*** 1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
add(s(X),Y) -> s(n__add(activate(X),Y))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Weak DP Rules:
Weak TRS Rules:
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
InnermostRuleRemoval
Proof:
Arguments of following rules are not normal-forms.
add(s(X),Y) -> s(n__add(activate(X),Y))
fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
All above mentioned rules can be savely removed.
*** 1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Weak DP Rules:
Weak TRS Rules:
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
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(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(0) = [0]
p(activate) = [1] x1 + [2]
p(add) = [1] x1 + [1] x2 + [0]
p(cons) = [1] x2 + [3]
p(from) = [1] x1 + [0]
p(fst) = [1] x1 + [1] x2 + [0]
p(len) = [1] x1 + [0]
p(n__add) = [1] x1 + [1] x2 + [0]
p(n__from) = [1] x1 + [7]
p(n__fst) = [1] x1 + [1] x2 + [0]
p(n__len) = [1] x1 + [0]
p(n__s) = [1] x1 + [2]
p(nil) = [0]
p(s) = [1] x1 + [0]
Following rules are strictly oriented:
activate(X) = [1] X + [2]
> [1] X + [0]
= X
activate(n__from(X)) = [1] X + [9]
> [1] X + [2]
= from(activate(X))
activate(n__s(X)) = [1] X + [4]
> [1] X + [0]
= s(X)
len(cons(X,Z)) = [1] Z + [3]
> [1] Z + [2]
= s(n__len(activate(Z)))
Following rules are (at-least) weakly oriented:
activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [4]
= add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [4]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1] X + [2]
>= [1] X + [2]
= len(activate(X))
add(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__add(X1,X2)
add(0(),X) = [1] X + [0]
>= [1] X + [0]
= X
from(X) = [1] X + [0]
>= [1] X + [12]
= cons(X,n__from(n__s(X)))
from(X) = [1] X + [0]
>= [1] X + [7]
= n__from(X)
fst(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__fst(X1,X2)
fst(0(),Z) = [1] Z + [0]
>= [0]
= nil()
len(X) = [1] X + [0]
>= [1] X + [0]
= n__len(X)
len(nil()) = [0]
>= [0]
= 0()
s(X) = [1] X + [0]
>= [1] X + [2]
= n__s(X)
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(nil()) -> 0()
s(X) -> n__s(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__from(X)) -> from(activate(X))
activate(n__s(X)) -> s(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
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(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(0) = [8]
p(activate) = [1] x1 + [2]
p(add) = [1] x1 + [1] x2 + [2]
p(cons) = [1] x2 + [4]
p(from) = [1] x1 + [0]
p(fst) = [1] x1 + [1] x2 + [0]
p(len) = [1] x1 + [0]
p(n__add) = [1] x1 + [1] x2 + [0]
p(n__from) = [1] x1 + [0]
p(n__fst) = [1] x1 + [1] x2 + [0]
p(n__len) = [1] x1 + [1]
p(n__s) = [1] x1 + [9]
p(nil) = [0]
p(s) = [1] x1 + [1]
Following rules are strictly oriented:
activate(n__len(X)) = [1] X + [3]
> [1] X + [2]
= len(activate(X))
add(X1,X2) = [1] X1 + [1] X2 + [2]
> [1] X1 + [1] X2 + [0]
= n__add(X1,X2)
add(0(),X) = [1] X + [10]
> [1] X + [0]
