/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:
 .(1(),x) -> x
 .(x,1()) -> x
 .(i(x),x) -> 1()
 .(x,i(x)) -> 1()
 i(1()) -> 1()
 i(i(x)) -> x
 .(i(y),.(y,z)) -> z
 .(y,.(i(y),z)) -> z

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [.](x0, x1) = x0 + x1 + 3,
   
   [1] = 6,
   
   [i](x0) = 2x0 + 3
  orientation:
   .(1(),x) = x + 9 >= x = x
   
   .(x,1()) = x + 9 >= x = x
   
   .(i(x),x) = 3x + 6 >= 6 = 1()
   
   .(x,i(x)) = 3x + 6 >= 6 = 1()
   
   i(1()) = 15 >= 6 = 1()
   
   i(i(x)) = 4x + 9 >= x = x
   
   .(i(y),.(y,z)) = 3y + z + 9 >= z = z
   
   .(y,.(i(y),z)) = 3y + z + 9 >= z = z
  problem:
   .(i(x),x) -> 1()
   .(x,i(x)) -> 1()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 1 0]     [1 0 0]     [1]
    [.](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0]
                  [0 1 0]     [0 0 0]     [1],
    
          [1]
    [1] = [0]
          [1],
    
              [1 1 1]     [0]
    [i](x0) = [0 0 0]x0 + [1]
              [1 0 0]     [0]
   orientation:
                [2 1 1]    [2]    [1]      
    .(i(x),x) = [1 0 0]x + [0] >= [0] = 1()
                [0 0 0]    [2]    [1]      
    
                [2 2 1]    [1]    [1]      
    .(x,i(x)) = [0 0 1]x + [0] >= [0] = 1()
                [0 1 0]    [1]    [1]      
   problem:
    .(x,i(x)) -> 1()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 0 0]     [1]
     [.](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [0]
                   [0 0 0]     [0 0 1]     [0],
     
           [0]
     [1] = [0]
           [1],
     
               [1 0 0]     [0]
     [i](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1]
    orientation:
                 [2 0 0]    [1]    [0]      
     .(x,i(x)) = [1 0 0]x + [0] >= [0] = 1()
                 [0 0 0]    [1]    [1]      
    problem:
     
    Qed