/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:
  a(a(b(x1))) -> b(a(x1))
  c(b(x1)) -> b(c(a(x1)))
 weak:
  a(x1) -> a(c(a(x1)))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]  
   [c](x0) = [0 0]x0,
   
             [1 1]  
   [a](x0) = [1 1]x0,
   
             [1 1]     [1]
   [b](x0) = [0 0]x0 + [0]
  orientation:
                 [2 2]     [2]    [2 2]     [1]           
   a(a(b(x1))) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b(a(x1))
   
              [1 1]     [1]    [1 1]     [1]              
   c(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(c(a(x1)))
   
           [1 1]      [1 1]                
   a(x1) = [1 1]x1 >= [1 1]x1 = a(c(a(x1)))
  problem:
   strict:
    c(b(x1)) -> b(c(a(x1)))
   weak:
    a(x1) -> a(c(a(x1)))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
              [0 7]  
    [c](x0) = [6 3]x0,
    
              [0  -&]  
    [a](x0) = [-& -&]x0,
    
              [2 6]  
    [b](x0) = [6 0]x0
   orientation:
               [13 7 ]      [12 -&]                
    c(b(x1)) = [9  12]x1 >= [6  -&]x1 = b(c(a(x1)))
    
            [0  -&]      [0  -&]                
    a(x1) = [-& -&]x1 >= [-& -&]x1 = a(c(a(x1)))
   problem:
    strict:
     
    weak:
     a(x1) -> a(c(a(x1)))
   Qed