= X
fst(0(),Z) = [1] Z + [8]
> [0]
= nil()
Following rules are (at-least) weakly oriented:
activate(X) = [1] X + [2]
>= [1] X + [0]
= X
activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [6]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1] X + [2]
>= [1] X + [2]
= from(activate(X))
activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [4]
= fst(activate(X1),activate(X2))
activate(n__s(X)) = [1] X + [11]
>= [1] X + [1]
= s(X)
from(X) = [1] X + [0]
>= [1] X + [13]
= cons(X,n__from(n__s(X)))
from(X) = [1] X + [0]
>= [1] X + [0]
= n__from(X)
fst(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__fst(X1,X2)
len(X) = [1] X + [0]
>= [1] X + [1]
= n__len(X)
len(cons(X,Z)) = [1] Z + [4]
>= [1] Z + [4]
= s(n__len(activate(Z)))
len(nil()) = [0]
>= [8]
= 0()
s(X) = [1] X + [1]
>= [1] X + [9]
= n__s(X)
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
len(X) -> n__len(X)
len(nil()) -> 0()
s(X) -> n__s(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__from(X)) -> from(activate(X))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(0(),Z) -> nil()
len(cons(X,Z)) -> s(n__len(activate(Z)))
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
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(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(0) = [1]
p(activate) = [1] x1 + [6]
p(add) = [1] x1 + [1] x2 + [0]
p(cons) = [1] x2 + [7]
p(from) = [1] x1 + [1]
p(fst) = [1] x1 + [1] x2 + [1]
p(len) = [1] x1 + [1]
p(n__add) = [1] x1 + [1] x2 + [0]
p(n__from) = [1] x1 + [4]
p(n__fst) = [1] x1 + [1] x2 + [0]
p(n__len) = [1] x1 + [2]
p(n__s) = [1] x1 + [2]
p(nil) = [1]
p(s) = [1] x1 + [0]
Following rules are strictly oriented:
fst(X1,X2) = [1] X1 + [1] X2 + [1]
> [1] X1 + [1] X2 + [0]
= n__fst(X1,X2)
len(nil()) = [2]
> [1]
= 0()
Following rules are (at-least) weakly oriented:
activate(X) = [1] X + [6]
>= [1] X + [0]
= X
activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [6]
>= [1] X1 + [1] X2 + [12]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1] X + [10]
>= [1] X + [7]
= from(activate(X))
activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [6]
>= [1] X1 + [1] X2 + [13]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1] X + [8]
>= [1] X + [7]
= len(activate(X))
activate(n__s(X)) = [1] X + [8]
>= [1] X + [0]
= s(X)
add(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__add(X1,X2)
add(0(),X) = [1] X + [1]
>= [1] X + [0]
= X
from(X) = [1] X + [1]
>= [1] X + [13]
= cons(X,n__from(n__s(X)))
from(X) = [1] X + [1]
>= [1] X + [4]
= n__from(X)
fst(0(),Z) = [1] Z + [2]
>= [1]
= nil()
len(X) = [1] X + [1]
>= [1] X + [2]
= n__len(X)
len(cons(X,Z)) = [1] Z + [8]
>= [1] Z + [8]
= s(n__len(activate(Z)))
s(X) = [1] X + [0]
>= [1] X + [2]
= n__s(X)
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
len(X) -> n__len(X)
s(X) -> n__s(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__from(X)) -> from(activate(X))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
