/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0  1 ]  
   [c](x0) = [-& 0 ]x0,
   
             [0 0]  
   [a](x0) = [0 1]x0,
   
             [1 1]  
   [b](x0) = [0 0]x0
  orientation:
                 [2 3]      [1 2]                
   b(c(a(x1))) = [1 2]x1 >= [1 2]x1 = a(b(a(x1)))
   
                 [1 2]      [0  1 ]                
   a(a(a(x1))) = [2 3]x1 >= [-& 0 ]x1 = c(c(c(x1)))
   
                 [1 2]      [1 2]                
   a(a(a(x1))) = [2 3]x1 >= [1 2]x1 = a(b(a(x1)))
   
                 [1 2]      [1 2]                
   c(c(a(x1))) = [0 1]x1 >= [0 1]x1 = c(a(c(x1)))
   
                 [2 2]      [1 2]                
   b(a(b(x1))) = [1 1]x1 >= [0 1]x1 = b(c(c(x1)))
   
                 [2 2]      [1 1]                
   c(a(b(x1))) = [1 1]x1 >= [1 1]x1 = a(c(b(x1)))
  problem:
   strict:
    b(c(a(x1))) -> a(b(a(x1)))
    a(a(a(x1))) -> a(b(a(x1)))
   weak:
    c(c(a(x1))) -> c(a(c(x1)))
    b(a(b(x1))) -> b(c(c(x1)))
    c(a(b(x1))) -> a(c(b(x1)))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 0]     [0]
    [c](x0) = [0 0]x0 + [1],
    
              [1 0]     [1]
    [a](x0) = [0 0]x0 + [0],
    
              [1 1]  
    [b](x0) = [0 0]x0
   orientation:
                  [1 0]     [2]    [1 0]     [2]              
    b(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b(a(x1)))
    
                  [1 0]     [3]    [1 0]     [2]              
    a(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b(a(x1)))
    
                  [1 0]     [1]    [1 0]     [1]              
    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(a(c(x1)))
    
                  [1 1]     [1]    [1 0]     [1]              
    b(a(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(c(c(x1)))
    
                  [1 1]     [1]    [1 1]     [1]              
    c(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a(c(b(x1)))
   problem:
    strict:
     b(c(a(x1))) -> a(b(a(x1)))
    weak:
     c(c(a(x1))) -> c(a(c(x1)))
     b(a(b(x1))) -> b(c(c(x1)))
     c(a(b(x1))) -> a(c(b(x1)))
   LPO Processor:
    precedence:
     b > c ~ a
    problem:
     strict:
      
     weak:
      c(c(a(x1))) -> c(a(c(x1)))
      c(a(b(x1))) -> a(c(b(x1)))
    Qed