* Step 1: Sum WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(eqNatList[Match][Cons][Match][Cons][Ite]) = {1},
uargs(nolexicord[Ite][False][Ite]) = {1}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(!EQ) = [4]
p(0) = [1]
p(Cons) = [1] x2 + [0]
p(False) = [1]
p(Nil) = [1]
p(S) = [0]
p(True) = [0]
p(eqNatList) = [2]
p(eqNatList[Match][Cons][Match][Cons][Ite]) = [1] x1 + [6]
p(goal) = [5] x1 + [4] x3 + [5] x4 + [5] x5 + [1] x6 + [1]
p(nolexicord) = [4] x1 + [4] x3 + [2] x4 + [1] x5 + [1] x6 + [0]
p(nolexicord[Ite][False][Ite]) = [1] x1 + [4] x2 + [4] x4 + [2] x5 + [1] x6 + [1] x7 + [6]
p(number42) = [0]
Following rules are strictly oriented:
eqNatList(Cons(x,xs),Nil()) = [2]
> [1]
= False()
eqNatList(Nil(),Cons(y,ys)) = [2]
> [1]
= False()
eqNatList(Nil(),Nil()) = [2]
> [0]
= True()
goal(a1,b1,a2,b2,a3,b3) = [5] a1 + [4] a2 + [5] a3 + [5] b2 + [1] b3 + [1]
> [4] a1 + [4] a2 + [1] a3 + [2] b2 + [1] b3 + [0]
= nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) = [4] a2 + [1] a3 + [2] b2 + [1] b3 + [4]
> [1]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
Following rules are (at-least) weakly oriented:
!EQ(0(),0()) = [4]
>= [0]
= True()
!EQ(0(),S(y)) = [4]
>= [1]
= False()
!EQ(S(x),0()) = [4]
>= [1]
= False()
!EQ(S(x),S(y)) = [4]
>= [4]
= !EQ(x,y)
eqNatList(Cons(x,xs),Cons(y,ys)) = [2]
>= [10]
= eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) = [4] a2 + [1] a3 + [2] b2 + [1] b3 + [4] xs + [0]
>= [4] a2 + [1] a3 + [2] b2 + [1] b3 + [4] xs + [8]
= nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1),Cons(x,xs),b1,a2,b2,a3,b3)
nolexicord[Ite][False][Ite](False() = [1] xs + [11] xs' + [7]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs))
>= [1] xs + [11] xs' + [0]
= nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True() = [1] xs + [11] xs' + [6]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs'))
>= [1] xs + [11] xs' + [0]
= nolexicord(xs',xs',xs',xs',xs',xs)
number42() = [0]
>= [1]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(eqNatList[Match][Cons][Match][Cons][Ite]) = {1},
uargs(nolexicord[Ite][False][Ite]) = {1}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(!EQ) = [1]
p(0) = [1]
p(Cons) = [1] x1 + [0]
p(False) = [0]
p(Nil) = [1]
p(S) = [1] x1 + [1]
p(True) = [1]
p(eqNatList) = [1]
p(eqNatList[Match][Cons][Match][Cons][Ite]) = [1] x1 + [1]
p(goal) = [1] x3 + [3] x4 + [2] x5 + [5] x6 + [4]
p(nolexicord) = [1]
p(nolexicord[Ite][False][Ite]) = [1] x1 + [7]
p(number42) = [4]
Following rules are strictly oriented:
number42() = [4]
> [1]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
Following rules are (at-least) weakly oriented:
!EQ(0(),0()) = [1]
>= [1]
= True()
!EQ(0(),S(y)) = [1]
>= [0]
= False()
!EQ(S(x),0()) = [1]
>= [0]
= False()
!EQ(S(x),S(y)) = [1]
>= [1]
= !EQ(x,y)
eqNatList(Cons(x,xs),Cons(y,ys)) = [1]
>= [2]
= eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) = [1]
>= [0]
= False()
eqNatList(Nil(),Cons(y,ys)) = [1]
>= [0]
= False()
eqNatList(Nil(),Nil()) = [1]
>= [1]
= True()
goal(a1,b1,a2,b2,a3,b3) = [1] a2 + [2] a3 + [3] b2 + [5] b3 + [4]
>= [1]
= nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) = [1]
>= [8]
= nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1),Cons(x,xs),b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) = [1]
