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Runti Compl Inner Rewri 22807 pair #381904306
details
property
value
status
timeout (cpu)
benchmark
quicksortSize.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
Frederiksen_Others
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
294.561763048 seconds
cpu usage
1204.1319383
max memory
1.729019904E9
stage attributes
unavailable
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),?) * Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(Cons(x,xs),ys) -> Cons(x,app(xs,ys)) app(Nil(),ys) -> ys goal(xs) -> quicksort(xs) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() part(x,xs) -> app(quicksort(partLt(x,xs)),Cons(x,quicksort(partGt(x,xs)))) partGt(x,Nil()) -> Nil() partGt(x',Cons(x,xs)) -> partGt[Ite][True][Ite](>(x,x'),x',Cons(x,xs)) partLt(x,Nil()) -> Nil() partLt(x',Cons(x,xs)) -> partLt[Ite][True][Ite](<(x,x'),x',Cons(x,xs)) quicksort(Cons(x,Cons(x',xs))) -> part(x,Cons(x',xs)) 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) partGt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partGt(x',xs) partGt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partGt(x',xs)) partLt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partLt(x',xs) partLt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partLt(x',xs)) - Signature: {</2,>/2,app/2,goal/1,notEmpty/1,part/2,partGt/2,partGt[Ite][True][Ite]/3,partLt/2,partLt[Ite][True][Ite]/3 ,quicksort/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<,>,app,goal,notEmpty,part,partGt,partGt[Ite][True][Ite] ,partLt,partLt[Ite][True][Ite],quicksort} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(Cons(x,xs),ys) -> Cons(x,app(xs,ys)) app(Nil(),ys) -> ys goal(xs) -> quicksort(xs) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() part(x,xs) -> app(quicksort(partLt(x,xs)),Cons(x,quicksort(partGt(x,xs)))) partGt(x,Nil()) -> Nil() partGt(x',Cons(x,xs)) -> partGt[Ite][True][Ite](>(x,x'),x',Cons(x,xs)) partLt(x,Nil()) -> Nil() partLt(x',Cons(x,xs)) -> partLt[Ite][True][Ite](<(x,x'),x',Cons(x,xs)) quicksort(Cons(x,Cons(x',xs))) -> part(x,Cons(x',xs)) 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) partGt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partGt(x',xs) partGt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partGt(x',xs)) partLt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partLt(x',xs) partLt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partLt(x',xs)) - Signature: {</2,>/2,app/2,goal/1,notEmpty/1,part/2,partGt/2,partGt[Ite][True][Ite]/3,partLt/2,partLt[Ite][True][Ite]/3 ,quicksort/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<,>,app,goal,notEmpty,part,partGt,partGt[Ite][True][Ite] ,partLt,partLt[Ite][True][Ite],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){}] WORST_CASE(Omega(n^1),?)
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