```We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ 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)))
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

Arguments of following rules are not normal-forms:

{ fst(s(X), cons(Y, Z)) ->
cons(Y, n__fst(activate(X), activate(Z)))

All above mentioned rules can be savely removed.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [0]

[0] = [4]

[nil] = [0]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [0]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [0]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [0]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [4]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [0]
>= [1] X + [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [0]
>= [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[activate(n__len(X))] =  [1] X + [0]
>= [1] X + [0]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [4]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [0]
?  [4]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [0]
>= [1] Z + [0]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Weak Trs:
{ fst(0(), Z) -> nil()
, add(0(), X) -> X }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [1]

[0] = [4]

[nil] = [0]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [0]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [0]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [0]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [1]
>  [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [5]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [0]
?  [1] X1 + [1] X2 + [1]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [0]
>= [1] X + [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [0]
>= [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[activate(n__len(X))] =  [1] X + [0]
>= [1] X + [0]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [4]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [0]
?  [4]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [0]
>= [1] Z + [0]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, add(0(), X) -> X }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [0]

[0] = [4]

[nil] = [0]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [0]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [0]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [1]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [4]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [0]
>= [1] X + [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [0]
>= [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[activate(n__len(X))] =  [1] X + [0]
?  [1] X + [1]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [4]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [1]
>  [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [1]
?  [4]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [1]
>  [1] Z + [0]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
, len(nil()) -> 0() }
Weak Trs:
{ 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))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [4]

[0] = [4]

[nil] = [4]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [4]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [0]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [4]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [4]
>  [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [8]
>  [4]
=  [nil()]

[s(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [0]
?  [1] X1 + [1] X2 + [4]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [0]
>= [1] X + [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [0]
>= [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[activate(n__len(X))] =  [1] X + [0]
?  [1] X + [4]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
?  [1] X + [4]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [4]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [4]
>  [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [8]
>  [4]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [8]
>  [1] Z + [0]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [6]

[0] = [2]

[nil] = [0]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [4]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [1]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [2]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [4]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [6]
>  [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [8]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [1]
>  [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [1]
?  [1] X1 + [1] X2 + [8]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [1]
>= [1] X + [1]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [1]
>  [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [1]
?  [1] X1 + [1] X2 + [4]

[activate(n__len(X))] =  [1] X + [1]
?  [1] X + [5]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
?  [1] X + [4]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [2]
>  [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [4]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [4]
>  [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [4]
>  [2]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [8]
>  [1] Z + [1]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ s(X) -> n__s(X)
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, activate(X) -> X
, activate(n__s(X)) -> s(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [1]

[0] = [3]

[nil] = [0]

[s](x1) = [1] x1 + [0]

[cons](x1, x2) = [1] x2 + [4]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [0]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [4]

[n__s](x1) = [1] x1 + [4]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [4]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [1]
>  [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [4]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [0]
?  [1] X + [4]
=  [n__s(X)]

[activate(X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [0]
?  [1] X1 + [1] X2 + [1]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [4]
>  [1] X + [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [4]
>  [1] X + [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[activate(n__len(X))] =  [1] X + [0]
?  [1] X + [4]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
?  [1] X + [12]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
?  [1] X + [4]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [3]
>  [1] X + [0]
=  [X]

[len(X)] =  [1] X + [4]
>  [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [4]
>  [3]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [8]
>  [1] Z + [0]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ s(X) -> n__s(X)
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, activate(X) -> X
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)

The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1] x1 + [1] x2 + [6]

[0] = [0]

[nil] = [0]

[s](x1) = [1] x1 + [1]

[cons](x1, x2) = [1] x2 + [0]

[n__fst](x1, x2) = [1] x1 + [1] x2 + [0]

[activate](x1) = [1] x1 + [1]

[from](x1) = [1] x1 + [0]

[n__from](x1) = [1] x1 + [0]

[n__s](x1) = [1] x1 + [0]

[add](x1, x2) = [1] x1 + [1] x2 + [0]

[n__add](x1, x2) = [1] x1 + [1] x2 + [0]

[len](x1) = [1] x1 + [4]

[n__len](x1) = [1] x1 + [0]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1] X1 + [1] X2 + [6]
>  [1] X1 + [1] X2 + [0]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1] Z + [6]
>  [0]
=  [nil()]

[s(X)] =  [1] X + [1]
>  [1] X + [0]
=  [n__s(X)]

[activate(X)] =  [1] X + [1]
>  [1] X + [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1] X1 + [1] X2 + [1]
?  [1] X1 + [1] X2 + [8]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1] X + [1]
>= [1] X + [1]
=  [from(activate(X))]

[activate(n__s(X))] =  [1] X + [1]
>= [1] X + [1]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1] X1 + [1] X2 + [1]
?  [1] X1 + [1] X2 + [2]

[activate(n__len(X))] =  [1] X + [1]
?  [1] X + [5]
=  [len(activate(X))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1] X + [0]
>= [1] X + [0]
=  [n__from(X)]

[add(X1, X2)] =  [1] X1 + [1] X2 + [0]
>= [1] X1 + [1] X2 + [0]

[add(0(), X)] =  [1] X + [0]
>= [1] X + [0]
=  [X]

[len(X)] =  [1] X + [4]
>  [1] X + [0]
=  [n__len(X)]

[len(nil())] =  [4]
>  [0]
=  [0()]

[len(cons(X, Z))] =  [1] Z + [4]
>  [1] Z + [2]
=  [s(n__len(activate(Z)))]

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 2' to
orient following rules strictly.

