details

property	value
status	complete
benchmark	mapHard.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.3628 seconds
cpu usage	4.0975
user time	3.30384
system time	0.793664
max virtual memory	5676612.0
max residence set size	83372.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: ap(ap(map(),f),xs) -> ap(ap(ap(if(),ap(isEmpty(),xs)),f),xs) ap(ap(ap(if(),true()),f),xs) -> nil() ap(ap(ap(if(),false()),f),xs) -> ap(ap(cons(),ap(f,ap(last(),xs))),ap(ap(map(),f),ap(dropLast(),xs))) ap(isEmpty(),nil()) -> true() ap(isEmpty(),ap(ap(cons(),x),xs)) -> false() ap(last(),ap(ap(cons(),x),nil())) -> x ap(last(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) -> ap(last(),ap(ap(cons(),y),ys)) ap(dropLast(),nil()) -> nil() ap(dropLast(),ap(ap(cons(),x),nil())) -> nil() ap(dropLast(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) -> ap(ap(cons(),x),ap(dropLast(),ap(ap(cons(),y),ys))) Proof: Extended Uncurrying Processor: application symbol: ap symbol table: dropLast ==> dropLast0/0 dropLast1/1 last ==> last0/0 last1/1 cons ==> cons0/0 cons1/1 cons2/2 false ==> false0/0 nil ==> nil0/0 true ==> true0/0 isEmpty ==> isEmpty0/0 isEmpty1/1 if ==> if0/0 if1/1 if2/2 if3/3 map ==> map0/0 map1/1 map2/2 uncurry-rules: ap(map1(x5),x6) -> map2(x5,x6) ap(map0(),x5) -> map1(x5) ap(if2(x8,x9),x10) -> if3(x8,x9,x10) ap(if1(x8),x9) -> if2(x8,x9) ap(if0(),x8) -> if1(x8) ap(isEmpty0(),x12) -> isEmpty1(x12) ap(cons1(x17),x18) -> cons2(x17,x18) ap(cons0(),x17) -> cons1(x17) ap(last0(),x20) -> last1(x20) ap(dropLast0(),x22) -> dropLast1(x22) eta-rules: problem: map2(f,xs) -> if3(isEmpty1(xs),f,xs) if3(true0(),f,xs) -> nil0() if3(false0(),f,xs) -> cons2(ap(f,last1(xs)),map2(f,dropLast1(xs))) isEmpty1(nil0()) -> true0() isEmpty1(cons2(x,xs)) -> false0() last1(cons2(x,nil0())) -> x last1(cons2(x,cons2(y,ys))) -> last1(cons2(y,ys)) dropLast1(nil0()) -> nil0() dropLast1(cons2(x,nil0())) -> nil0() dropLast1(cons2(x,cons2(y,ys))) -> cons2(x,dropLast1(cons2(y,ys))) ap(map1(x5),x6) -> map2(x5,x6) ap(map0(),x5) -> map1(x5) ap(if2(x8,x9),x10) -> if3(x8,x9,x10) ap(if1(x8),x9) -> if2(x8,x9) ap(if0(),x8) -> if1(x8) ap(isEmpty0(),x12) -> isEmpty1(x12) ap(cons1(x17),x18) -> cons2(x17,x18) ap(cons0(),x17) -> cons1(x17) ap(last0(),x20) -> last1(x20) ap(dropLast0(),x22) -> dropLast1(x22) DP Processor: DPs: map{2,#}(f,xs) -> isEmpty{1,#}(xs) map{2,#}(f,xs) -> if{3,#}(isEmpty1(xs),f,xs) if{3,#}(false0(),f,xs) -> dropLast{1,#}(xs) if{3,#}(false0(),f,xs) -> map{2,#}(f,dropLast1(xs)) if{3,#}(false0(),f,xs) -> last{1,#}(xs) if{3,#}(false0(),f,xs) -> ap#(f,last1(xs)) last{1,#}(cons2(x,cons2(y,ys))) -> last{1,#}(cons2(y,ys)) dropLast{1,#}(cons2(x,cons2(y,ys))) -> dropLast{1,#}(cons2(y,ys)) ap#(map1(x5),x6) -> map{2,#}(x5,x6) ap#(if2(x8,x9),x10) -> if{3,#}(x8,x9,x10) ap#(isEmpty0(),x12) -> isEmpty{1,#}(x12) ap#(last0(),x20) -> last{1,#}(x20) ap#(dropLast0(),x22) -> dropLast{1,#}(x22) TRS: map2(f,xs) -> if3(isEmpty1(xs),f,xs) if3(true0(),f,xs) -> nil0() if3(false0(),f,xs) -> cons2(ap(f,last1(xs)),map2(f,dropLast1(xs))) isEmpty1(nil0()) -> true0() isEmpty1(cons2(x,xs)) -> false0() last1(cons2(x,nil0())) -> x last1(cons2(x,cons2(y,ys))) -> last1(cons2(y,ys)) dropLast1(nil0()) -> nil0() dropLast1(cons2(x,nil0())) -> nil0() dropLast1(cons2(x,cons2(y,ys))) -> cons2(x,dropLast1(cons2(y,ys))) ap(map1(x5),x6) -> map2(x5,x6) ap(map0(),x5) -> map1(x5) ap(if2(x8,x9),x10) -> if3(x8,x9,x10) ap(if1(x8),x9) -> if2(x8,x9) ap(if0(),x8) -> if1(x8) ap(isEmpty0(),x12) -> isEmpty1(x12) ap(cons1(x17),x18) -> cons2(x17,x18) ap(cons0(),x17) -> cons1(x17) ap(last0(),x20) -> last1(x20) ap(dropLast0(),x22) -> dropLast1(x22) popout

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