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(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(0) = [2]
p(activate) = [1] x1 + [2]
p(add) = [1] x1 + [1] x2 + [0]
p(cons) = [1] x2 + [5]
p(from) = [1] x1 + [0]
p(fst) = [1] x1 + [1] x2 + [0]
p(len) = [1] x1 + [0]
p(n__add) = [1] x1 + [1] x2 + [0]
p(n__from) = [1] x1 + [0]
p(n__fst) = [1] x1 + [1] x2 + [0]
p(n__len) = [1] x1 + [2]
p(n__s) = [1] x1 + [0]
p(nil) = [2]
p(s) = [1] x1 + [1]
Following rules are strictly oriented:
s(X) = [1] X + [1]
> [1] X + [0]
= n__s(X)
Following rules are (at-least) weakly oriented:
activate(X) = [1] X + [2]
>= [1] X + [0]
= X
activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [4]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1] X + [2]
>= [1] X + [2]
= from(activate(X))
activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [2]
>= [1] X1 + [1] X2 + [4]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1] X + [4]
>= [1] X + [2]
= len(activate(X))
activate(n__s(X)) = [1] X + [2]
>= [1] X + [1]
= s(X)
add(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__add(X1,X2)
add(0(),X) = [1] X + [2]
>= [1] X + [0]
= X
from(X) = [1] X + [0]
>= [1] X + [5]
= cons(X,n__from(n__s(X)))
from(X) = [1] X + [0]
>= [1] X + [0]
= n__from(X)
fst(X1,X2) = [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
= n__fst(X1,X2)
fst(0(),Z) = [1] Z + [2]
>= [2]
= nil()
len(X) = [1] X + [0]
>= [1] X + [2]
= n__len(X)
len(cons(X,Z)) = [1] Z + [5]
>= [1] Z + [5]
= s(n__len(activate(Z)))
len(nil()) = [2]
>= [2]
= 0()
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
len(X) -> n__len(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__from(X)) -> from(activate(X))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{activate,add,from,fst,len,s}
TcT has computed the following interpretation:
p(0) = [3]
[7]
p(activate) = [1 1] x1 + [0]
[0 4] [0]
p(add) = [1 0] x1 + [1 0] x2 + [3]
[0 1] [0 1] [0]
p(cons) = [0 0] x1 + [1 1] x2 + [0]
[0 1] [0 0] [0]
p(from) = [1 0] x1 + [0]
[0 1] [0]
p(fst) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
p(len) = [1 0] x1 + [4]
[0 1] [6]
p(n__add) = [1 0] x1 + [1 0] x2 + [3]
[0 1] [0 1] [0]
p(n__from) = [1 0] x1 + [0]
[0 1] [0]
p(n__fst) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
p(n__len) = [1 0] x1 + [2]
[0 1] [2]
p(n__s) = [1 0] x1 + [0]
[0 0] [0]
p(nil) = [0]
[6]
p(s) = [1 0] x1 + [0]
[0 0] [0]
Following rules are strictly oriented:
len(X) = [1 0] X + [4]
[0 1] [6]
> [1 0] X + [2]
[0 1] [2]
= n__len(X)
Following rules are (at-least) weakly oriented:
activate(X) = [1 1] X + [0]
[0 4] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n__add(X1,X2)) = [1 1] X1 + [1 1] X2 + [3]
[0 4] [0 4] [0]
>= [1 1] X1 + [1 1] X2 + [3]
[0 4] [0 4] [0]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1 1] X + [0]
[0 4] [0]
>= [1 1] X + [0]
[0 4] [0]
= from(activate(X))
activate(n__fst(X1,X2)) = [1 1] X1 + [1 1] X2 + [0]
[0 4] [0 4] [0]
>= [1 1] X1 + [1 1] X2 + [0]
[0 4] [0 4] [0]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1 1] X + [4]
