MAYBE

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

Strict Trs:
  { concat(leaf(), Y) -> Y
  , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
  , lessleaves(X, leaf()) -> false()
  , lessleaves(leaf(), cons(W, Z)) -> true()
  , lessleaves(cons(U, V), cons(W, Z)) ->
    lessleaves(concat(U, V), concat(W, Z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { concat^#(leaf(), Y) -> c_1()
  , concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
  , lessleaves^#(X, leaf()) -> c_3()
  , lessleaves^#(leaf(), cons(W, Z)) -> c_4()
  , lessleaves^#(cons(U, V), cons(W, Z)) ->
    c_5(lessleaves^#(concat(U, V), concat(W, Z)),
        concat^#(U, V),
        concat^#(W, Z)) }

and mark the set of starting terms.

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

Strict DPs:
  { concat^#(leaf(), Y) -> c_1()
  , concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
  , lessleaves^#(X, leaf()) -> c_3()
  , lessleaves^#(leaf(), cons(W, Z)) -> c_4()
  , lessleaves^#(cons(U, V), cons(W, Z)) ->
    c_5(lessleaves^#(concat(U, V), concat(W, Z)),
        concat^#(U, V),
        concat^#(W, Z)) }
Weak Trs:
  { concat(leaf(), Y) -> Y
  , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
  , lessleaves(X, leaf()) -> false()
  , lessleaves(leaf(), cons(W, Z)) -> true()
  , lessleaves(cons(U, V), cons(W, Z)) ->
    lessleaves(concat(U, V), concat(W, Z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3,4} by applications of
Pre({1,3,4}) = {2,5}. Here rules are labeled as follows:

  DPs:
    { 1: concat^#(leaf(), Y) -> c_1()
    , 2: concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
    , 3: lessleaves^#(X, leaf()) -> c_3()
    , 4: lessleaves^#(leaf(), cons(W, Z)) -> c_4()
    , 5: lessleaves^#(cons(U, V), cons(W, Z)) ->
         c_5(lessleaves^#(concat(U, V), concat(W, Z)),
             concat^#(U, V),
             concat^#(W, Z)) }

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

Strict DPs:
  { concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
  , lessleaves^#(cons(U, V), cons(W, Z)) ->
    c_5(lessleaves^#(concat(U, V), concat(W, Z)),
        concat^#(U, V),
        concat^#(W, Z)) }
Weak DPs:
  { concat^#(leaf(), Y) -> c_1()
  , lessleaves^#(X, leaf()) -> c_3()
  , lessleaves^#(leaf(), cons(W, Z)) -> c_4() }
Weak Trs:
  { concat(leaf(), Y) -> Y
  , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
  , lessleaves(X, leaf()) -> false()
  , lessleaves(leaf(), cons(W, Z)) -> true()
  , lessleaves(cons(U, V), cons(W, Z)) ->
    lessleaves(concat(U, V), concat(W, Z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

{ concat^#(leaf(), Y) -> c_1()
, lessleaves^#(X, leaf()) -> c_3()
, lessleaves^#(leaf(), cons(W, Z)) -> c_4() }

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

Strict DPs:
  { concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
  , lessleaves^#(cons(U, V), cons(W, Z)) ->
    c_5(lessleaves^#(concat(U, V), concat(W, Z)),
        concat^#(U, V),
        concat^#(W, Z)) }
Weak Trs:
  { concat(leaf(), Y) -> Y
  , concat(cons(U, V), Y) -> cons(U, concat(V, Y))
  , lessleaves(X, leaf()) -> false()
  , lessleaves(leaf(), cons(W, Z)) -> true()
  , lessleaves(cons(U, V), cons(W, Z)) ->
    lessleaves(concat(U, V), concat(W, Z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { concat(leaf(), Y) -> Y
    , concat(cons(U, V), Y) -> cons(U, concat(V, Y)) }

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

Strict DPs:
  { concat^#(cons(U, V), Y) -> c_2(concat^#(V, Y))
  , lessleaves^#(cons(U, V), cons(W, Z)) ->
    c_5(lessleaves^#(concat(U, V), concat(W, Z)),
        concat^#(U, V),
        concat^#(W, Z)) }
Weak Trs:
  { concat(leaf(), Y) -> Y
  , concat(cons(U, V), Y) -> cons(U, concat(V, Y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..