```We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^4)).

Strict Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

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

The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[a__2nd](x1) = [1] x1 + [4]

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

[mark](x1) = [0]

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

[from](x1) = [0]

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1] X + [4]
>  [1] X + [0]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1] X + [5]
>  [0]
=  [mark(Y)]

[mark(cons(X1, X2))] =  [0]
?  [1]
=  [cons(mark(X1), X2)]

[mark(from(X))] =  [0]
>= [0]
=  [a__from(mark(X))]

[mark(s(X))] =  [0]
>= [0]
=  [s(mark(X))]

[mark(2nd(X))] =  [0]
?  [4]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1] X + [0]
?  [1]
=  [cons(mark(X), from(s(X)))]

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

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^4)).

Strict Trs:
{ mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

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

The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[a__2nd](x1) = [1] x1 + [0]

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

[mark](x1) = [0]

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

[from](x1) = [0]

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1] X + [0]
>= [1] X + [0]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1] X + [0]
>= [0]
=  [mark(Y)]

[mark(cons(X1, X2))] =  [0]
>= [0]
=  [cons(mark(X1), X2)]

[mark(from(X))] =  [0]
?  [4]
=  [a__from(mark(X))]

[mark(s(X))] =  [0]
>= [0]
=  [s(mark(X))]

[mark(2nd(X))] =  [0]
>= [0]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1] X + [4]
>  [0]
=  [cons(mark(X), from(s(X)))]

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

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^4)).

Strict Trs:
{ mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X)) }
Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

We use the processor 'matrix interpretation of dimension 4' to
orient following rules strictly.

Trs: { mark(2nd(X)) -> a__2nd(mark(X)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^4)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[1 0 0 0]      [1]
[a__2nd](x1) = [1 0 0 0] x1 + [1]
[1 0 0 0]      [0]
[0 0 0 1]      [1]

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

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

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

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

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1 0 0 0]     [1]
[1 0 0 0] X + [1]
[1 0 0 0]     [0]
[0 0 0 1]     [1]
>= [1 0 0 0]     [1]
[0 0 0 0] X + [0]
[0 0 0 0]     [0]
[0 0 0 1]     [1]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1 0 0 0]     [1 0 0 1]     [0 1 1 0]     [1]
[1 0 0 0] X + [1 0 0 1] Y + [0 1 1 0] Z + [1]
[1 0 0 0]     [1 0 0 1]     [0 1 1 0]     [0]
[0 0 0 1]     [0 0 0 1]     [0 0 0 0]     [1]
>  [1 0 0 1]     [0]
[1 0 0 1] Y + [1]
[1 0 0 1]     [0]
[0 0 0 1]     [1]
=  [mark(Y)]

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

[mark(from(X))] =  [1 0 0 2]     [1]
[1 0 0 2] X + [2]
[1 0 0 2]     [1]
[0 0 0 1]     [2]
>= [1 0 0 2]     [1]
[1 0 0 2] X + [2]
[1 0 0 2]     [1]
[0 0 0 1]     [2]
=  [a__from(mark(X))]

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

[mark(2nd(X))] =  [1 0 0 1]     [2]
[1 0 0 1] X + [3]
[1 0 0 1]     [2]
[0 0 0 1]     [2]
>  [1 0 0 1]     [1]
[1 0 0 1] X + [1]
[1 0 0 1]     [0]
[0 0 0 1]     [2]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1 0 0 1]     [0]
[1 0 0 1] X + [1]
[1 0 0 1]     [0]
[0 0 0 1]     [1]
>= [1 0 0 1]     [0]
[0 0 0 1] X + [1]
[1 0 0 1]     [0]
[0 0 0 1]     [1]
=  [cons(mark(X), from(s(X)))]

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

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^4)).

Strict Trs:
{ mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X)) }
Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

We use the processor 'matrix interpretation of dimension 4' to
orient following rules strictly.

Trs: { mark(s(X)) -> s(mark(X)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^4)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[1 0 0 1]      [0]
[a__2nd](x1) = [0 1 0 1] x1 + [0]
[0 0 1 0]      [1]
[0 0 0 1]      [1]

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

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

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

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

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1 0 0 1]     [0]
[0 1 0 1] X + [0]
[0 0 1 0]     [1]
[0 0 0 1]     [1]
>= [1 0 0 1]     [0]
[0 0 0 1] X + [0]
[0 0 1 0]     [0]
[0 0 0 1]     [1]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1 0 0 1]     [1 0 0 1]     [0 1 1 0]     [0]
[1 0 0 1] X + [1 0 0 1] Y + [0 1 1 0] Z + [0]
[0 0 0 1]     [0 0 0 1]     [0 0 1 0]     [1]
[0 0 0 1]     [0 0 0 1]     [0 0 1 0]     [1]
>= [1 0 0 1]     [0]
[1 0 0 1] Y + [0]
[0 0 0 1]     [1]
[0 0 0 1]     [1]
=  [mark(Y)]

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

[mark(from(X))] =  [1 0 0 2]     [2]
[1 0 0 2] X + [2]
[0 0 0 1]     [2]
[0 0 0 1]     [2]
>= [1 0 0 2]     [2]
[1 0 0 2] X + [1]
[0 0 0 1]     [2]
[0 0 0 1]     [2]
=  [a__from(mark(X))]

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

[mark(2nd(X))] =  [1 0 0 2]     [1]
[1 0 0 2] X + [1]
[0 0 0 1]     [2]
[0 0 0 1]     [2]
>= [1 0 0 2]     [1]
[1 0 0 2] X + [1]
[0 0 0 1]     [2]
[0 0 0 1]     [2]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1 0 0 1]     [1]
[1 0 0 1] X + [0]
[0 0 0 1]     [1]
[0 0 0 1]     [1]
>  [1 0 0 1]     [0]
[1 0 0 1] X + [0]
[0 0 0 1]     [1]
[0 0 0 1]     [1]
=  [cons(mark(X), from(s(X)))]

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

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^4)).

