details

property	value
status	complete
benchmark	#3.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.62675 seconds
cpu usage	5.08955
user time	4.00949
system time	1.08006
max virtual memory	4677744.0
max residence set size	82940.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) low(n,nil()) -> nil() low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) if_low(true(),n,add(m,x)) -> add(m,low(n,x)) if_low(false(),n,add(m,x)) -> low(n,x) high(n,nil()) -> nil() high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) if_high(true(),n,add(m,x)) -> high(n,x) if_high(false(),n,add(m,x)) -> add(m,high(n,x)) quicksort(nil()) -> nil() quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) Proof: DP Processor: DPs: minus#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) le#(s(x),s(y)) -> le#(x,y) app#(add(n,x),y) -> app#(x,y) low#(n,add(m,x)) -> le#(m,n) low#(n,add(m,x)) -> if_low#(le(m,n),n,add(m,x)) if_low#(true(),n,add(m,x)) -> low#(n,x) if_low#(false(),n,add(m,x)) -> low#(n,x) high#(n,add(m,x)) -> le#(m,n) high#(n,add(m,x)) -> if_high#(le(m,n),n,add(m,x)) if_high#(true(),n,add(m,x)) -> high#(n,x) if_high#(false(),n,add(m,x)) -> high#(n,x) quicksort#(add(n,x)) -> high#(n,x) quicksort#(add(n,x)) -> quicksort#(high(n,x)) quicksort#(add(n,x)) -> low#(n,x) quicksort#(add(n,x)) -> quicksort#(low(n,x)) quicksort#(add(n,x)) -> app#(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) low(n,nil()) -> nil() low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) if_low(true(),n,add(m,x)) -> add(m,low(n,x)) if_low(false(),n,add(m,x)) -> low(n,x) high(n,nil()) -> nil() high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) if_high(true(),n,add(m,x)) -> high(n,x) if_high(false(),n,add(m,x)) -> add(m,high(n,x)) quicksort(nil()) -> nil() quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) TDG Processor: DPs: minus#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) le#(s(x),s(y)) -> le#(x,y) app#(add(n,x),y) -> app#(x,y) low#(n,add(m,x)) -> le#(m,n) low#(n,add(m,x)) -> if_low#(le(m,n),n,add(m,x)) if_low#(true(),n,add(m,x)) -> low#(n,x) if_low#(false(),n,add(m,x)) -> low#(n,x) high#(n,add(m,x)) -> le#(m,n) high#(n,add(m,x)) -> if_high#(le(m,n),n,add(m,x)) if_high#(true(),n,add(m,x)) -> high#(n,x) if_high#(false(),n,add(m,x)) -> high#(n,x) quicksort#(add(n,x)) -> high#(n,x) quicksort#(add(n,x)) -> quicksort#(high(n,x)) quicksort#(add(n,x)) -> low#(n,x) quicksort#(add(n,x)) -> quicksort#(low(n,x)) quicksort#(add(n,x)) -> app#(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) low(n,nil()) -> nil() low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) if_low(true(),n,add(m,x)) -> add(m,low(n,x)) if_low(false(),n,add(m,x)) -> low(n,x) high(n,nil()) -> nil() high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard