/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:
 g(x) -> h(x,x)
 s(x) -> h(x,0())
 s(x) -> h(0(),x)
 f(g(x)) -> g(g(f(x)))
 g(s(x)) -> s(s(g(x)))
 h(f(x),g(x)) -> f(s(x))
 s(0()) -> f(0())
 s(s(0())) -> f(s(0()))
 f(s(0())) -> 0()
 s(s(s(s(s(s(s(0()))))))) -> f(s(s(0())))
 f(s(s(0()))) -> s(s(s(s(s(0())))))
 f(s(s(x))) -> h(f(x),g(h(x,x)))

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [f](x0) = -1x0 + 2x0x0,
   
   [0] = 0,
   
   [s](x0) = x0 + 1,
   
   [h](x0, x1) = x0 + x1,
   
   [g](x0) = 4x0 + 4
  orientation:
   g(x) = 4x + 4 >= 2x = h(x,x)
   
   s(x) = x + 1 >= x = h(x,0())
   
   s(x) = x + 1 >= x = h(0(),x)
   
   f(g(x)) = 60x + 32x*x + 28 >= -16x + 32x*x + 20 = g(g(f(x)))
   
   g(s(x)) = 4x + 8 >= 4x + 6 = s(s(g(x)))
   
   h(f(x),g(x)) = 3x + 2x*x + 4 >= 3x + 2x*x + 1 = f(s(x))
   
   s(0()) = 1 >= 0 = f(0())
   
   s(s(0())) = 2 >= 1 = f(s(0()))
   
   f(s(0())) = 1 >= 0 = 0()
   
   s(s(s(s(s(s(s(0()))))))) = 7 >= 6 = f(s(s(0())))
   
   f(s(s(0()))) = 6 >= 5 = s(s(s(s(s(0())))))
   
   f(s(s(x))) = 7x + 2x*x + 6 >= 7x + 2x*x + 4 = h(f(x),g(h(x,x)))
  problem:
   
  Qed