/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 strict:
  b(b(x1)) -> c(d(x1))
  c(c(x1)) -> d(d(d(x1)))
  d(d(d(x1))) -> a(c(x1))
 weak:
  a(a(x1)) -> b(c(x1))
  b(c(x1)) -> a(a(x1))

Proof:
 String Reversal Processor:
  strict:
   b(b(x1)) -> d(c(x1))
   c(c(x1)) -> d(d(d(x1)))
   d(d(d(x1))) -> c(a(x1))
  weak:
   a(a(x1)) -> c(b(x1))
   c(b(x1)) -> a(a(x1))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = 9x0,
    
    [c](x0) = 9x0,
    
    [d](x0) = 6x0,
    
    [b](x0) = 9x0
   orientation:
    b(b(x1)) = 18x1 >= 15x1 = d(c(x1))
    
    c(c(x1)) = 18x1 >= 18x1 = d(d(d(x1)))
    
    d(d(d(x1))) = 18x1 >= 18x1 = c(a(x1))
    
    a(a(x1)) = 18x1 >= 18x1 = c(b(x1))
    
    c(b(x1)) = 18x1 >= 18x1 = a(a(x1))
   problem:
    strict:
     c(c(x1)) -> d(d(d(x1)))
     d(d(d(x1))) -> c(a(x1))
    weak:
     a(a(x1)) -> c(b(x1))
     c(b(x1)) -> a(a(x1))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [a](x0) = 1x0,
     
     [c](x0) = 2x0,
     
     [d](x0) = 1x0,
     
     [b](x0) = x0
    orientation:
     c(c(x1)) = 4x1 >= 3x1 = d(d(d(x1)))
     
     d(d(d(x1))) = 3x1 >= 3x1 = c(a(x1))
     
     a(a(x1)) = 2x1 >= 2x1 = c(b(x1))
     
     c(b(x1)) = 2x1 >= 2x1 = a(a(x1))
    problem:
     strict:
      d(d(d(x1))) -> c(a(x1))
     weak:
      a(a(x1)) -> c(b(x1))
      c(b(x1)) -> a(a(x1))
    String Reversal Processor:
     strict:
      d(d(d(x1))) -> a(c(x1))
     weak:
      a(a(x1)) -> b(c(x1))
      b(c(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
                 [0  -&]  
       [a](x0) = [0  0 ]x0,
       
                 [0  -&]  
       [c](x0) = [0  0 ]x0,
       
                 [0  1 ]  
       [d](x0) = [0  -&]x0,
       
                 [0  -&]  
       [b](x0) = [0  0 ]x0
      orientation:
                     [1 2]      [0  -&]             
       d(d(d(x1))) = [1 1]x1 >= [0  0 ]x1 = a(c(x1))
       
                  [0  -&]      [0  -&]             
       a(a(x1)) = [0  0 ]x1 >= [0  0 ]x1 = b(c(x1))
       
                  [0  -&]      [0  -&]             
       b(c(x1)) = [0  0 ]x1 >= [0  0 ]x1 = a(a(x1))
      problem:
       strict:
        
       weak:
        a(a(x1)) -> b(c(x1))
        b(c(x1)) -> a(a(x1))
      Qed