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Runti Compl Inner Rewri 22807 pair #381904390
details
property
value
status
timeout (cpu)
benchmark
quicksort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
AProVE_06
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
294.415695906 seconds
cpu usage
1233.50685881
max memory
9.609302016E9
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(add(n,x),y) -> add(n,app(x,y)) app(nil(),y) -> y head(add(n,x)) -> n high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) high(n,nil()) -> nil() if_high(false(),n,add(m,x)) -> add(m,high(n,x)) if_high(true(),n,add(m,x)) -> high(n,x) if_low(false(),n,add(m,x)) -> low(n,x) if_low(true(),n,add(m,x)) -> add(m,low(n,x)) if_qs(false(),x,n,y) -> app(quicksort(x),add(n,quicksort(y))) if_qs(true(),x,n,y) -> nil() isempty(add(n,x)) -> false() isempty(nil()) -> true() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) low(n,nil()) -> nil() quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) tail(add(n,x)) -> x - Signature: {app/2,head/1,high/2,if_high/3,if_low/3,if_qs/4,isempty/1,le/2,low/2,quicksort/1,tail/1} / {0/0,add/2 ,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,head,high,if_high,if_low,if_qs,isempty,le,low ,quicksort,tail} and constructors {0,add,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(add(n,x),y) -> add(n,app(x,y)) app(nil(),y) -> y head(add(n,x)) -> n high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) high(n,nil()) -> nil() if_high(false(),n,add(m,x)) -> add(m,high(n,x)) if_high(true(),n,add(m,x)) -> high(n,x) if_low(false(),n,add(m,x)) -> low(n,x) if_low(true(),n,add(m,x)) -> add(m,low(n,x)) if_qs(false(),x,n,y) -> app(quicksort(x),add(n,quicksort(y))) if_qs(true(),x,n,y) -> nil() isempty(add(n,x)) -> false() isempty(nil()) -> true() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) low(n,nil()) -> nil() quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) tail(add(n,x)) -> x - Signature: {app/2,head/1,high/2,if_high/3,if_low/3,if_qs/4,isempty/1,le/2,low/2,quicksort/1,tail/1} / {0/0,add/2 ,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,head,high,if_high,if_low,if_qs,isempty,le,low ,quicksort,tail} and constructors {0,add,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: app(y,z){y -> add(x,y)} = app(add(x,y),z) ->^+ add(x,app(y,z)) = C[app(y,z) = app(y,z){}] WORST_CASE(Omega(n^1),?)
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