/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]  
   [a](x0) = [0 0]x0,
   
             [1 1]     [0]
   [b](x0) = [0 0]x0 + [1],
   
               
   [c](x0) = x0
  orientation:
                 [1 1]      [1 1]                
   a(a(b(x1))) = [0 0]x1 >= [0 0]x1 = a(c(b(x1)))
   
                       [1 0]                
   c(c(c(x1))) = x1 >= [0 0]x1 = a(b(a(x1)))
   
                 [1 1]     [1]    [1 0]     [0]              
   b(c(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
   
                 [1 1]     [1]    [1 1]                
   b(b(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 = c(a(b(x1)))
   
                 [1 1]     [2]    [1 1]     [1]              
   b(b(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a(b(b(x1)))
   
                 [1 1]     [1]    [1 1]     [0]              
   b(b(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(c(x1)))
   
                 [1 0]     [0]    [1 0]                
   b(a(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 = a(c(c(x1)))
  problem:
   strict:
    a(a(b(x1))) -> a(c(b(x1)))
    c(c(c(x1))) -> a(b(a(x1)))
   weak:
    b(a(a(x1))) -> a(c(c(x1)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a](x0) = 2x0 + 8,
    
    [b](x0) = 2x0 + 2,
    
    [c](x0) = 2x0 + 7
   orientation:
    a(a(b(x1))) = 8x1 + 32 >= 8x1 + 30 = a(c(b(x1)))
    
    c(c(c(x1))) = 8x1 + 49 >= 8x1 + 44 = a(b(a(x1)))
    
    b(a(a(x1))) = 8x1 + 50 >= 8x1 + 50 = a(c(c(x1)))
   problem:
    strict:
     
    weak:
     b(a(a(x1))) -> a(c(c(x1)))
   Qed