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:
  runtime complexity
Answer:
  YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  The following argument positions are usable:
    Uargs(+) = {1, 2}
  
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [*](x1, x2) = [2] x2 + [0]         
                                       
    [+](x1, x2) = [1] x1 + [1] x2 + [4]
  
  The order satisfies the following ordering constraints:
  
    [*(x, +(y, z))] = [2] y + [2] z + [8]  
                    > [2] y + [2] z + [4]  
                    = [+(*(x, y), *(x, z))]
                                           

We return to the main proof.

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

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

Empty rules are trivially bounded

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