MAYBE

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

Strict Trs:
  { *(x, +(y, z)) -> +(*(x, y), *(x, z))
  , *(x, 1()) -> x
  , *(+(x, y), z) -> +(*(x, z), *(y, z))
  , *(1(), y) -> y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z))
  , *^#(x, 1()) -> c_2()
  , *^#(+(x, y), z) -> c_3(*^#(x, z), *^#(y, z))
  , *^#(1(), y) -> 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, z)) -> c_1(*^#(x, y), *^#(x, z))
  , *^#(x, 1()) -> c_2()
  , *^#(+(x, y), z) -> c_3(*^#(x, z), *^#(y, z))
  , *^#(1(), y) -> c_4() }
Strict Trs:
  { *(x, +(y, z)) -> +(*(x, y), *(x, z))
  , *(x, 1()) -> x
  , *(+(x, y), z) -> +(*(x, z), *(y, z))
  , *(1(), y) -> y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z))
  , *^#(x, 1()) -> c_2()
  , *^#(+(x, y), z) -> c_3(*^#(x, z), *^#(y, z))
  , *^#(1(), y) -> c_4() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_1) = {1, 2}, Uargs(c_3) = {1, 2}

TcT has computed following constructor-restricted matrix
interpretation.

    [+](x1, x2) = [1] x1 + [1] x2 + [1]
                                       
            [1] = [2]                  
                                       
  [*^#](x1, x2) = [1]                  
                                       
  [c_1](x1, x2) = [1] x1 + [1] x2 + [1]
                                       
          [c_2] = [0]                  
                                       
  [c_3](x1, x2) = [1] x1 + [1] x2 + [1]
                                       
          [c_4] = [0]                  

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Strict DPs:
  { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z))
  , *^#(+(x, y), z) -> c_3(*^#(x, z), *^#(y, z)) }
Weak DPs:
  { *^#(x, 1()) -> c_2()
  , *^#(1(), y) -> c_4() }
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()
, *^#(1(), y) -> c_4() }

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

Strict DPs:
  { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z))
  , *^#(+(x, y), z) -> c_3(*^#(x, z), *^#(y, z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..