[0 4] [8]
>= [1 1] X + [4]
[0 4] [6]
= len(activate(X))
activate(n__s(X)) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= s(X)
add(X1,X2) = [1 0] X1 + [1 0] X2 + [3]
[0 1] [0 1] [0]
>= [1 0] X1 + [1 0] X2 + [3]
[0 1] [0 1] [0]
= n__add(X1,X2)
add(0(),X) = [1 0] X + [6]
[0 1] [7]
>= [1 0] X + [0]
[0 1] [0]
= X
from(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= cons(X,n__from(n__s(X)))
from(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= n__from(X)
fst(X1,X2) = [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [0]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [0]
= n__fst(X1,X2)
fst(0(),Z) = [1 0] Z + [3]
[0 1] [7]
>= [0]
[6]
= nil()
len(cons(X,Z)) = [0 0] X + [1 1] Z + [4]
[0 1] [0 0] [6]
>= [1 1] Z + [2]
[0 0] [0]
= s(n__len(activate(Z)))
len(nil()) = [4]
[12]
>= [3]
[7]
= 0()
s(X) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= n__s(X)
*** 1.1.1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__from(X)) -> from(activate(X))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{activate,add,from,fst,len,s}
TcT has computed the following interpretation:
p(0) = [5]
[0]
p(activate) = [1 1] x1 + [0]
[0 1] [0]
p(add) = [1 0] x1 + [1 0] x2 + [1]
[0 1] [0 1] [2]
p(cons) = [0 7] x1 + [1 4] x2 + [0]
[0 1] [0 1] [0]
p(from) = [1 7] x1 + [4]
[0 1] [0]
p(fst) = [1 5] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
p(len) = [1 0] x1 + [2]
[0 1] [1]
p(n__add) = [1 0] x1 + [1 0] x2 + [1]
[0 1] [0 1] [2]
p(n__from) = [1 7] x1 + [4]
[0 1] [0]
p(n__fst) = [1 5] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
p(n__len) = [1 0] x1 + [2]
[0 1] [1]
p(n__s) = [1 0] x1 + [0]
[0 0] [0]
p(nil) = [4]
[0]
p(s) = [1 0] x1 + [0]
[0 0] [0]
Following rules are strictly oriented:
activate(n__add(X1,X2)) = [1 1] X1 + [1 1] X2 + [3]
[0 1] [0 1] [2]
> [1 1] X1 + [1 1] X2 + [1]
[0 1] [0 1] [2]
= add(activate(X1),activate(X2))
Following rules are (at-least) weakly oriented:
activate(X) = [1 1] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n__from(X)) = [1 8] X + [4]
[0 1] [0]
>= [1 8] X + [4]
[0 1] [0]
= from(activate(X))
activate(n__fst(X1,X2)) = [1 6] X1 + [1 1] X2 + [0]
[0 1] [0 1] [0]
>= [1 6] X1 + [1 1] X2 + [0]
[0 1] [0 1] [0]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1 1] X + [3]
[0 1] [1]
>= [1 1] X + [2]
[0 1] [1]
= len(activate(X))
activate(n__s(X)) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= s(X)
add(X1,X2) = [1 0] X1 + [1 0] X2 + [1]
[0 1] [0 1] [2]
>= [1 0] X1 + [1 0] X2 + [1]
[0 1] [0 1] [2]
= n__add(X1,X2)
add(0(),X) = [1 0] X + [6]
[0 1] [2]
>= [1 0] X + [0]
[0 1] [0]
= X
from(X) = [1 7] X + [4]
[0 1] [0]
>= [1 7] X + [4]
[0 1] [0]
= cons(X,n__from(n__s(X)))
from(X) = [1 7] X + [4]
[0 1] [0]
>= [1 7] X + [4]
[0 1] [0]
= n__from(X)
fst(X1,X2) = [1 5] X1 + [1 0] X2 + [0]
[0 1] [0 1] [0]
>= [1 5] X1 + [1 0] X2 + [0]
[0 1] [0 1] [0]
= n__fst(X1,X2)
fst(0(),Z) = [1 0] Z + [5]
[0 1] [0]
>= [4]
[0]
= nil()
len(X) = [1 0] X + [2]
[0 1] [1]
>= [1 0] X + [2]
