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TRS Standard pair #487072742
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
n183.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
3.94549 seconds
cpu usage
14.3923
user time
12.6893
system time
1.70293
max virtual memory
5908220.0
max residence set size
112696.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() isZero(0()) -> true() isZero(s(x)) -> false() head(cons(x,xs)) -> x tail(cons(x,xs)) -> xs tail(nil()) -> nil() p(s(s(x))) -> s(p(s(x))) p(s(0())) -> 0() p(0()) -> 0() inc(s(x)) -> s(inc(x)) inc(0()) -> s(0()) sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) if(true(),b,y,xs,ys,x) -> y if(false(),true(),y,xs,ys,x) -> sumList(xs,y) if(false(),false(),y,xs,ys,x) -> sumList(ys,x) sum(xs) -> sumList(xs,0()) Proof: DP Processor: DPs: p#(s(s(x))) -> p#(s(x)) inc#(s(x)) -> inc#(x) sumList#(xs,y) -> inc#(y) sumList#(xs,y) -> p#(head(xs)) sumList#(xs,y) -> tail#(xs) sumList#(xs,y) -> head#(xs) sumList#(xs,y) -> isZero#(head(xs)) sumList#(xs,y) -> isEmpty#(xs) sumList#(xs,y) -> if#(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) if#(false(),true(),y,xs,ys,x) -> sumList#(xs,y) if#(false(),false(),y,xs,ys,x) -> sumList#(ys,x) sum#(xs) -> sumList#(xs,0()) TRS: isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() isZero(0()) -> true() isZero(s(x)) -> false() head(cons(x,xs)) -> x tail(cons(x,xs)) -> xs tail(nil()) -> nil() p(s(s(x))) -> s(p(s(x))) p(s(0())) -> 0() p(0()) -> 0() inc(s(x)) -> s(inc(x)) inc(0()) -> s(0()) sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) if(true(),b,y,xs,ys,x) -> y if(false(),true(),y,xs,ys,x) -> sumList(xs,y) if(false(),false(),y,xs,ys,x) -> sumList(ys,x) sum(xs) -> sumList(xs,0()) TDG Processor: DPs: p#(s(s(x))) -> p#(s(x)) inc#(s(x)) -> inc#(x) sumList#(xs,y) -> inc#(y) sumList#(xs,y) -> p#(head(xs)) sumList#(xs,y) -> tail#(xs) sumList#(xs,y) -> head#(xs) sumList#(xs,y) -> isZero#(head(xs)) sumList#(xs,y) -> isEmpty#(xs) sumList#(xs,y) -> if#(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) if#(false(),true(),y,xs,ys,x) -> sumList#(xs,y) if#(false(),false(),y,xs,ys,x) -> sumList#(ys,x) sum#(xs) -> sumList#(xs,0()) TRS: isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() isZero(0()) -> true() isZero(s(x)) -> false() head(cons(x,xs)) -> x tail(cons(x,xs)) -> xs tail(nil()) -> nil() p(s(s(x))) -> s(p(s(x))) p(s(0())) -> 0() p(0()) -> 0() inc(s(x)) -> s(inc(x)) inc(0()) -> s(0()) sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) if(true(),b,y,xs,ys,x) -> y if(false(),true(),y,xs,ys,x) -> sumList(xs,y) if(false(),false(),y,xs,ys,x) -> sumList(ys,x) sum(xs) -> sumList(xs,0()) graph: 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)) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> isEmpty#(xs) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> isZero#(head(xs)) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> head#(xs) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> tail#(xs) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> p#(head(xs)) sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> inc#(y) if#(false(),true(),y,xs,ys,x) -> sumList#(xs,y) -> sumList#(xs,y) ->
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