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Runti Compl Full Rewri 10127 pair #381902848
details
property
value
status
complete
benchmark
sumList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
295.421793938 seconds
cpu usage
497.662227168
max memory
2.556801024E9
stage attributes
key
value
output-size
2897
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: head(cons(x,xs)) -> x if(false(),false(),y,xs,ys,x) -> sumList(ys,x) if(false(),true(),y,xs,ys,x) -> sumList(xs,y) if(true(),b,y,xs,ys,x) -> y inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() isZero(0()) -> true() isZero(s(x)) -> false() p(0()) -> 0() p(s(0())) -> 0() p(s(s(x))) -> s(p(s(x))) sum(xs) -> sumList(xs,0()) sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) tail(cons(x,xs)) -> xs tail(nil()) -> nil() - Signature: {head/1,if/6,inc/1,isEmpty/1,isZero/1,p/1,sum/1,sumList/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {head,if,inc,isEmpty,isZero,p,sum,sumList,tail} 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: head(cons(x,xs)) -> x if(false(),false(),y,xs,ys,x) -> sumList(ys,x) if(false(),true(),y,xs,ys,x) -> sumList(xs,y) if(true(),b,y,xs,ys,x) -> y inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() isZero(0()) -> true() isZero(s(x)) -> false() p(0()) -> 0() p(s(0())) -> 0() p(s(s(x))) -> s(p(s(x))) sum(xs) -> sumList(xs,0()) sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) tail(cons(x,xs)) -> xs tail(nil()) -> nil() - Signature: {head/1,if/6,inc/1,isEmpty/1,isZero/1,p/1,sum/1,sumList/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {head,if,inc,isEmpty,isZero,p,sum,sumList,tail} and constructors {0 ,cons,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: inc(x){x -> s(x)} = inc(s(x)) ->^+ s(inc(x)) = C[inc(x) = inc(x){}] WORST_CASE(Omega(n^1),?)
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