Problem:
 0(0(0(0(x1)))) -> 0(0(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(1(0(x1))))

Proof:
 String Reversal Processor:
  0(0(0(0(x1)))) -> 1(1(0(0(x1))))
  1(0(0(1(x1)))) -> 0(1(0(0(x1))))
  DP Processor:
   DPs:
    0#(0(0(0(x1)))) -> 1#(0(0(x1)))
    0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
    1#(0(0(1(x1)))) -> 0#(x1)
    1#(0(0(1(x1)))) -> 0#(0(x1))
    1#(0(0(1(x1)))) -> 1#(0(0(x1)))
    1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
   TRS:
    0(0(0(0(x1)))) -> 1(1(0(0(x1))))
    1(0(0(1(x1)))) -> 0(1(0(0(x1))))
   TDG Processor:
    DPs:
     0#(0(0(0(x1)))) -> 1#(0(0(x1)))
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
     1#(0(0(1(x1)))) -> 0#(x1)
     1#(0(0(1(x1)))) -> 0#(0(x1))
     1#(0(0(1(x1)))) -> 1#(0(0(x1)))
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
    TRS:
     0(0(0(0(x1)))) -> 1(1(0(0(x1))))
     1(0(0(1(x1)))) -> 0(1(0(0(x1))))
    graph:
     1#(0(0(1(x1)))) -> 1#(0(0(x1))) ->
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
     1#(0(0(1(x1)))) -> 1#(0(0(x1))) ->
     1#(0(0(1(x1)))) -> 1#(0(0(x1)))
     1#(0(0(1(x1)))) -> 1#(0(0(x1))) -> 1#(0(0(1(x1)))) -> 0#(0(x1))
     1#(0(0(1(x1)))) -> 1#(0(0(x1))) -> 1#(0(0(1(x1)))) -> 0#(x1)
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1)))) ->
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1)))) ->
     0#(0(0(0(x1)))) -> 1#(0(0(x1)))
     1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
     1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 1#(0(0(x1)))
     1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
     1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 1#(0(0(x1)))
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1)))) ->
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1)))) ->
     1#(0(0(1(x1)))) -> 1#(0(0(x1)))
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1)))) ->
     1#(0(0(1(x1)))) -> 0#(0(x1))
     0#(0(0(0(x1)))) -> 1#(1(0(0(x1)))) -> 1#(0(0(1(x1)))) -> 0#(x1)
     0#(0(0(0(x1)))) -> 1#(0(0(x1))) ->
     1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
     0#(0(0(0(x1)))) -> 1#(0(0(x1))) ->
     1#(0(0(1(x1)))) -> 1#(0(0(x1)))
     0#(0(0(0(x1)))) -> 1#(0(0(x1))) -> 1#(0(0(1(x1)))) -> 0#(0(x1))
     0#(0(0(0(x1)))) -> 1#(0(0(x1))) -> 1#(0(0(1(x1)))) -> 0#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      0(0(0(0(x1)))) -> 1(1(0(0(x1))))
      1(0(0(1(x1)))) -> 0(1(0(0(x1))))
     interpretation:
      [1#](x0) = 1x0,
      
      [0#](x0) = 1x0,
      
      [1](x0) = 1x0,
      
      [0](x0) = 1x0
     orientation:
      0#(0(0(0(x1)))) = 4x1 >= 3x1 = 1#(0(0(x1)))
      
      0#(0(0(0(x1)))) = 4x1 >= 4x1 = 1#(1(0(0(x1))))
      
      1#(0(0(1(x1)))) = 4x1 >= 1x1 = 0#(x1)
      
      1#(0(0(1(x1)))) = 4x1 >= 2x1 = 0#(0(x1))
      
      1#(0(0(1(x1)))) = 4x1 >= 3x1 = 1#(0(0(x1)))
      
      1#(0(0(1(x1)))) = 4x1 >= 4x1 = 0#(1(0(0(x1))))
      
      0(0(0(0(x1)))) = 4x1 >= 4x1 = 1(1(0(0(x1))))
      
      1(0(0(1(x1)))) = 4x1 >= 4x1 = 0(1(0(0(x1))))
     problem:
      DPs:
       0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
       1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
      TRS:
       0(0(0(0(x1)))) -> 1(1(0(0(x1))))
       1(0(0(1(x1)))) -> 0(1(0(0(x1))))
     Restore Modifier:
      DPs:
       0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
       1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
      TRS:
       0(0(0(0(x1)))) -> 1(1(0(0(x1))))
       1(0(0(1(x1)))) -> 0(1(0(0(x1))))
      EDG Processor:
       DPs:
        0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
        1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
       TRS:
        0(0(0(0(x1)))) -> 1(1(0(0(x1))))
        1(0(0(1(x1)))) -> 0(1(0(0(x1))))
       graph:
        1#(0(0(1(x1)))) -> 0#(1(0(0(x1)))) ->
        0#(0(0(0(x1)))) -> 1#(1(0(0(x1))))
        0#(0(0(0(x1)))) -> 1#(1(0(0(x1)))) -> 1#(0(0(1(x1)))) -> 0#(1(0(0(x1))))
       Loop Processor:
        loop length: 15
        terms:
         1(0(0(1(0(0(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(0(0(0(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(0(0(0(0(1(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(0(0(0(0(1(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(1(0(1(0(0(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(1(0(0(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(0(1(0(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(1(0(0(1(1(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(0(1(0(0(1(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(0(0(1(0(0(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         0(0(0(0(1(0(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         1(1(0(0(1(0(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         1(0(1(0(0(0(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
         1(0(1(0(0(1(1(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))
        context: []
        substitution:
         x1 -> x1
        Qed