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

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [g1](x0, x1, x2) = 2x0 + 4x2 + x0x0 + x1x1 + 5,
   
   [h](x0, x1) = 2x1 + x0x0 + 4,
   
   [f](x0, x1) = 5x0 + 7x1 + 7x0x0 + 7x1x1 + 7,
   
   [g2](x0, x1, x2) = 5x1 + 2x2 + x0x0 + x1x1 + 2x2x2 + 6
  orientation:
   f(x,y) = 5x + 7x*x + 7y + 7y*y + 7 >= 2x + 2x*x + 4y + 5 = g1(x,x,y)
   
   f(x,y) = 5x + 7x*x + 7y + 7y*y + 7 >= 4x + x*x + 2y + y*y + 5 = g1(y,x,x)
   
   f(x,y) = 5x + 7x*x + 7y + 7y*y + 7 >= x*x + 7y + 3y*y + 6 = g2(x,y,y)
   
   f(x,y) = 5x + 7x*x + 7y + 7y*y + 7 >= 2x + 2x*x + 5y + 2y*y + 6 = g2(y,y,x)
   
   g1(x,x,y) = 2x + 2x*x + 4y + 5 >= x*x + 2y + 4 = h(x,y)
   
   g1(y,x,x) = 4x + x*x + 2y + y*y + 5 >= x*x + 2y + 4 = h(x,y)
   
   g2(x,y,y) = x*x + 7y + 3y*y + 6 >= x*x + 2y + 4 = h(x,y)
   
   g2(y,y,x) = 2x + 2x*x + 5y + 2y*y + 6 >= x*x + 2y + 4 = h(x,y)
   
   h(x,x) = 2x + x*x + 4 >= x = x
  problem:
   
  Qed