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Runti Compl Full Rewri 10127 pair #381902289
details
property
value
status
complete
benchmark
qsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
295.417894125 seconds
cpu usage
722.041879551
max memory
3.081048064E9
stage attributes
key
value
output-size
3076
starexec-result
WORST_CASE(Omega(n^1),?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /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: append(cons(x,xs),ys()) -> cons(x,append(xs,ys())) append(nil(),ys()) -> ys() filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs) filterhigh(n,nil()) -> nil() filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs) filterlow(n,nil()) -> nil() ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) if1(false(),n,x,xs) -> cons(x,filterlow(n,xs)) if1(true(),n,x,xs) -> filterlow(n,xs) if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs)) if2(true(),n,x,xs) -> filterhigh(n,xs) qsort(cons(x,xs)) -> append(qsort(filterlow(x,cons(x,xs))),cons(x,qsort(filterhigh(x,cons(x,xs))))) qsort(nil()) -> nil() - Signature: {append/2,filterhigh/2,filterlow/2,ge/2,if1/4,if2/4,qsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,ys/0} - Obligation: runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,if1,if2,qsort} and constructors {0 ,cons,false,nil,s,true,ys} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(cons(x,xs),ys()) -> cons(x,append(xs,ys())) append(nil(),ys()) -> ys() filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs) filterhigh(n,nil()) -> nil() filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs) filterlow(n,nil()) -> nil() ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) if1(false(),n,x,xs) -> cons(x,filterlow(n,xs)) if1(true(),n,x,xs) -> filterlow(n,xs) if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs)) if2(true(),n,x,xs) -> filterhigh(n,xs) qsort(cons(x,xs)) -> append(qsort(filterlow(x,cons(x,xs))),cons(x,qsort(filterhigh(x,cons(x,xs))))) qsort(nil()) -> nil() - Signature: {append/2,filterhigh/2,filterlow/2,ge/2,if1/4,if2/4,qsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,ys/0} - Obligation: runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,if1,if2,qsort} and constructors {0 ,cons,false,nil,s,true,ys} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: append(y,ys()){y -> cons(x,y)} = append(cons(x,y),ys()) ->^+ cons(x,append(y,ys())) = C[append(y,ys()) = append(y,ys()){}] WORST_CASE(Omega(n^1),?)
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