>= [1]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False() = [7]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs))
>= [1]
= nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True() = [8]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs'))
>= [1]
= nolexicord(xs',xs',xs',xs',xs',xs)
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(eqNatList[Match][Cons][Match][Cons][Ite]) = {1},
uargs(nolexicord[Ite][False][Ite]) = {1}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(!EQ) = [2]
p(0) = [0]
p(Cons) = [1] x2 + [0]
p(False) = [1]
p(Nil) = [0]
p(S) = [0]
p(True) = [1]
p(eqNatList) = [4]
p(eqNatList[Match][Cons][Match][Cons][Ite]) = [1] x1 + [0]
p(goal) = [5] x1 + [5] x3 + [5] x4 + [2] x5 + [5]
p(nolexicord) = [3] x3 + [2] x4 + [2]
p(nolexicord[Ite][False][Ite]) = [1] x1 + [3] x4 + [2] x5 + [4]
p(number42) = [0]
Following rules are strictly oriented:
eqNatList(Cons(x,xs),Cons(y,ys)) = [4]
> [2]
= eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
Following rules are (at-least) weakly oriented:
!EQ(0(),0()) = [2]
>= [1]
= True()
!EQ(0(),S(y)) = [2]
>= [1]
= False()
!EQ(S(x),0()) = [2]
>= [1]
= False()
!EQ(S(x),S(y)) = [2]
>= [2]
= !EQ(x,y)
eqNatList(Cons(x,xs),Nil()) = [4]
>= [1]
= False()
eqNatList(Nil(),Cons(y,ys)) = [4]
>= [1]
= False()
eqNatList(Nil(),Nil()) = [4]
>= [1]
= True()
goal(a1,b1,a2,b2,a3,b3) = [5] a1 + [5] a2 + [2] a3 + [5] b2 + [5]
>= [3] a2 + [2] b2 + [2]
= nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) = [3] a2 + [2] b2 + [2]
>= [3] a2 + [2] b2 + [8]
= nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1),Cons(x,xs),b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) = [3] a2 + [2] b2 + [2]
>= [0]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False() = [5] xs' + [5]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs))
>= [5] xs' + [2]
= nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True() = [5] xs' + [5]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs'))
>= [5] xs' + [2]
= nolexicord(xs',xs',xs',xs',xs',xs)
number42() = [0]
>= [0]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 5: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity (Just 1))), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
+ Details:
We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity (Just 1))):
The following argument positions are considered usable:
uargs(eqNatList[Match][Cons][Match][Cons][Ite]) = {1},
uargs(nolexicord[Ite][False][Ite]) = {1}
Following symbols are considered usable:
{!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite],number42}
TcT has computed the following interpretation:
p(!EQ) = [0 0] x_1 + [0]
[2 0] [2]
p(0) = [1]
[0]
p(Cons) = [1 1] x_2 + [0]
[0 0] [0]
p(False) = [0]
[1]
p(Nil) = [1]
[2]
p(S) = [1 3] x_1 + [0]
[0 0] [2]
p(True) = [0]
[1]
p(eqNatList) = [0 0] x_1 + [0 0] x_2 + [0]
[0 2] [0 1] [0]
p(eqNatList[Match][Cons][Match][Cons][Ite]) = [1 0] x_1 + [0]
[0 0] [0]
p(goal) = [2 0] x_1 + [0 3] x_2 + [3 2] x_3 + [1 0] x_4 + [0 2] x_5 + [2 0] x_6 + [2]
[0 2] [3 3] [3 2] [1 0] [0 1] [2 2] [1]
p(nolexicord) = [2 0] x_1 + [0 3] x_2 + [2 1] x_3 + [0 0] x_5 + [1]
[0 1] [3 3] [3 1] [0 1] [1]
p(nolexicord[Ite][False][Ite]) = [2 3] x_1 + [2 0] x_2 + [0 0] x_3 + [2 0] x_4 + [0]
