/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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
 .(.(x,y),z) -> .(x,.(y,z))
 i(.(x,y)) -> .(i(y),i(x))

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