Problem:
 -(+(x,-(x))) -> 0()
 +(x,-(x)) -> 0()
 -(+(0(),0())) -> 0()
 +(0(),0()) -> 0()
 -(0()) -> 0()

Proof:
 Church Rosser Transformation Processor (kb):
  -(+(x,-(x))) -> 0()
  +(x,-(x)) -> 0()
  -(+(0(),0())) -> 0()
  +(0(),0()) -> 0()
  -(0()) -> 0()
  critical peaks: joinable
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [0] = [1]
          [0],
    
                  [1 0 0]     [1 1 0]     [0]
    [+](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 0 0]     [0 0 0]     [0],
    
              [1 0 0]     [0]
    [-](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0]
   orientation:
                   [2 0 0]    [1]    [0]      
    -(+(x,-(x))) = [0 0 0]x + [1] >= [1] = 0()
                   [0 0 0]    [0]    [0]      
    
                [2 0 0]    [1]    [0]      
    +(x,-(x)) = [0 0 0]x + [1] >= [1] = 0()
                [0 0 0]    [0]    [0]      
    
                    [1]    [0]      
    -(+(0(),0())) = [1] >= [1] = 0()
                    [0]    [0]      
    
                 [1]    [0]      
    +(0(),0()) = [1] >= [1] = 0()
                 [0]    [0]      
    
             [0]    [0]      
    -(0()) = [1] >= [1] = 0()
             [0]    [0]      
   problem:
    -(0()) -> 0()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [0] = [0]
           [0],
     
               [1 0 0]     [1]
     [-](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0]
    orientation:
              [1]    [0]      
     -(0()) = [0] >= [0] = 0()
              [0]    [0]      
    problem:
     
    Qed