MAYBE

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

Strict Trs:
  { max(L(x)) -> x
  , max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
  , max(N(L(0()), L(y))) -> y
  , max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { max^#(L(x)) -> c_1()
  , max^#(N(L(x), N(y, z))) ->
    c_2(max^#(N(L(x), L(max(N(y, z))))), max^#(N(y, z)))
  , max^#(N(L(0()), L(y))) -> c_3()
  , max^#(N(L(s(x)), L(s(y)))) -> c_4(max^#(N(L(x), L(y)))) }

and mark the set of starting terms.

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

Strict DPs:
  { max^#(L(x)) -> c_1()
  , max^#(N(L(x), N(y, z))) ->
    c_2(max^#(N(L(x), L(max(N(y, z))))), max^#(N(y, z)))
  , max^#(N(L(0()), L(y))) -> c_3()
  , max^#(N(L(s(x)), L(s(y)))) -> c_4(max^#(N(L(x), L(y)))) }
Weak Trs:
  { max(L(x)) -> x
  , max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
  , max(N(L(0()), L(y))) -> y
  , max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: max^#(L(x)) -> c_1()
    , 2: max^#(N(L(x), N(y, z))) ->
         c_2(max^#(N(L(x), L(max(N(y, z))))), max^#(N(y, z)))
    , 3: max^#(N(L(0()), L(y))) -> c_3()
    , 4: max^#(N(L(s(x)), L(s(y)))) -> c_4(max^#(N(L(x), L(y)))) }

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

Strict DPs:
  { max^#(N(L(x), N(y, z))) ->
    c_2(max^#(N(L(x), L(max(N(y, z))))), max^#(N(y, z)))
  , max^#(N(L(s(x)), L(s(y)))) -> c_4(max^#(N(L(x), L(y)))) }
Weak DPs:
  { max^#(L(x)) -> c_1()
  , max^#(N(L(0()), L(y))) -> c_3() }
Weak Trs:
  { max(L(x)) -> x
  , max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
  , max(N(L(0()), L(y))) -> y
  , max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) }
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.

{ max^#(L(x)) -> c_1()
, max^#(N(L(0()), L(y))) -> c_3() }

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

Strict DPs:
  { max^#(N(L(x), N(y, z))) ->
    c_2(max^#(N(L(x), L(max(N(y, z))))), max^#(N(y, z)))
  , max^#(N(L(s(x)), L(s(y)))) -> c_4(max^#(N(L(x), L(y)))) }
Weak Trs:
  { max(L(x)) -> x
  , max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
  , max(N(L(0()), L(y))) -> y
  , max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..