MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs: { f(h(x), y) -> h(f(y, f(x, h(f(a(), a()))))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

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

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

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

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

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

We are left with following problem, upon which TcT provides the
certificate MAYBE.

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

The input cannot be shown compatible

Arrrr..