MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { +^#(0(), y) -> c_1()
  , +^#(s(x), 0()) -> c_2()
  , +^#(s(x), s(y)) -> c_3(+^#(s(x), +(y, 0())), +^#(y, 0())) }

and mark the set of starting terms.

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

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

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

  DPs:
    { 1: +^#(0(), y) -> c_1()
    , 2: +^#(s(x), 0()) -> c_2()
    , 3: +^#(s(x), s(y)) -> c_3(+^#(s(x), +(y, 0())), +^#(y, 0())) }

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

Strict DPs:
  { +^#(s(x), s(y)) -> c_3(+^#(s(x), +(y, 0())), +^#(y, 0())) }
Weak DPs:
  { +^#(0(), y) -> c_1()
  , +^#(s(x), 0()) -> c_2() }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), 0()) -> s(x)
  , +(s(x), s(y)) -> s(+(s(x), +(y, 0()))) }
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.

{ +^#(0(), y) -> c_1()
, +^#(s(x), 0()) -> c_2() }

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

Strict DPs:
  { +^#(s(x), s(y)) -> c_3(+^#(s(x), +(y, 0())), +^#(y, 0())) }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), 0()) -> s(x)
  , +(s(x), s(y)) -> s(+(s(x), +(y, 0()))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  { +^#(s(x), s(y)) -> c_3(+^#(s(x), +(y, 0())), +^#(y, 0())) }

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

Strict DPs: { +^#(s(x), s(y)) -> c_1(+^#(s(x), +(y, 0()))) }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), 0()) -> s(x)
  , +(s(x), s(y)) -> s(+(s(x), +(y, 0()))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..