YES

Problem:
 *(e(),x) -> x
 *(-(x),x) -> e()
 *(*(x,y),z) -> *(x,*(y,z))
 *(-(x),*(x,y)) -> y
 *(x,e()) -> x
 -(e()) -> e()
 -(-(x)) -> x
 *(x,-(x)) -> e()
 *(x,*(-(x),y)) -> y
 -(*(x,y)) -> *(-(y),-(x))

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [-](x0) = 2x0 + 3,
   
   [*](x0, x1) = x0 + x1 + 3,
   
   [e] = 6
  orientation:
   *(e(),x) = x + 9 >= x = x
   
   *(-(x),x) = 3x + 6 >= 6 = e()
   
   *(*(x,y),z) = x + y + z + 6 >= x + y + z + 6 = *(x,*(y,z))
   
   *(-(x),*(x,y)) = 3x + y + 9 >= y = y
   
   *(x,e()) = x + 9 >= x = x
   
   -(e()) = 15 >= 6 = e()
   
   -(-(x)) = 4x + 9 >= x = x
   
   *(x,-(x)) = 3x + 6 >= 6 = e()
   
   *(x,*(-(x),y)) = 3x + y + 9 >= y = y
   
   -(*(x,y)) = 2x + 2y + 9 >= 2x + 2y + 9 = *(-(y),-(x))
  problem:
   *(-(x),x) -> e()
   *(*(x,y),z) -> *(x,*(y,z))
   *(x,-(x)) -> e()
   -(*(x,y)) -> *(-(y),-(x))
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [-](x0) = 6x0,
    
    [*](x0, x1) = x0 + x1 + 4,
    
    [e] = 4
   orientation:
    *(-(x),x) = 7x + 4 >= 4 = e()
    
    *(*(x,y),z) = x + y + z + 8 >= x + y + z + 8 = *(x,*(y,z))
    
    *(x,-(x)) = 7x + 4 >= 4 = e()
    
    -(*(x,y)) = 6x + 6y + 24 >= 6x + 6y + 4 = *(-(y),-(x))
   problem:
    *(-(x),x) -> e()
    *(*(x,y),z) -> *(x,*(y,z))
    *(x,-(x)) -> e()
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [-](x0) = 4x0 + 1,
     
     [*](x0, x1) = 4x0 + x1,
     
     [e] = 1
    orientation:
     *(-(x),x) = 17x + 4 >= 1 = e()
     
     *(*(x,y),z) = 16x + 4y + z >= 4x + 4y + z = *(x,*(y,z))
     
     *(x,-(x)) = 8x + 1 >= 1 = e()
    problem:
     *(*(x,y),z) -> *(x,*(y,z))
     *(x,-(x)) -> e()
    DP Processor:
     DPs:
      *#(*(x,y),z) -> *#(y,z)
      *#(*(x,y),z) -> *#(x,*(y,z))
     TRS:
      *(*(x,y),z) -> *(x,*(y,z))
      *(x,-(x)) -> e()
     Subterm Criterion Processor:
      simple projection:
       pi(*#) = 0
      problem:
       DPs:
        
       TRS:
        *(*(x,y),z) -> *(x,*(y,z))
        *(x,-(x)) -> e()
      Qed