Trs:

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [0]

[0] = [0]
[0]

[nil] = [0]
[0]

[s](x1) = [1 0] x1 + [0]
[0 0]      [0]

[cons](x1, x2) = [0 0] x1 + [1 1] x2 + [0]
[0 1]      [0 0]      [0]

[n__fst](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [0]

[activate](x1) = [1 1] x1 + [0]
[0 1]      [0]

[from](x1) = [1 0] x1 + [0]
[0 1]      [0]

[n__from](x1) = [1 0] x1 + [0]
[0 1]      [0]

[n__s](x1) = [1 0] x1 + [0]
[0 0]      [0]

[add](x1, x2) = [1 0] x1 + [1 0] x2 + [4]
[0 1]      [0 1]      [1]

[n__add](x1, x2) = [1 0] x1 + [1 0] x2 + [4]
[0 1]      [0 1]      [1]

[len](x1) = [1 0] x1 + [1]
[0 1]      [1]

[n__len](x1) = [1 0] x1 + [0]
[0 1]      [1]

The order satisfies the following ordering constraints:

[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 + [0]
[0 1]     [0]
>= [0]
[0]
=  [nil()]

[s(X)] =  [1 0] X + [0]
[0 0]     [0]
>= [1 0] X + [0]
[0 0]     [0]
=  [n__s(X)]

[activate(X)] =  [1 1] X + [0]
[0 1]     [0]
>= [1 0] X + [0]
[0 1]     [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1 1] X1 + [1 1] X2 + [0]
[0 1]      [0 1]      [0]
>= [1 1] X1 + [1 1] X2 + [0]
[0 1]      [0 1]      [0]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1 1] X + [0]
[0 1]     [0]
>= [1 1] X + [0]
[0 1]     [0]
=  [from(activate(X))]

[activate(n__s(X))] =  [1 0] X + [0]
[0 0]     [0]
>= [1 0] X + [0]
[0 0]     [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1 1] X1 + [1 1] X2 + [5]
[0 1]      [0 1]      [1]
>  [1 1] X1 + [1 1] X2 + [4]
[0 1]      [0 1]      [1]

[activate(n__len(X))] =  [1 1] X + [1]
[0 1]     [1]
>= [1 1] X + [1]
[0 1]     [1]
=  [len(activate(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)]

[add(X1, X2)] =  [1 0] X1 + [1 0] X2 + [4]
[0 1]      [0 1]      [1]
>= [1 0] X1 + [1 0] X2 + [4]
[0 1]      [0 1]      [1]

[add(0(), X)] =  [1 0] X + [4]
[0 1]     [1]
>  [1 0] X + [0]
[0 1]     [0]
=  [X]

[len(X)] =  [1 0] X + [1]
[0 1]     [1]
>  [1 0] X + [0]
[0 1]     [1]
=  [n__len(X)]

[len(nil())] =  [1]
[1]
>  [0]
[0]
=  [0()]

[len(cons(X, Z))] =  [1 1] Z + [0 0] X + [1]
[0 0]     [0 1]     [1]
>  [1 1] Z + [0]
[0 0]     [0]
=  [s(n__len(activate(Z)))]

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 2' to
orient following rules strictly.

