MAYBE

Problem:
 minus(0()) -> 0()
 +(x,0()) -> x
 +(0(),y) -> y
 +(minus(1()),1()) -> 0()
 minus(minus(x)) -> x
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,+(y,z)) -> +(+(x,y),z)
 +(minus(+(x,1())),1()) -> minus(x)

Proof:
 Complexity Transformation Processor:
  strict:
   minus(0()) -> 0()
   +(x,0()) -> x
   +(0(),y) -> y
   +(minus(1()),1()) -> 0()
   minus(minus(x)) -> x
   +(x,minus(y)) -> minus(+(minus(x),y))
   +(x,+(y,z)) -> +(+(x,y),z)
   +(minus(+(x,1())),1()) -> minus(x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [1] = 0,
     
     [+](x0, x1) = x0 + x1 + 1,
     
     [minus](x0) = x0,
     
     [0] = 0
    orientation:
     minus(0()) = 0 >= 0 = 0()
     
     +(x,0()) = x + 1 >= x = x
     
     +(0(),y) = y + 1 >= y = y
     
     +(minus(1()),1()) = 1 >= 0 = 0()
     
     minus(minus(x)) = x >= x = x
     
     +(x,minus(y)) = x + y + 1 >= x + y + 1 = minus(+(minus(x),y))
     
     +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
     
     +(minus(+(x,1())),1()) = x + 2 >= x = minus(x)
    problem:
     strict:
      minus(0()) -> 0()
      minus(minus(x)) -> x
      +(x,minus(y)) -> minus(+(minus(x),y))
      +(x,+(y,z)) -> +(+(x,y),z)
     weak:
      +(x,0()) -> x
      +(0(),y) -> y
      +(minus(1()),1()) -> 0()
      +(minus(+(x,1())),1()) -> minus(x)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [1] = 1,
       
       [+](x0, x1) = x0 + x1,
       
       [minus](x0) = x0 + 1,
       
       [0] = 0
      orientation:
       minus(0()) = 1 >= 0 = 0()
       
       minus(minus(x)) = x + 2 >= x = x
       
       +(x,minus(y)) = x + y + 1 >= x + y + 2 = minus(+(minus(x),y))
       
       +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
       
       +(x,0()) = x >= x = x
       
       +(0(),y) = y >= y = y
       
       +(minus(1()),1()) = 3 >= 0 = 0()
       
       +(minus(+(x,1())),1()) = x + 3 >= x + 1 = minus(x)
      problem:
       strict:
        +(x,minus(y)) -> minus(+(minus(x),y))
        +(x,+(y,z)) -> +(+(x,y),z)
       weak:
        minus(0()) -> 0()
        minus(minus(x)) -> x
        +(x,0()) -> x
        +(0(),y) -> y
        +(minus(1()),1()) -> 0()
        +(minus(+(x,1())),1()) -> minus(x)
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
               [0]
         [1] = [0],
         
                            [1 1]     [0]
         [+](x0, x1) = x0 + [0 1]x1 + [1],
         
                         
         [minus](x0) = x0,
         
               [0]
         [0] = [0]
        orientation:
                             [1 1]    [0]        [1 1]    [0]                       
         +(x,minus(y)) = x + [0 1]y + [1] >= x + [0 1]y + [1] = minus(+(minus(x),y))
         
                           [1 1]    [1 2]    [1]        [1 1]    [1 1]    [0]              
         +(x,+(y,z)) = x + [0 1]y + [0 1]z + [2] >= x + [0 1]y + [0 1]z + [2] = +(+(x,y),z)
         
                      [0]    [0]      
         minus(0()) = [0] >= [0] = 0()
         
                                     
         minus(minus(x)) = x >= x = x
         
                        [0]         
         +(x,0()) = x + [1] >= x = x
         
                    [1 1]    [0]         
         +(0(),y) = [0 1]y + [1] >= y = y
         
                             [0]    [0]      
         +(minus(1()),1()) = [1] >= [0] = 0()
         
                                      [0]                
         +(minus(+(x,1())),1()) = x + [2] >= x = minus(x)
        problem:
         strict:
          +(x,minus(y)) -> minus(+(minus(x),y))
         weak:
          +(x,+(y,z)) -> +(+(x,y),z)
          minus(0()) -> 0()
          minus(minus(x)) -> x
          +(x,0()) -> x
          +(0(),y) -> y
          +(minus(1()),1()) -> 0()
          +(minus(+(x,1())),1()) -> minus(x)
        Open