details

property	value
status	complete
benchmark	aprove01.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	Secret_07_TRS

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.262869 seconds
cpu usage	0.071766
user time	0.049714
system time	0.022052
max virtual memory	113188.0
max residence set size	6548.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE Input TRS: 1: times(x,y) -> sum(generate(x,y)) 2: generate(x,y) -> gen(x,y,0()) 3: gen(x,y,z) -> if(ge(z,x),x,y,z) 4: if(true(),x,y,z) -> nil() 5: if(false(),x,y,z) -> cons(y,gen(x,y,s(z))) 6: sum(xs) -> sum2(xs,0()) 7: sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y) 8: ifsum(true(),b,xs,y) -> y 9: ifsum(false(),b,xs,y) -> ifsum2(b,xs,y) 10: ifsum2(true(),xs,y) -> sum2(tail(xs),y) 11: ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y)) 12: isNil(nil()) -> true() 13: isNil(cons(x,xs)) -> false() 14: tail(nil()) -> nil() 15: tail(cons(x,xs)) -> xs 16: head(cons(x,xs)) -> x 17: head(nil()) -> error() 18: isZero(0()) -> true() 19: isZero(s(0())) -> false() 20: isZero(s(s(x))) -> isZero(s(x)) 21: p(0()) -> s(s(0())) 22: p(s(0())) -> 0() 23: p(s(s(x))) -> s(p(s(x))) 24: ge(x,0()) -> true() 25: ge(0(),s(y)) -> false() 26: ge(s(x),s(y)) -> ge(x,y) 27: a() -> c() 28: a() -> d() Number of strict rules: 28 Direct POLO(bPol) ... failed. Uncurrying isZero p 1: times(x,y) -> sum(generate(x,y)) 2: generate(x,y) -> gen(x,y,0()) 3: gen(x,y,z) -> if(ge(z,x),x,y,z) 4: if(true(),x,y,z) -> nil() 5: if(false(),x,y,z) -> cons(y,gen(x,y,s(z))) 6: sum(xs) -> sum2(xs,0()) 7: sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y) 8: ifsum(true(),b,xs,y) -> y 9: ifsum(false(),b,xs,y) -> ifsum2(b,xs,y) 10: ifsum2(true(),xs,y) -> sum2(tail(xs),y) 11: ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y)) 12: isNil(nil()) -> true() 13: isNil(cons(x,xs)) -> false() 14: tail(nil()) -> nil() 15: tail(cons(x,xs)) -> xs 16: head(cons(x,xs)) -> x 17: head(nil()) -> error() 18: isZero^1_0() -> true() 19: isZero^1_s(0()) -> false() 20: isZero^1_s(s(x)) -> isZero^1_s(x) 21: p^1_0() -> s(s(0())) 22: p^1_s(0()) -> 0() 23: p^1_s(s(x)) -> s(p^1_s(x)) 24: ge(x,0()) -> true() 25: ge(0(),s(y)) -> false() 26: ge(s(x),s(y)) -> ge(x,y) 27: a() -> c() 28: a() -> d() 29: p(0()) ->= p^1_0() 30: p(s(_1)) ->= p^1_s(_1) 31: isZero(0()) ->= isZero^1_0() 32: isZero(s(_1)) ->= isZero^1_s(_1) Number of strict rules: 28 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #generate(x,y) -> #gen(x,y,0()) #2: #p(0()) ->? #p^1_0() #3: #sum(xs) -> #sum2(xs,0()) #4: #ifsum(false(),b,xs,y) -> #ifsum2(b,xs,y) #5: #ifsum2(false(),xs,y) -> #sum2(cons(p(head(xs)),tail(xs)),s(y)) #6: #ifsum2(false(),xs,y) -> #p(head(xs)) #7: #ifsum2(false(),xs,y) -> #head(xs) #8: #ifsum2(false(),xs,y) -> #tail(xs) #9: #p^1_s(s(x)) -> #p^1_s(x) #10: #isZero(0()) ->? #isZero^1_0() #11: #p(s(_1)) ->? #p^1_s(_1) #12: #isZero^1_s(s(x)) -> #isZero^1_s(x) #13: #sum2(xs,y) -> #ifsum(isNil(xs),isZero(head(xs)),xs,y) #14: #sum2(xs,y) -> #isNil(xs) #15: #sum2(xs,y) -> #isZero(head(xs)) #16: #sum2(xs,y) -> #head(xs) #17: #ifsum2(true(),xs,y) -> #sum2(tail(xs),y) #18: #ifsum2(true(),xs,y) -> #tail(xs) #19: #if(false(),x,y,z) -> #gen(x,y,s(z)) #20: #isZero(s(_1)) ->? #isZero^1_s(_1) #21: #ge(s(x),s(y)) -> #ge(x,y) #22: #gen(x,y,z) -> #if(ge(z,x),x,y,z) #23: #gen(x,y,z) -> #ge(z,x) #24: #times(x,y) -> #sum(generate(x,y)) #25: #times(x,y) -> #generate(x,y) Number of SCCs: 5, DPs: 9 SCC { #9 } POLO(Sum)... succeeded. a w: 0 d w: 0 s w: x1 + 1 #p^1_0 w: 0 popout

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actions

all output return to TRS Standard