details

property	value
status	complete
benchmark	qsortlast.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.681094 seconds
cpu usage	0.6
user time	0.58
system time	0.02
max virtual memory	356996.0
max residence set size	7192.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE Input TRS: 1: qsort(nil()) -> nil() 2: qsort(cons(x,xs)) -> append(qsort(filterlow(last(cons(x,xs)),cons(x,xs))),cons(last(cons(x,xs)),qsort(filterhigh(last(cons(x,xs)),cons(x,xs))))) 3: filterlow(n,nil()) -> nil() 4: filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs) 5: if1(true(),n,x,xs) -> filterlow(n,xs) 6: if1(false(),n,x,xs) -> cons(x,filterlow(n,xs)) 7: filterhigh(n,nil()) -> nil() 8: filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs) 9: if2(true(),n,x,xs) -> filterhigh(n,xs) 10: if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs)) 11: ge(x,0()) -> true() 12: ge(0(),s(x)) -> false() 13: ge(s(x),s(y)) -> ge(x,y) 14: append(nil(),ys()) -> ys() 15: append(cons(x,xs),ys()) -> cons(x,append(xs,ys())) 16: last(nil()) -> 0() 17: last(cons(x,nil())) -> x 18: last(cons(x,cons(y,xs))) -> last(cons(y,xs)) Number of strict rules: 18 Direct POLO(bPol) ... failed. Uncurrying last 1: qsort(nil()) -> nil() 2: qsort(cons(x,xs)) -> append(qsort(filterlow(last^1_cons(x,xs),cons(x,xs))),cons(last^1_cons(x,xs),qsort(filterhigh(last^1_cons(x,xs),cons(x,xs))))) 3: filterlow(n,nil()) -> nil() 4: filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs) 5: if1(true(),n,x,xs) -> filterlow(n,xs) 6: if1(false(),n,x,xs) -> cons(x,filterlow(n,xs)) 7: filterhigh(n,nil()) -> nil() 8: filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs) 9: if2(true(),n,x,xs) -> filterhigh(n,xs) 10: if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs)) 11: ge(x,0()) -> true() 12: ge(0(),s(x)) -> false() 13: ge(s(x),s(y)) -> ge(x,y) 14: append(nil(),ys()) -> ys() 15: append(cons(x,xs),ys()) -> cons(x,append(xs,ys())) 16: last^1_nil() -> 0() 17: last^1_cons(x,nil()) -> x 18: last^1_cons(x,cons(y,xs)) -> last^1_cons(y,xs) 19: last(cons(_1,_2)) ->= last^1_cons(_1,_2) 20: last(nil()) ->= last^1_nil() Number of strict rules: 18 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #qsort(cons(x,xs)) -> #append(qsort(filterlow(last^1_cons(x,xs),cons(x,xs))),cons(last^1_cons(x,xs),qsort(filterhigh(last^1_cons(x,xs),cons(x,xs))))) #2: #qsort(cons(x,xs)) -> #qsort(filterlow(last^1_cons(x,xs),cons(x,xs))) #3: #qsort(cons(x,xs)) -> #filterlow(last^1_cons(x,xs),cons(x,xs)) #4: #qsort(cons(x,xs)) -> #last^1_cons(x,xs) #5: #qsort(cons(x,xs)) -> #last^1_cons(x,xs) #6: #qsort(cons(x,xs)) -> #qsort(filterhigh(last^1_cons(x,xs),cons(x,xs))) #7: #qsort(cons(x,xs)) -> #filterhigh(last^1_cons(x,xs),cons(x,xs)) #8: #qsort(cons(x,xs)) -> #last^1_cons(x,xs) #9: #if1(false(),n,x,xs) -> #filterlow(n,xs) #10: #ge(s(x),s(y)) -> #ge(x,y) #11: #if2(true(),n,x,xs) -> #filterhigh(n,xs) #12: #last(nil()) ->? #last^1_nil() #13: #if2(false(),n,x,xs) -> #filterhigh(n,xs) #14: #if1(true(),n,x,xs) -> #filterlow(n,xs) #15: #last(cons(_1,_2)) ->? #last^1_cons(_1,_2) #16: #filterhigh(n,cons(x,xs)) -> #if2(ge(x,n),n,x,xs) #17: #filterhigh(n,cons(x,xs)) -> #ge(x,n) #18: #append(cons(x,xs),ys()) -> #append(xs,ys()) #19: #filterlow(n,cons(x,xs)) -> #if1(ge(n,x),n,x,xs) #20: #filterlow(n,cons(x,xs)) -> #ge(n,x) #21: #last^1_cons(x,cons(y,xs)) -> #last^1_cons(y,xs) Number of SCCs: 6, DPs: 11 SCC { #18 } POLO(Sum)... succeeded. s w: 0 #append w: x1 if1 w: 0 false w: 0 #ge w: 0 filterlow w: 0 last^1_nil w: 0 qsort w: 0 true w: 0 #last w: 0 #if1 w: 0 #last^1_nil w: 0 if2 w: 0 #qsort w: 0 append w: 0 0 w: 0 ge w: 0 #last^1_cons w: 0 last w: 0 nil w: 0 #filterlow w: 0 last^1_cons w: 0 cons w: x2 + 1 filterhigh w: 0 ys w: 0 #filterhigh w: 0 #if2 w: 0 USABLE RULES: { } Removed DPs: #18 Number of SCCs: 5, DPs: 10 popout

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job log

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actions

all output return to TRS Standard