/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

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

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [k](x0) = -1x0 + 3x0x0,
   
   [h](x0, x1) = x0 + x1,
   
   [g](x0) = 6x0 + 5,
   
   [f](x0) = -1x0 + 2x0x0,
   
   [s](x0) = x0 + 1,
   
   [0] = 0
  orientation:
   s(s(0())) = 2 >= 1 = f(s(0()))
   
   g(x) = 6x + 5 >= 2x = h(x,x)
   
   s(x) = x + 1 >= x = h(x,0())
   
   s(x) = x + 1 >= x = h(0(),x)
   
   f(g(x)) = 114x + 72x*x + 45 >= -36x + 72x*x + 35 = g(g(f(x)))
   
   g(s(x)) = 6x + 11 >= 6x + 7 = s(s(g(x)))
   
   h(f(x),g(x)) = 5x + 2x*x + 5 >= 3x + 2x*x + 1 = f(s(x))
   
   s(0()) = 1 >= 0 = k(0())
   
   s(k(0())) = 1 >= 0 = 0()
   
   s(s(s(0()))) = 3 >= 2 = k(s(0()))
   
   k(s(0())) = 2 >= 1 = s(0())
   
   s(s(s(s(s(s(s(s(s(s(s(0()))))))))))) = 11 >= 10 = k(s(s(0())))
   
   k(s(s(0()))) = 10 >= 9 = s(s(s(s(s(s(s(s(s(0())))))))))
   
   h(k(x),g(x)) = 5x + 3x*x + 5 >= 5x + 3x*x + 2 = k(s(x))
  problem:
   
  Qed