details

property	value
status	complete
benchmark	thiemann17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.166963 seconds
cpu usage	0.048762
user time	0.024032
system time	0.02473
max virtual memory	113188.0
max residence set size	9312.0

stage attributes

key	value
starexec-result	YES

output

YES Input TRS: 1: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) 2: sum(cons(0(),x),y) -> sum(x,y) 3: sum(nil(),y) -> y 4: empty(nil()) -> true() 5: empty(cons(n,x)) -> false() 6: tail(nil()) -> nil() 7: tail(cons(n,x)) -> x 8: head(cons(n,x)) -> n 9: weight(x) -> if(empty(x),empty(tail(x)),x) 10: if(true(),b,x) -> weight_undefined_error() 11: if(false(),b,x) -> if2(b,x) 12: if2(true(),x) -> head(x) 13: if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) Number of strict rules: 13 Direct POLO(bPol) ... failed. Uncurrying sum 1: sum^1_cons(s(n),x,cons(m,y)) -> sum^1_cons(n,x,cons(s(m),y)) 2: sum^1_cons(0(),x,y) -> sum(x,y) 3: sum^1_nil(y) -> y 4: empty(nil()) -> true() 5: empty(cons(n,x)) -> false() 6: tail(nil()) -> nil() 7: tail(cons(n,x)) -> x 8: head(cons(n,x)) -> n 9: weight(x) -> if(empty(x),empty(tail(x)),x) 10: if(true(),b,x) -> weight_undefined_error() 11: if(false(),b,x) -> if2(b,x) 12: if2(true(),x) -> head(x) 13: if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) 14: sum(cons(_1,_2),_3) ->= sum^1_cons(_1,_2,_3) 15: sum(nil(),_1) ->= sum^1_nil(_1) Number of strict rules: 13 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #sum^1_cons(0(),x,y) -> #sum(x,y) #2: #if2(false(),x) -> #weight(sum(x,cons(0(),tail(tail(x))))) #3: #if2(false(),x) -> #sum(x,cons(0(),tail(tail(x)))) #4: #if2(false(),x) -> #tail(tail(x)) #5: #if2(false(),x) -> #tail(x) #6: #weight(x) -> #if(empty(x),empty(tail(x)),x) #7: #weight(x) -> #empty(x) #8: #weight(x) -> #empty(tail(x)) #9: #weight(x) -> #tail(x) #10: #if(false(),b,x) -> #if2(b,x) #11: #if2(true(),x) -> #head(x) #12: #sum(cons(_1,_2),_3) ->? #sum^1_cons(_1,_2,_3) #13: #sum^1_cons(s(n),x,cons(m,y)) -> #sum^1_cons(n,x,cons(s(m),y)) #14: #sum(nil(),_1) ->? #sum^1_nil(_1) Number of SCCs: 2, DPs: 6 SCC { #2 #6 #10 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #empty w: max(x1 - 1, 0) s w: max(x1 - 1, 0) #weight w: max(x1 - 12218, 0) sum^1_cons w: max(x3 + 1, 0) #sum^1_nil w: max(x1 - 1, 0) false w: 48868 #head w: max(x1 - 1, 0) true w: 1 sum w: max(x2 + 1, 0) if2 w: max(x1 - 1, 0) tail w: max(x1 - 24434, 0) 0 w: 1 if w: max(x3 - 1, 0) sum^1_nil w: max(x1 + 1, 0) nil w: 0 #tail w: 0 #sum^1_cons w: 0 weight_undefined_error w: 0 weight w: 0 head w: max(x1 - 1, 0) cons w: max(x2 + 36652, 0) #if w: max(x1 - 24435, x2 - 12217, x3 - 24431, 0) empty w: max(x1 + 12216, 0) #sum w: 0 #if2 w: max(x1 - 24432, x2 - 24432, 0) USABLE RULES: { 1..7 14 15 } Removed DPs: #2 #10 Number of SCCs: 1, DPs: 3 SCC { #1 #12 #13 } POLO(Sum)... succeeded. #empty w: 0 s w: x1 + 2 #weight w: 0 sum^1_cons w: x1 + x2 + x3 #sum^1_nil w: 0 false w: 2 #head w: 0 true w: 2 sum w: 2 if2 w: 0 tail w: 0 0 w: 1 if w: 0 sum^1_nil w: 3 nil w: 1 #tail w: 0 #sum^1_cons w: x1 + x2 + 12212 popout

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actions

all output return to TRS Standard