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Runti Compl Inner Rewri 22807 pair #381904350
details
property
value
status
complete
benchmark
minsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
294.62970686 seconds
cpu usage
1188.66848701
max memory
4.547301376E9
stage attributes
key
value
output-size
3003
starexec-result
WORST_CASE(Omega(n^1),?)
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: eq(0(),0()) -> true() eq(0(),s(y)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if1(false(),x,y,xs) -> min(cons(y,xs)) if1(true(),x,y,xs) -> min(cons(x,xs)) if2(false(),x,y,xs) -> cons(y,rm(x,xs)) if2(true(),x,y,xs) -> rm(x,xs) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs) min(cons(x,nil())) -> x min(nil()) -> 0() minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs)))) minsort(nil()) -> nil() rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs) rm(x,nil()) -> nil() - Signature: {eq/2,if1/4,if2/4,le/2,min/1,minsort/1,rm/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,if1,if2,le,min,minsort,rm} 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: eq(0(),0()) -> true() eq(0(),s(y)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if1(false(),x,y,xs) -> min(cons(y,xs)) if1(true(),x,y,xs) -> min(cons(x,xs)) if2(false(),x,y,xs) -> cons(y,rm(x,xs)) if2(true(),x,y,xs) -> rm(x,xs) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs) min(cons(x,nil())) -> x min(nil()) -> 0() minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs)))) minsort(nil()) -> nil() rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs) rm(x,nil()) -> nil() - Signature: {eq/2,if1/4,if2/4,le/2,min/1,minsort/1,rm/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,if1,if2,le,min,minsort,rm} and constructors {0,cons ,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: eq(x,y){x -> s(x),y -> s(y)} = eq(s(x),s(y)) ->^+ eq(x,y) = C[eq(x,y) = eq(x,y){}] WORST_CASE(Omega(n^1),?)
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