YES(O(1),O(n^1))

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

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

We add the following innermost weak dependency pairs:

Strict DPs: { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict DPs: { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z)) }
Strict Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

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

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict DPs: { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

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

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

TcT has computed the following constructor-restricted matrix
interpretation.

    [+](x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                  [0 0]      [0 0]      [0]
                                           
  [*^#](x1, x2) = [1 0] x2 + [0]           
                  [0 0]      [0]           
                                           
  [c_1](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                  [0 1]      [0 1]      [0]

The following symbols are considered usable

  {*^#}

The order satisfies the following ordering constraints:

  [*^#(x, +(y, z))] = [1 0] y + [1 0] z + [1]    
                      [0 0]     [0 0]     [0]    
                    > [1 0] y + [1 0] z + [0]    
                      [0 0]     [0 0]     [0]    
                    = [c_1(*^#(x, y), *^#(x, z))]
                                                 

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 YES(O(1),O(1)).

Weak DPs: { *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

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

{ *^#(x, +(y, z)) -> c_1(*^#(x, y), *^#(x, z)) }

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(1)).

Rules: Empty
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

Hurray, we answered YES(O(1),O(n^1))