Strict Trs:
{ mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X)) }
Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

We use the processor 'matrix interpretation of dimension 4' to
orient following rules strictly.

Trs: { mark(from(X)) -> a__from(mark(X)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^4)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[1 0 1 0]      [0]
[a__2nd](x1) = [1 0 1 0] x1 + [0]
[0 0 1 0]      [0]
[0 0 1 1]      [0]

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

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

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

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

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1 0 1 0]     [0]
[1 0 1 0] X + [0]
[0 0 1 0]     [0]
[0 0 1 1]     [0]
>= [1 0 1 0]     [0]
[0 0 1 0] X + [0]
[0 0 1 0]     [0]
[0 0 1 0]     [0]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1 0 1 0]     [1 0 2 0]     [0 0 0 1]     [0]
[1 0 1 0] X + [1 0 2 0] Y + [0 0 0 1] Z + [0]
[0 0 1 0]     [0 0 1 0]     [0 0 0 0]     [0]
[1 0 1 0]     [1 0 1 0]     [0 0 0 1]     [0]
>= [1 0 1 0]     [0]
[1 0 1 0] Y + [0]
[0 0 1 0]     [0]
[1 0 1 0]     [0]
=  [mark(Y)]

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

[mark(from(X))] =  [1 0 2 0]     [2]
[1 0 2 0] X + [2]
[0 0 1 0]     [1]
[1 0 2 0]     [2]
>  [1 0 2 0]     [1]
[1 0 2 0] X + [1]
[0 0 1 0]     [1]
[1 0 2 0]     [1]
=  [a__from(mark(X))]

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

[mark(2nd(X))] =  [1 0 2 0]     [0]
[1 0 2 0] X + [0]
[0 0 1 0]     [0]
[1 0 2 0]     [0]
>= [1 0 2 0]     [0]
[1 0 2 0] X + [0]
[0 0 1 0]     [0]
[1 0 2 0]     [0]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1 0 1 0]     [1]
[0 0 1 1] X + [1]
[0 0 1 0]     [1]
[1 0 1 0]     [1]
>= [1 0 1 0]     [1]
[0 0 1 0] X + [0]
[0 0 1 0]     [1]
[1 0 1 0]     [0]
=  [cons(mark(X), from(s(X)))]

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

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^4)).

Strict Trs: { mark(cons(X1, X2)) -> cons(mark(X1), X2) }
Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^4))

We use the processor 'matrix interpretation of dimension 4' to
orient following rules strictly.

Trs: { mark(cons(X1, X2)) -> cons(mark(X1), X2) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^4)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
The following argument positions are usable:
Uargs(a__2nd) = {1}, Uargs(cons) = {1}, Uargs(a__from) = {1},
Uargs(s) = {1}

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

[1 0 0 1]      [0]
[a__2nd](x1) = [0 1 0 0] x1 + [0]
[1 1 0 0]      [0]
[0 0 0 1]      [0]

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

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

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

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

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

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

The order satisfies the following ordering constraints:

[a__2nd(X)] =  [1 0 0 1]     [0]
[0 1 0 0] X + [0]
[1 1 0 0]     [0]
[0 0 0 1]     [0]
>= [1 0 0 1]     [0]
[0 1 0 0] X + [0]
[0 0 0 0]     [0]
[0 0 0 1]     [0]
=  [2nd(X)]

[a__2nd(cons(X, cons(Y, Z)))] =  [1 0 0 1]     [1 0 0 1]     [0 1 0 0]     [2]
[0 0 0 1] X + [0 0 0 1] Y + [0 1 0 0] Z + [0]
[1 0 0 1]     [1 0 0 1]     [0 1 0 0]     [1]
[0 0 0 1]     [0 0 0 1]     [0 1 0 0]     [1]
>  [1 0 0 1]     [0]
[0 0 0 1] Y + [0]
[1 0 0 1]     [1]
[0 0 0 1]     [0]
=  [mark(Y)]

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

[mark(from(X))] =  [1 0 0 2]     [1]
[0 0 0 1] X + [1]
[1 0 0 2]     [2]
[0 0 0 1]     [1]
>= [1 0 0 2]     [1]
[0 0 0 1] X + [1]
[1 0 0 2]     [1]
[0 0 0 1]     [1]
=  [a__from(mark(X))]

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

[mark(2nd(X))] =  [1 0 0 2]     [0]
[0 0 0 1] X + [0]
[1 0 0 2]     [1]
[0 0 0 1]     [0]
>= [1 0 0 2]     [0]
[0 0 0 1] X + [0]
[1 0 0 2]     [0]
[0 0 0 1]     [0]
=  [a__2nd(mark(X))]

[a__from(X)] =  [1 0 0 1]     [1]
[0 0 0 1] X + [1]
[1 0 0 1]     [1]
[0 0 0 1]     [1]
>  [1 0 0 1]     [0]
[0 0 0 1] X + [0]
[1 0 0 1]     [1]
[0 0 0 1]     [1]
=  [cons(mark(X), from(s(X)))]

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

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

Weak Trs:
{ a__2nd(X) -> 2nd(X)
, a__2nd(cons(X, cons(Y, Z))) -> mark(Y)
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(from(X)) -> a__from(mark(X))
, mark(s(X)) -> s(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__from(X) -> from(X) }
Obligation:
innermost runtime complexity