YES

Problem:
 *(i(x),x) -> 1()
 *(1(),y) -> y
 *(x,0()) -> 0()
 *(*(x,y),z) -> *(x,*(y,z))

Proof:
 DP Processor:
  DPs:
   *#(*(x,y),z) -> *#(y,z)
   *#(*(x,y),z) -> *#(x,*(y,z))
  TRS:
   *(i(x),x) -> 1()
   *(1(),y) -> y
   *(x,0()) -> 0()
   *(*(x,y),z) -> *(x,*(y,z))
  Restore Modifier:
   DPs:
    *#(*(x,y),z) -> *#(y,z)
    *#(*(x,y),z) -> *#(x,*(y,z))
   TRS:
    *(i(x),x) -> 1()
    *(1(),y) -> y
    *(x,0()) -> 0()
    *(*(x,y),z) -> *(x,*(y,z))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 4/4
    DPs:
     *#(*(x,y),z) -> *#(y,z)
     *#(*(x,y),z) -> *#(x,*(y,z))
    TRS:
     *(i(x),x) -> 1()
     *(1(),y) -> y
     *(x,0()) -> 0()
     *(*(x,y),z) -> *(x,*(y,z))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [*#](x0, x1) = x0 + x1 + 1,
      
      [0] = 1,
      
      [1] = 0,
      
      [*](x0, x1) = x0 + x1 + 1,
      
      [i](x0) = 1
     orientation:
      *#(*(x,y),z) = x + y + z + 2 >= y + z + 1 = *#(y,z)
      
      *#(*(x,y),z) = x + y + z + 2 >= x + y + z + 2 = *#(x,*(y,z))
      
      *(i(x),x) = x + 2 >= 0 = 1()
      
      *(1(),y) = y + 1 >= y = y
      
      *(x,0()) = x + 2 >= 1 = 0()
      
      *(*(x,y),z) = x + y + z + 2 >= x + y + z + 2 = *(x,*(y,z))
     problem:
      DPs:
       *#(*(x,y),z) -> *#(x,*(y,z))
      TRS:
       *(i(x),x) -> 1()
       *(1(),y) -> y
       *(x,0()) -> 0()
       *(*(x,y),z) -> *(x,*(y,z))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [*#](x0, x1) = x0,
       
       [0] = 1,
       
       [1] = 0,
       
       [*](x0, x1) = x0 + x1 + 1,
       
       [i](x0) = 1
      orientation:
       *#(*(x,y),z) = x + y + 1 >= x = *#(x,*(y,z))
       
       *(i(x),x) = x + 2 >= 0 = 1()
       
       *(1(),y) = y + 1 >= y = y
       
       *(x,0()) = x + 2 >= 1 = 0()
       
       *(*(x,y),z) = x + y + z + 2 >= x + y + z + 2 = *(x,*(y,z))
      problem:
       DPs:
        
       TRS:
        *(i(x),x) -> 1()
        *(1(),y) -> y
        *(x,0()) -> 0()
        *(*(x,y),z) -> *(x,*(y,z))
      Qed