[0 1] [1]
= n__len(X)
len(cons(X,Z)) = [0 7] X + [1 4] Z + [2]
[0 1] [0 1] [1]
>= [1 1] Z + [2]
[0 0] [0]
= s(n__len(activate(Z)))
len(nil()) = [6]
[1]
>= [5]
[0]
= 0()
s(X) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= n__s(X)
*** 1.1.1.1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{activate,add,from,fst,len,s}
TcT has computed the following interpretation:
p(0) = [2]
[1]
p(activate) = [1 2] x1 + [0]
[4 1] [0]
p(add) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [4]
p(cons) = [0 0] x1 + [1 4] x2 + [0]
[0 1] [0 1] [0]
p(from) = [1 0] x1 + [0]
[0 1] [0]
p(fst) = [1 0] x1 + [1 0] x2 + [4]
[0 1] [0 1] [4]
p(len) = [1 0] x1 + [0]
[0 1] [0]
p(n__add) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [4]
p(n__from) = [1 0] x1 + [0]
[0 1] [0]
p(n__fst) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [4]
p(n__len) = [1 0] x1 + [0]
[0 1] [0]
p(n__s) = [1 0] x1 + [0]
[0 0] [0]
p(nil) = [6]
[2]
p(s) = [1 0] x1 + [0]
[0 0] [0]
Following rules are strictly oriented:
activate(n__fst(X1,X2)) = [1 2] X1 + [1 2] X2 + [8]
[4 1] [4 1] [4]
> [1 2] X1 + [1 2] X2 + [4]
[4 1] [4 1] [4]
= fst(activate(X1),activate(X2))
Following rules are (at-least) weakly oriented:
activate(X) = [1 2] X + [0]
[4 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n__add(X1,X2)) = [1 2] X1 + [1 2] X2 + [8]
[4 1] [4 1] [4]
>= [1 2] X1 + [1 2] X2 + [0]
[4 1] [4 1] [4]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1 2] X + [0]
[4 1] [0]
>= [1 2] X + [0]
[4 1] [0]
= from(activate(X))
activate(n__len(X)) = [1 2] X + [0]
[4 1] [0]
>= [1 2] X + [0]
[4 1] [0]
= len(activate(X))
activate(n__s(X)) = [1 0] X + [0]
[4 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= s(X)
add(X1,X2) = [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [4]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [4]
= n__add(X1,X2)
add(0(),X) = [1 0] X + [2]
[0 1] [5]
>= [1 0] X + [0]
[0 1] [0]
= X
from(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= cons(X,n__from(n__s(X)))
from(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= n__from(X)
fst(X1,X2) = [1 0] X1 + [1 0] X2 + [4]
[0 1] [0 1] [4]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [4]
= n__fst(X1,X2)
fst(0(),Z) = [1 0] Z + [6]
[0 1] [5]
>= [6]
[2]
= nil()
len(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= n__len(X)
len(cons(X,Z)) = [0 0] X + [1 4] Z + [0]
[0 1] [0 1] [0]
>= [1 2] Z + [0]
[0 0] [0]
= s(n__len(activate(Z)))
len(nil()) = [6]
[2]
>= [2]
[1]
= 0()
s(X) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= n__s(X)
*** 1.1.1.1.1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{activate,add,from,fst,len,s}
TcT has computed the following interpretation:
p(0) = [1]
[5]
p(activate) = [1 1] x1 + [0]
[0 4] [0]
p(add) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [4]
p(cons) = [1 1] x2 + [0]
[0 0] [2]
p(from) = [1 0] x1 + [1]
[0 1] [4]
p(fst) = [1 0] x1 + [1 0] x2 + [3]
[0 1] [0 1] [3]
p(len) = [1 0] x1 + [0]
[0 1] [0]