[0 0] [0 1] [3 2] [3 0] [1]
p(number42) = [3]
[0]
Following rules are strictly oriented:
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) = [2 1] a2 + [0 0] a3 + [0 3] b1 + [2 2] xs + [1]
[3 1] [0 1] [3 3] [0 0] [1]
> [2 0] a2 + [0 3] b1 + [2 2] xs + [0]
[3 0] [3 2] [0 0] [1]
= nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1),Cons(x,xs),b1,a2,b2,a3,b3)
Following rules are (at-least) weakly oriented:
!EQ(0(),0()) = [0]
[4]
>= [0]
[1]
= True()
!EQ(0(),S(y)) = [0]
[4]
>= [0]
[1]
= False()
!EQ(S(x),0()) = [0 0] x + [0]
[2 6] [2]
>= [0]
[1]
= False()
!EQ(S(x),S(y)) = [0 0] x + [0]
[2 6] [2]
>= [0 0] x + [0]
[2 0] [2]
= !EQ(x,y)
eqNatList(Cons(x,xs),Cons(y,ys)) = [0]
[0]
>= [0]
[0]
= eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) = [0]
[2]
>= [0]
[1]
= False()
eqNatList(Nil(),Cons(y,ys)) = [0]
[4]
>= [0]
[1]
= False()
eqNatList(Nil(),Nil()) = [0]
[6]
>= [0]
[1]
= True()
goal(a1,b1,a2,b2,a3,b3) = [2 0] a1 + [3 2] a2 + [0 2] a3 + [0 3] b1 + [1 0] b2 + [2 0] b3 + [2]
[0 2] [3 2] [0 1] [3 3] [1 0] [2 2] [1]
>= [2 0] a1 + [2 1] a2 + [0 0] a3 + [0 3] b1 + [1]
[0 1] [3 1] [0 1] [3 3] [1]
= nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) = [2 1] a2 + [0 0] a3 + [0 3] b1 + [3]
[3 1] [0 1] [3 3] [3]
>= [3]
[0]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False() = [4 4] xs' + [3]
,Cons(x',xs') [6 6] [1]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs))
>= [4 4] xs' + [1]
[6 6] [1]
= nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True() = [4 4] xs' + [3]
,Cons(x',xs') [6 6] [1]
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs'))
>= [4 4] xs' + [1]
[6 6] [1]
= nolexicord(xs',xs',xs',xs',xs',xs)
number42() = [3]
[0]
>= [3]
[0]
= Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
* Step 6: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
!EQ(0(),0()) -> True()
!EQ(0(),S(y)) -> False()
!EQ(S(x),0()) -> False()
!EQ(S(x),S(y)) -> !EQ(x,y)
eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Match][Cons][Match][Cons][Ite](!EQ(x,y),y,ys,x,xs)
eqNatList(Cons(x,xs),Nil()) -> False()
eqNatList(Nil(),Cons(y,ys)) -> False()
eqNatList(Nil(),Nil()) -> True()
goal(a1,b1,a2,b2,a3,b3) -> nolexicord(a1,b1,a2,b2,a3,b3)
nolexicord(Cons(x,xs),b1,a2,b2,a3,b3) -> nolexicord[Ite][False][Ite](eqNatList(Cons(x,xs),b1)
,Cons(x,xs)
,b1
,a2
,b2
,a3
,b3)
nolexicord(Nil(),b1,a2,b2,a3,b3) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
nolexicord[Ite][False][Ite](False()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)) -> nolexicord(xs',xs',xs',xs',xs',xs)
nolexicord[Ite][False][Ite](True()
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x',xs')
,Cons(x,xs)
,Cons(x',xs')) -> nolexicord(xs',xs',xs',xs',xs',xs)
number42() -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil()))))))))))))))))))))))))))))))))))))))))))
- Signature:
{!EQ/2,eqNatList/2,goal/6,nolexicord/6,nolexicord[Ite][False][Ite]/7,number42/0} / {0/0,Cons/2,False/0,Nil/0
,S/1,True/0,eqNatList[Match][Cons][Match][Cons][Ite]/5}
- Obligation:
innermost runtime complexity wrt. defined symbols {!EQ,eqNatList,goal,nolexicord,nolexicord[Ite][False][Ite]
,number42} and constructors {0,Cons,False,Nil,S,True,eqNatList[Match][Cons][Match][Cons][Ite]}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))