/export/starexec/sandbox2/solver/bin/starexec_run_Itrs /export/starexec/sandbox2/benchmark/theBenchmark.itrs /export/starexec/sandbox2/output/output_files


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MAYBE

DP problem for innermost termination.
P =
  eval#(x, y, z) -> eval#(x, y - 1, z + y) [x >= 0 && z * z * z >= y]
  eval#(I0, I1, I2) -> eval#(I0 - 1, I1 - 1, I2) [I0 >= 0 && I2 * I2 * I2 >= I1]
R = 
  eval(x, y, z) -> eval(x, y - 1, z + y) [x >= 0 && z * z * z >= y]
  eval(I0, I1, I2) -> eval(I0 - 1, I1 - 1, I2) [I0 >= 0 && I2 * I2 * I2 >= I1]

We use the reverse value criterion with the projection function NU:
  NU[eval#(z1,z2,z3)] = z1

This gives the following inequalities:
  x >= 0 && z * z * z >= y  ==>  x >= x
  I0 >= 0 && I2 * I2 * I2 >= I1  ==>  I0 > I0 - 1  with  I0 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  eval#(x, y, z) -> eval#(x, y - 1, z + y) [x >= 0 && z * z * z >= y]
R = 
  eval(x, y, z) -> eval(x, y - 1, z + y) [x >= 0 && z * z * z >= y]
  eval(I0, I1, I2) -> eval(I0 - 1, I1 - 1, I2) [I0 >= 0 && I2 * I2 * I2 >= I1]