p(n__add) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [1]
p(n__from) = [1 0] x1 + [0]
[0 1] [1]
p(n__fst) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [3]
p(n__len) = [1 0] x1 + [0]
[0 1] [0]
p(n__s) = [1 0] x1 + [0]
[0 0] [0]
p(nil) = [4]
[5]
p(s) = [1 0] x1 + [0]
[0 0] [0]
Following rules are strictly oriented:
from(X) = [1 0] X + [1]
[0 1] [4]
> [1 0] X + [0]
[0 1] [1]
= n__from(X)
Following rules are (at-least) weakly oriented:
activate(X) = [1 1] X + [0]
[0 4] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n__add(X1,X2)) = [1 1] X1 + [1 1] X2 + [1]
[0 4] [0 4] [4]
>= [1 1] X1 + [1 1] X2 + [0]
[0 4] [0 4] [4]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1 1] X + [1]
[0 4] [4]
>= [1 1] X + [1]
[0 4] [4]
= from(activate(X))
activate(n__fst(X1,X2)) = [1 1] X1 + [1 1] X2 + [3]
[0 4] [0 4] [12]
>= [1 1] X1 + [1 1] X2 + [3]
[0 4] [0 4] [3]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1 1] X + [0]
[0 4] [0]
>= [1 1] X + [0]
[0 4] [0]
= len(activate(X))
activate(n__s(X)) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= s(X)
add(X1,X2) = [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [4]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [1]
= n__add(X1,X2)
add(0(),X) = [1 0] X + [1]
[0 1] [9]
>= [1 0] X + [0]
[0 1] [0]
= X
from(X) = [1 0] X + [1]
[0 1] [4]
>= [1 0] X + [1]
[0 0] [2]
= cons(X,n__from(n__s(X)))
fst(X1,X2) = [1 0] X1 + [1 0] X2 + [3]
[0 1] [0 1] [3]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1] [0 1] [3]
= n__fst(X1,X2)
fst(0(),Z) = [1 0] Z + [4]
[0 1] [8]
>= [4]
[5]
= nil()
len(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= n__len(X)
len(cons(X,Z)) = [1 1] Z + [0]
[0 0] [2]
>= [1 1] Z + [0]
[0 0] [0]
= s(n__len(activate(Z)))
len(nil()) = [4]
[5]
>= [1]
[5]
= 0()
s(X) = [1 0] X + [0]
[0 0] [0]
>= [1 0] X + [0]
[0 0] [0]
= n__s(X)
*** 1.1.1.1.1.1.1.1.1.1 Progress [(O(1),O(n^3))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
from(X) -> cons(X,n__from(n__s(X)))
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(add) = {1,2},
uargs(from) = {1},
uargs(fst) = {1,2},
uargs(len) = {1},
uargs(n__len) = {1},
uargs(s) = {1}
Following symbols are considered usable:
{activate,add,from,fst,len,s}
TcT has computed the following interpretation:
p(0) = [0]
[2]
[0]
p(activate) = [1 0 2] [0]
[0 1 0] x1 + [1]
[2 0 1] [0]
p(add) = [1 0 0] [1 2 0] [1]
[0 0 0] x1 + [0 1 0] x2 + [1]
[0 0 1] [0 0 1] [3]
p(cons) = [1 2 0] [0]
[0 0 1] x2 + [0]
[0 0 0] [0]
p(from) = [1 1 0] [3]
[0 0 0] x1 + [2]
[0 0 1] [2]
p(fst) = [1 0 0] [1 0 0] [1]
[0 0 0] x1 + [0 1 0] x2 + [0]
[0 0 1] [0 0 1] [1]
p(len) = [1 2 0] [3]
[0 0 0] x1 + [2]
[0 0 1] [3]
p(n__add) = [1 0 0] [1 2 0] [1]
[0 0 0] x1 + [0 1 0] x2 + [1]
[0 0 1] [0 0 1] [2]
p(n__from) = [1 1 0] [0]
[0 0 0] x1 + [1]
[0 0 1] [2]
p(n__fst) = [1 0 0] [1 0 0] [1]
[0 0 0] x1 + [0 1 0] x2 + [0]
[0 0 1] [0 0 1] [0]
p(n__len) = [1 2 0] [1]
[0 0 0] x1 + [2]
[0 0 1] [3]
p(n__s) = [1 0 0] [0]
[0 0 0] x1 + [0]
[0 0 0] [0]
p(nil) = [0]
[0]
[1]
p(s) = [1 0 0] [0]