Trs:
{ activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__len(X)) -> len(activate(X)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1 0] x1 + [1 0] x2 + [5]
[0 1]      [0 1]      [2]

[0] = [4]
[0]

[nil] = [6]
[0]

[s](x1) = [1 0] x1 + [1]
[0 0]      [0]

[cons](x1, x2) = [1 6] x2 + [0]
[0 0]      [0]

[n__fst](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [2]

[activate](x1) = [1 5] x1 + [1]
[1 1]      [0]

[from](x1) = [1 0] x1 + [1]
[0 1]      [1]

[n__from](x1) = [1 0] x1 + [1]
[0 1]      [0]

[n__s](x1) = [1 0] x1 + [0]
[0 0]      [0]

[add](x1, x2) = [1 0] x1 + [1 0] x2 + [7]
[0 1]      [0 1]      [1]

[n__add](x1, x2) = [1 0] x1 + [1 0] x2 + [7]
[0 1]      [0 1]      [1]

[len](x1) = [1 0] x1 + [2]
[0 1]      [1]

[n__len](x1) = [1 0] x1 + [0]
[0 1]      [1]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1 0] X1 + [1 0] X2 + [5]
[0 1]      [0 1]      [2]
>  [1 0] X1 + [1 0] X2 + [0]
[0 1]      [0 1]      [2]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1 0] Z + [9]
[0 1]     [2]
>  [6]
[0]
=  [nil()]

[s(X)] =  [1 0] X + [1]
[0 0]     [0]
>  [1 0] X + [0]
[0 0]     [0]
=  [n__s(X)]

[activate(X)] =  [1 5] X + [1]
[1 1]     [0]
>  [1 0] X + [0]
[0 1]     [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1 5] X1 + [1 5] X2 + [11]
[1 1]      [1 1]      [2]
>  [1 5] X1 + [1 5] X2 + [7]
[1 1]      [1 1]      [2]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1 5] X + [2]
[1 1]     [1]
>= [1 5] X + [2]
[1 1]     [1]
=  [from(activate(X))]

[activate(n__s(X))] =  [1 0] X + [1]
[1 0]     [0]
>= [1 0] X + [1]
[0 0]     [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1 5] X1 + [1 5] X2 + [13]
[1 1]      [1 1]      [8]
>  [1 5] X1 + [1 5] X2 + [9]
[1 1]      [1 1]      [1]

[activate(n__len(X))] =  [1 5] X + [6]
[1 1]     [1]
>  [1 5] X + [3]
[1 1]     [1]
=  [len(activate(X))]

[from(X)] =  [1 0] X + [1]
[0 1]     [1]
>= [1 0] X + [1]
[0 0]     [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1 0] X + [1]
[0 1]     [1]
>= [1 0] X + [1]
[0 1]     [0]
=  [n__from(X)]

[add(X1, X2)] =  [1 0] X1 + [1 0] X2 + [7]
[0 1]      [0 1]      [1]
>= [1 0] X1 + [1 0] X2 + [7]
[0 1]      [0 1]      [1]

[add(0(), X)] =  [1 0] X + [11]
[0 1]     [1]
>  [1 0] X + [0]
[0 1]     [0]
=  [X]

[len(X)] =  [1 0] X + [2]
[0 1]     [1]
>  [1 0] X + [0]
[0 1]     [1]
=  [n__len(X)]

[len(nil())] =  [8]
[1]
>  [4]
[0]
=  [0()]

[len(cons(X, Z))] =  [1 6] Z + [2]
[0 0]     [1]
>= [1 5] Z + [2]
[0 0]     [0]
=  [s(n__len(activate(Z)))]

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
{ from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 2' to
orient following rules strictly.

Trs: { from(X) -> n__from(X) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA) and not(IDA(1)).

