YES

Problem:
 *(x,*(y,z)) -> *(otimes(x,y),z)
 *(1(),y) -> y
 *(+(x,y),z) -> oplus(*(x,z),*(y,z))
 *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))

Proof:
 DP Processor:
  DPs:
   *#(x,*(y,z)) -> *#(otimes(x,y),z)
   *#(+(x,y),z) -> *#(y,z)
   *#(+(x,y),z) -> *#(x,z)
   *#(x,oplus(y,z)) -> *#(x,z)
   *#(x,oplus(y,z)) -> *#(x,y)
  TRS:
   *(x,*(y,z)) -> *(otimes(x,y),z)
   *(1(),y) -> y
   *(+(x,y),z) -> oplus(*(x,z),*(y,z))
   *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
  Usable Rule Processor:
   DPs:
    *#(x,*(y,z)) -> *#(otimes(x,y),z)
    *#(+(x,y),z) -> *#(y,z)
    *#(+(x,y),z) -> *#(x,z)
    *#(x,oplus(y,z)) -> *#(x,z)
    *#(x,oplus(y,z)) -> *#(x,y)
   TRS:
    
   Matrix Interpretation Processor: dim=4
    
    usable rules:
     
    interpretation:
     [*#](x0, x1) = [1 0 1 1]x0 + [1 1 1 1]x1 + [1],
     
                       [1 0 1 1]     [0 0 1 0]     [1]
                       [1 0 1 1]     [0 0 1 1]     [1]
     [oplus](x0, x1) = [0 1 0 0]x0 + [0 0 1 1]x1 + [0]
                       [0 0 0 0]     [1 1 0 0]     [0],
     
                   [1 1 0 0]     [0 0 1 0]     [1]
                   [0 0 0 0]     [0 0 0 0]     [0]
     [+](x0, x1) = [0 1 1 0]x0 + [0 0 1 0]x1 + [1]
                   [0 1 0 1]     [1 1 1 1]     [0],
     
                        [0 0 0 0]     [0 0 0 0]     [0]
                        [0 0 0 0]     [0 0 0 0]     [0]
     [otimes](x0, x1) = [0 0 0 0]x0 + [1 0 0 0]x1 + [0]
                        [1 0 0 0]     [1 1 0 0]     [1],
     
                   [1 0 0 0]     [0 0 0 0]     [0]
                   [0 0 0 0]     [0 1 0 0]     [1]
     [*](x0, x1) = [0 1 0 0]x0 + [0 1 0 0]x1 + [0]
                   [1 0 1 0]     [1 0 1 1]     [1]
    orientation:
     *#(x,*(y,z)) = [1 0 1 1]x + [2 1 1 0]y + [1 2 1 1]z + [3] >= [1 0 0 0]x + [2 1 0 0]y + [1 1 1 1]z + [2] = *#(otimes(x,y),z)
     
     *#(+(x,y),z) = [1 3 1 1]x + [1 1 3 1]y + [1 1 1 1]z + [3] >= [1 0 1 1]y + [1 1 1 1]z + [1] = *#(y,z)
     
     *#(+(x,y),z) = [1 3 1 1]x + [1 1 3 1]y + [1 1 1 1]z + [3] >= [1 0 1 1]x + [1 1 1 1]z + [1] = *#(x,z)
     
     *#(x,oplus(y,z)) = [1 0 1 1]x + [2 1 2 2]y + [1 1 3 2]z + [3] >= [1 0 1 1]x + [1 1 1 1]z + [1] = *#(x,z)
     
     *#(x,oplus(y,z)) = [1 0 1 1]x + [2 1 2 2]y + [1 1 3 2]z + [3] >= [1 0 1 1]x + [1 1 1 1]y + [1] = *#(x,y)
    problem:
     DPs:
      
     TRS:
      
    Qed