MAYBE

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

Strict Trs:
  { *(X, +(Y, 1())) -> +(*(X, +(Y, *(1(), 0()))), X)
  , *(X, 1()) -> X
  , *(X, 0()) -> X
  , *(X, 0()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { *^#(X, +(Y, 1())) ->
    c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0()))
  , *^#(X, 1()) -> c_2()
  , *^#(X, 0()) -> c_3()
  , *^#(X, 0()) -> c_4() }

and mark the set of starting terms.

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

Strict DPs:
  { *^#(X, +(Y, 1())) ->
    c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0()))
  , *^#(X, 1()) -> c_2()
  , *^#(X, 0()) -> c_3()
  , *^#(X, 0()) -> c_4() }
Weak Trs:
  { *(X, +(Y, 1())) -> +(*(X, +(Y, *(1(), 0()))), X)
  , *(X, 1()) -> X
  , *(X, 0()) -> X
  , *(X, 0()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: *^#(X, +(Y, 1())) ->
         c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0()))
    , 2: *^#(X, 1()) -> c_2()
    , 3: *^#(X, 0()) -> c_3()
    , 4: *^#(X, 0()) -> c_4() }

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

Strict DPs:
  { *^#(X, +(Y, 1())) ->
    c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0())) }
Weak DPs:
  { *^#(X, 1()) -> c_2()
  , *^#(X, 0()) -> c_3()
  , *^#(X, 0()) -> c_4() }
Weak Trs:
  { *(X, +(Y, 1())) -> +(*(X, +(Y, *(1(), 0()))), X)
  , *(X, 1()) -> X
  , *(X, 0()) -> X
  , *(X, 0()) -> 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.

{ *^#(X, 1()) -> c_2()
, *^#(X, 0()) -> c_3()
, *^#(X, 0()) -> c_4() }

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

Strict DPs:
  { *^#(X, +(Y, 1())) ->
    c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0())) }
Weak Trs:
  { *(X, +(Y, 1())) -> +(*(X, +(Y, *(1(), 0()))), X)
  , *(X, 1()) -> X
  , *(X, 0()) -> X
  , *(X, 0()) -> 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:

  { *^#(X, +(Y, 1())) ->
    c_1(*^#(X, +(Y, *(1(), 0()))), *^#(1(), 0())) }

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

Strict DPs: { *^#(X, +(Y, 1())) -> c_1(*^#(X, +(Y, *(1(), 0())))) }
Weak Trs:
  { *(X, +(Y, 1())) -> +(*(X, +(Y, *(1(), 0()))), X)
  , *(X, 1()) -> X
  , *(X, 0()) -> X
  , *(X, 0()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..