,xs),ys) -> Cons(x,app(xs,ys)) app(Nil(),ys) -> ys notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() part(x,Nil(),xs1,xs2) -> app(xs1,xs2) part(x',Cons(x,xs),xs1,xs2) -> part[Ite](>(x',x),x',Cons(x,xs),xs1,xs2) qs(x',Cons(x,xs)) -> app(Cons(x,Nil()),Cons(x',quicksort(xs))) quicksort(Cons(x,Cons(x',xs))) -> qs(x,part(x,Cons(x',xs),Nil(),Nil())) quicksort(Cons(x,Nil())) -> Cons(x,Nil()) quicksort(Nil()) -> Nil() - Weak TRS: <(x,0()) -> False() <(0(),S(y)) -> True() <(S(x),S(y)) -> <(x,y) >(0(),y) -> False() >(S(x),0()) -> True() >(S(x),S(y)) -> >(x,y) part[False][Ite](False(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,xs1,xs2) part[False][Ite](True(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,xs1,Cons(x,xs2)) part[Ite](False(),x',Cons(x,xs),xs1,xs2) -> part[False][Ite](<(x',x),x',Cons(x,xs),xs1,xs2) part[Ite](True(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,Cons(x,xs1),xs2) - Signature: {</2,>/2,app/2,notEmpty/1,part/4,part[False][Ite]/5,part[Ite]/5,qs/2,quicksort/1} / {0/0,Cons/2,False/0 ,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<,>,app,notEmpty,part,part[False][Ite],part[Ite],qs ,quicksort} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: app(y,z){y -> Cons(x,y)} = app(Cons(x,y),z) ->^+ Cons(x,app(y,z)) = C[app(y,z) = app(y,z){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: app(Cons(x,xs),ys) -> Cons(x,app(xs,ys)) app(Nil(),ys) -> ys notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() part(x,Nil(),xs1,xs2) -> app(xs1,xs2) part(x',Cons(x,xs),xs1,xs2) -> part[Ite](>(x',x),x',Cons(x,xs),xs1,xs2) qs(x',Cons(x,xs)) -> app(Cons(x,Nil()),Cons(x',quicksort(xs))) quicksort(Cons(x,Cons(x',xs))) -> qs(x,part(x,Cons(x',xs),Nil(),Nil())) quicksort(Cons(x,Nil())) -> Cons(x,Nil()) quicksort(Nil()) -> Nil() - Weak TRS: <(x,0()) -> False() <(0(),S(y)) -> True() <(S(x),S(y)) -> <(x,y) >(0(),y) -> False() >(S(x),0()) -> True() >(S(x),S(y)) -> >(x,y) part[False][Ite](False(),x',Cons(x,xs),xs1,xs2) -> part(x',xs,xs1,xs2)
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