[fst](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [0]

[0] = [0]
[4]

[nil] = [0]
[4]

[s](x1) = [1 0] x1 + [0]
[0 0]      [0]

[cons](x1, x2) = [1 1] x2 + [0]
[0 0]      [0]

[n__fst](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [0]

[activate](x1) = [1 1] x1 + [0]
[0 1]      [0]

[from](x1) = [1 0] x1 + [1]
[0 1]      [1]

[n__from](x1) = [1 0] x1 + [0]
[0 1]      [1]

[n__s](x1) = [1 0] x1 + [0]
[0 0]      [0]

[add](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [1]

[n__add](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1]      [0 1]      [1]

[len](x1) = [1 0] x1 + [0]
[0 1]      [0]

[n__len](x1) = [1 0] x1 + [0]
[0 1]      [0]

The order satisfies the following ordering constraints:

[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 + [0]
[0 1]     [4]
>= [0]
[4]
=  [nil()]

[s(X)] =  [1 0] X + [0]
[0 0]     [0]
>= [1 0] X + [0]
[0 0]     [0]
=  [n__s(X)]

[activate(X)] =  [1 1] X + [0]
[0 1]     [0]
>= [1 0] X + [0]
[0 1]     [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1 1] X1 + [1 1] X2 + [0]
[0 1]      [0 1]      [0]
>= [1 1] X1 + [1 1] X2 + [0]
[0 1]      [0 1]      [0]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1 1] X + [1]
[0 1]     [1]
>= [1 1] X + [1]
[0 1]     [1]
=  [from(activate(X))]

[activate(n__s(X))] =  [1 0] X + [0]
[0 0]     [0]
>= [1 0] X + [0]
[0 0]     [0]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1 1] X1 + [1 1] X2 + [1]
[0 1]      [0 1]      [1]
>  [1 1] X1 + [1 1] X2 + [0]
[0 1]      [0 1]      [1]

[activate(n__len(X))] =  [1 1] X + [0]
[0 1]     [0]
>= [1 1] X + [0]
[0 1]     [0]
=  [len(activate(X))]

[from(X)] =  [1 0] X + [1]
[0 1]     [1]
>= [1 0] X + [1]
[0 0]     [0]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1 0] X + [1]
[0 1]     [1]
>  [1 0] X + [0]
[0 1]     [1]
=  [n__from(X)]

[add(X1, X2)] =  [1 0] X1 + [1 0] X2 + [0]
[0 1]      [0 1]      [1]
>= [1 0] X1 + [1 0] X2 + [0]
[0 1]      [0 1]      [1]

[add(0(), X)] =  [1 0] X + [0]
[0 1]     [5]
>= [1 0] X + [0]
[0 1]     [0]
=  [X]

[len(X)] =  [1 0] X + [0]
[0 1]     [0]
>= [1 0] X + [0]
[0 1]     [0]
=  [n__len(X)]

[len(nil())] =  [0]
[4]
>= [0]
[4]
=  [0()]

[len(cons(X, Z))] =  [1 1] Z + [0]
[0 0]     [0]
>= [1 1] Z + [0]
[0 0]     [0]
=  [s(n__len(activate(Z)))]

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs: { from(X) -> cons(X, n__from(n__s(X))) }
Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> n__from(X)
, len(X) -> n__len(X)
, len(nil()) -> 0()
, len(cons(X, Z)) -> s(n__len(activate(Z))) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 3' to
orient following rules strictly.

Trs: { from(X) -> cons(X, n__from(n__s(X))) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(from) = {1},
Uargs(add) = {1, 2}, Uargs(len) = {1}, Uargs(n__len) = {1}

TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA) and not(IDA(1)).

[1 0 0]      [1 0 0]      [6]
[fst](x1, x2) = [0 1 0] x1 + [0 1 0] x2 + [1]
[0 0 1]      [0 0 1]      [1]

[3]
[0] = [0]
[0]

[4]
[nil] = [0]
[0]

[1 0 0]      [4]
[s](x1) = [0 0 0] x1 + [0]
[0 0 0]      [2]

[0 0 0]      [1 7 0]      [0]
[cons](x1, x2) = [0 1 0] x1 + [0 0 0] x2 + [4]
[0 0 1]      [0 0 1]      [1]

[1 0 0]      [1 0 0]      [5]
[n__fst](x1, x2) = [0 1 0] x1 + [0 1 0] x2 + [0]
[0 0 1]      [0 0 1]      [1]

[1 7 2]      [1]
[activate](x1) = [0 7 2] x1 + [1]
[0 0 2]      [0]

[1 0 0]      [6]
[from](x1) = [0 1 0] x1 + [4]
