/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:
 f(x,y,w,w,a()) -> g1(x,x,y,w)
 f(x,y,w,a(),a()) -> g1(y,x,x,w)
 f(x,y,a(),a(),w) -> g2(x,y,y,w)
 f(x,y,a(),w,w) -> g2(y,y,x,w)
 g1(x,x,y,a()) -> h(x,y)
 g1(y,x,x,a()) -> h(x,y)
 g2(x,y,y,a()) -> h(x,y)
 g2(y,y,x,a()) -> h(x,y)
 h(x,x) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h](x0, x1) = x0 + x1 + 2,
   
   [f](x0, x1, x2, x3, x4) = 4x0 + 4x1 + 2x2 + 4x3 + x4 + 6,
   
   [g2](x0, x1, x2, x3) = 2x0 + x1 + x2 + x3 + 2,
   
   [a] = 0,
   
   [g1](x0, x1, x2, x3) = x0 + x1 + 2x2 + x3 + 3
  orientation:
   f(x,y,w,w,a()) = 6w + 4x + 4y + 6 >= w + 2x + 2y + 3 = g1(x,x,y,w)
   
   f(x,y,w,a(),a()) = 2w + 4x + 4y + 6 >= w + 3x + y + 3 = g1(y,x,x,w)
   
   f(x,y,a(),a(),w) = w + 4x + 4y + 6 >= w + 2x + 2y + 2 = g2(x,y,y,w)
   
   f(x,y,a(),w,w) = 5w + 4x + 4y + 6 >= w + x + 3y + 2 = g2(y,y,x,w)
   
   g1(x,x,y,a()) = 2x + 2y + 3 >= x + y + 2 = h(x,y)
   
   g1(y,x,x,a()) = 3x + y + 3 >= x + y + 2 = h(x,y)
   
   g2(x,y,y,a()) = 2x + 2y + 2 >= x + y + 2 = h(x,y)
   
   g2(y,y,x,a()) = x + 3y + 2 >= x + y + 2 = h(x,y)
   
   h(x,x) = 2x + 2 >= x = x
  problem:
   g2(x,y,y,a()) -> h(x,y)
   g2(y,y,x,a()) -> h(x,y)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 0 0]  
    [h](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
                           [1 0 0]     [1 0 0]     [1 0 0]     [1 1 1]  
    [g2](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3
                           [0 0 0]     [0 0 0]     [0 0 0]     [0 0 0]  ,
    
          [0]
    [a] = [1]
          [1]
   orientation:
                    [1 0 0]    [2 0 0]    [2]    [1 0 0]    [1 0 0]          
    g2(x,y,y,a()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = h(x,y)
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
    
                    [1 0 0]    [2 0 0]    [2]    [1 0 0]    [1 0 0]          
    g2(y,y,x,a()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = h(x,y)
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
   problem:
    
   Qed