/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:
 c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
 c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
 c(c(a(a(y,0()),x))) -> c(y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0) = 2x0,
   
   [0] = 1,
   
   [a](x0, x1) = x0 + 2x1,
   
   [b](x0, x1) = x0 + 6x1
  orientation:
   c(c(c(a(x,y)))) = 8x + 16y >= 6x + 16y = b(c(c(c(c(y)))),x)
   
   c(c(b(c(y),0()))) = 8y + 24 >= 8y + 17 = a(0(),c(c(a(y,0()))))
   
   c(c(a(a(y,0()),x))) = 8x + 4y + 8 >= 2y = c(y)
  problem:
   c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [c](x0) = [0 1 1]x0
              [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]     [1]
    [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 0 0]     [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]     [0]
    [b](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 0 0]     [0 0 0]     [0]
   orientation:
                      [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [0]                     
    c(c(c(a(x,y)))) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = b(c(c(c(c(y)))),x)
                      [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                     
   problem:
    
   Qed