MAYBE

Problem:
 a(lambda(x),y) -> lambda(a(x,1()))
 a(lambda(x),y) -> lambda(a(x,a(y,t())))
 a(a(x,y),z) -> a(x,a(y,z))
 lambda(x) -> x
 a(x,y) -> x
 a(x,y) -> y

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