[0 0 1]      [4]

[1 0 0]      [3]
[n__from](x1) = [0 1 0] x1 + [0]
[0 0 1]      [2]

[1 0 0]      [2]
[n__s](x1) = [0 0 0] x1 + [0]
[0 0 0]      [1]

[1 0 0]      [1 0 0]      [6]
[add](x1, x2) = [0 1 2] x1 + [0 1 0] x2 + [2]
[0 0 0]      [0 0 1]      [6]

[1 0 0]      [1 0 0]      [0]
[n__add](x1, x2) = [0 1 2] x1 + [0 1 0] x2 + [0]
[0 0 0]      [0 0 1]      [4]

[1 0 3]      [7]
[len](x1) = [0 1 5] x1 + [0]
[0 0 0]      [3]

[1 0 0]      [4]
[n__len](x1) = [0 1 2] x1 + [0]
[0 0 0]      [3]

The order satisfies the following ordering constraints:

[fst(X1, X2)] =  [1 0 0]      [1 0 0]      [6]
[0 1 0] X1 + [0 1 0] X2 + [1]
[0 0 1]      [0 0 1]      [1]
>  [1 0 0]      [1 0 0]      [5]
[0 1 0] X1 + [0 1 0] X2 + [0]
[0 0 1]      [0 0 1]      [1]
=  [n__fst(X1, X2)]

[fst(0(), Z)] =  [1 0 0]     [9]
[0 1 0] Z + [1]
[0 0 1]     [1]
>  [4]
[0]
[0]
=  [nil()]

[s(X)] =  [1 0 0]     [4]
[0 0 0] X + [0]
[0 0 0]     [2]
>  [1 0 0]     [2]
[0 0 0] X + [0]
[0 0 0]     [1]
=  [n__s(X)]

[activate(X)] =  [1 7 2]     [1]
[0 7 2] X + [1]
[0 0 2]     [0]
>  [1 0 0]     [0]
[0 1 0] X + [0]
[0 0 1]     [0]
=  [X]

[activate(n__fst(X1, X2))] =  [1 7 2]      [1 7 2]      [8]
[0 7 2] X1 + [0 7 2] X2 + [3]
[0 0 2]      [0 0 2]      [2]
>= [1 7 2]      [1 7 2]      [8]
[0 7 2] X1 + [0 7 2] X2 + [3]
[0 0 2]      [0 0 2]      [1]
=  [fst(activate(X1), activate(X2))]

[activate(n__from(X))] =  [1 7 2]     [8]
[0 7 2] X + [5]
[0 0 2]     [4]
>  [1 7 2]     [7]
[0 7 2] X + [5]
[0 0 2]     [4]
=  [from(activate(X))]

[activate(n__s(X))] =  [1 0 0]     [5]
[0 0 0] X + [3]
[0 0 0]     [2]
>  [1 0 0]     [4]
[0 0 0] X + [0]
[0 0 0]     [2]
=  [s(X)]

[activate(n__add(X1, X2))] =  [1 7 14]      [1 7 2]      [9]
[0 7 14] X1 + [0 7 2] X2 + [9]
[0 0  0]      [0 0 2]      [8]
>  [1 7 2]      [1 7 2]      [8]
[0 7 6] X1 + [0 7 2] X2 + [4]
[0 0 0]      [0 0 2]      [6]

[activate(n__len(X))] =  [1 7 14]     [11]
[0 7 14] X + [7]
[0 0  0]     [6]
>  [1 7  8]     [8]
[0 7 12] X + [1]
[0 0  0]     [3]
=  [len(activate(X))]

[from(X)] =  [1 0 0]     [6]
[0 1 0] X + [4]
[0 0 1]     [4]
>  [1 0 0]     [5]
[0 1 0] X + [4]
[0 0 1]     [4]
=  [cons(X, n__from(n__s(X)))]

[from(X)] =  [1 0 0]     [6]
[0 1 0] X + [4]
[0 0 1]     [4]
>  [1 0 0]     [3]
[0 1 0] X + [0]
[0 0 1]     [2]
=  [n__from(X)]

[add(X1, X2)] =  [1 0 0]      [1 0 0]      [6]
[0 1 2] X1 + [0 1 0] X2 + [2]
[0 0 0]      [0 0 1]      [6]
>  [1 0 0]      [1 0 0]      [0]
[0 1 2] X1 + [0 1 0] X2 + [0]
[0 0 0]      [0 0 1]      [4]

[add(0(), X)] =  [1 0 0]     [9]
[0 1 0] X + [2]
[0 0 1]     [6]
>  [1 0 0]     [0]
[0 1 0] X + [0]
[0 0 1]     [0]
=  [X]

[len(X)] =  [1 0 3]     [7]
[0 1 5] X + [0]
[0 0 0]     [3]
>  [1 0 0]     [4]
[0 1 2] X + [0]
[0 0 0]     [3]
=  [n__len(X)]

[len(nil())] =  [11]
[0]
[3]
>  [3]
[0]
[0]
=  [0()]

[len(cons(X, Z))] =  [1 7 3]     [0 0 3]     [10]
[0 0 5] Z + [0 1 5] X + [9]
[0 0 0]     [0 0 0]     [3]
>  [1 7 2]     [9]
[0 0 0] Z + [0]
[0 0 0]     [2]
=  [s(n__len(activate(Z)))]

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(1)).

Weak Trs:
{ fst(X1, X2) -> n__fst(X1, X2)
, fst(0(), Z) -> nil()
, s(X) -> n__s(X)
, activate(X) -> X
, activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
, activate(n__from(X)) -> from(activate(X))
, activate(n__s(X)) -> s(X)
, activate(n__len(X)) -> len(activate(X))
, from(X) -> cons(X, n__from(n__s(X)))
, from(X) -> n__from(X)