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

Strict Trs: { h(f(x, y)) -> f(y, f(h(h(x)), a())) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

We add the following dependency tuples:

Strict DPs: { h^#(f(x, y)) -> c_1(h^#(h(x)), h^#(x)) }

and mark the set of starting terms.

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

Strict DPs: { h^#(f(x, y)) -> c_1(h^#(h(x)), h^#(x)) }
Weak Trs: { h(f(x, y)) -> f(y, f(h(h(x)), a())) }
Obligation:
innermost runtime complexity
YES(O(1),O(n^1))

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

DPs:
{ 1: h^#(f(x, y)) -> c_1(h^#(h(x)), h^#(x)) }

Sub-proof:
----------
The following argument positions are usable:
Uargs(c_1) = {1, 2}

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

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

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

[a] = [0]
[0]

[h^#](x1) = [3 0] x1 + [0]
[0 1]      [0]

[c_1](x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 0]      [0 0]      [0]

The order satisfies the following ordering constraints:

[h(f(x, y))] =  [0 0] x + [1 1] y + [2]
[4 4]     [0 0]     [10]
>= [0 0] x + [1 1] y + [2]
[4 4]     [0 0]     [10]
=  [f(y, f(h(h(x)), a()))]

[h^#(f(x, y))] =  [3 3] x + [0 0] y + [6]
[0 0]     [1 1]     [2]
>  [3 3] x + [1]
[0 0]     [0]
=  [c_1(h^#(h(x)), h^#(x))]

The strictly oriented rules are moved into the weak component.

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

Weak DPs: { h^#(f(x, y)) -> c_1(h^#(h(x)), h^#(x)) }
Weak Trs: { h(f(x, y)) -> f(y, f(h(h(x)), a())) }
Obligation:
innermost runtime complexity
YES(O(1),O(1))

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ h^#(f(x, y)) -> c_1(h^#(h(x)), h^#(x)) }

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

Weak Trs: { h(f(x, y)) -> f(y, f(h(h(x)), a())) }
Obligation:
innermost runtime complexity
YES(O(1),O(1))

No rule is usable, rules are removed from the input problem.

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

Rules: Empty
Obligation:
innermost runtime complexity