[0 0 0] x1 + [0]
[0 0 0] [0]
Following rules are strictly oriented:
from(X) = [1 1 0] [3]
[0 0 0] X + [2]
[0 0 1] [2]
> [1 0 0] [2]
[0 0 0] X + [2]
[0 0 0] [0]
= cons(X,n__from(n__s(X)))
Following rules are (at-least) weakly oriented:
activate(X) = [1 0 2] [0]
[0 1 0] X + [1]
[2 0 1] [0]
>= [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= X
activate(n__add(X1,X2)) = [1 0 2] [1 2 2] [5]
[0 0 0] X1 + [0 1 0] X2 + [2]
[2 0 1] [2 4 1] [4]
>= [1 0 2] [1 2 2] [3]
[0 0 0] X1 + [0 1 0] X2 + [2]
[2 0 1] [2 0 1] [3]
= add(activate(X1),activate(X2))
activate(n__from(X)) = [1 1 2] [4]
[0 0 0] X + [2]
[2 2 1] [2]
>= [1 1 2] [4]
[0 0 0] X + [2]
[2 0 1] [2]
= from(activate(X))
activate(n__fst(X1,X2)) = [1 0 2] [1 0 2] [1]
[0 0 0] X1 + [0 1 0] X2 + [1]
[2 0 1] [2 0 1] [2]
>= [1 0 2] [1 0 2] [1]
[0 0 0] X1 + [0 1 0] X2 + [1]
[2 0 1] [2 0 1] [1]
= fst(activate(X1),activate(X2))
activate(n__len(X)) = [1 2 2] [7]
[0 0 0] X + [3]
[2 4 1] [5]
>= [1 2 2] [5]
[0 0 0] X + [2]
[2 0 1] [3]
= len(activate(X))
activate(n__s(X)) = [1 0 0] [0]
[0 0 0] X + [1]
[2 0 0] [0]
>= [1 0 0] [0]
[0 0 0] X + [0]
[0 0 0] [0]
= s(X)
add(X1,X2) = [1 0 0] [1 2 0] [1]
[0 0 0] X1 + [0 1 0] X2 + [1]
[0 0 1] [0 0 1] [3]
>= [1 0 0] [1 2 0] [1]
[0 0 0] X1 + [0 1 0] X2 + [1]
[0 0 1] [0 0 1] [2]
= n__add(X1,X2)
add(0(),X) = [1 2 0] [1]
[0 1 0] X + [1]
[0 0 1] [3]
>= [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= X
from(X) = [1 1 0] [3]
[0 0 0] X + [2]
[0 0 1] [2]
>= [1 1 0] [0]
[0 0 0] X + [1]
[0 0 1] [2]
= n__from(X)
fst(X1,X2) = [1 0 0] [1 0 0] [1]
[0 0 0] X1 + [0 1 0] X2 + [0]
[0 0 1] [0 0 1] [1]
>= [1 0 0] [1 0 0] [1]
[0 0 0] X1 + [0 1 0] X2 + [0]
[0 0 1] [0 0 1] [0]
= n__fst(X1,X2)
fst(0(),Z) = [1 0 0] [1]
[0 1 0] Z + [0]
[0 0 1] [1]
>= [0]
[0]
[1]
= nil()
len(X) = [1 2 0] [3]
[0 0 0] X + [2]
[0 0 1] [3]
>= [1 2 0] [1]
[0 0 0] X + [2]
[0 0 1] [3]
= n__len(X)
len(cons(X,Z)) = [1 2 2] [3]
[0 0 0] Z + [2]
[0 0 0] [3]
>= [1 2 2] [3]
[0 0 0] Z + [0]
[0 0 0] [0]
= s(n__len(activate(Z)))
len(nil()) = [3]
[2]
[4]
>= [0]
[2]
[0]
= 0()
s(X) = [1 0 0] [0]
[0 0 0] X + [0]
[0 0 0] [0]
>= [1 0 0] [0]
[0 0 0] X + [0]
[0 0 0] [0]
= n__s(X)
*** 1.1.1.1.1.1.1.1.1.1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
activate(X) -> X
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__from(X)) -> from(activate(X))
activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2))
activate(n__len(X)) -> len(activate(X))
activate(n__s(X)) -> s(X)
add(X1,X2) -> n__add(X1,X2)
add(0(),X) -> X
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
fst(X1,X2) -> n__fst(X1,X2)
fst(0(),Z) -> nil()
len(X) -> n__len(X)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil()) -> 0()
s(X) -> n__s(X)
Signature:
{activate/1,add/2,from/1,fst/2,len/1,s/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,n__s/1,nil/0}
Obligation:
Innermost
basic terms: {activate,add,from,fst,len,s}/{0,cons,n__add,n__from,n__fst,n__len,n__s,nil}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).