/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files


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MAYBE

DP problem for innermost termination.
P =
  init#(x1, x2) -> f1#(rnd1, rnd2) 
  f2#(I0, I1) -> f2#(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
  f2#(I3, I4) -> f2#(I3 + 1, I5) [I3 <= -5 - 1 /\ I3 <= 0 /\ I3 <= -1]
  f2#(I6, I7) -> f2#(-5, I8) [-5 = I6]
  f1#(I9, I10) -> f2#(-1 * I10, I11) [0 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 * I10 <= 0]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f2(I0, I1) -> f2(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
  f2(I3, I4) -> f2(I3 + 1, I5) [I3 <= -5 - 1 /\ I3 <= 0 /\ I3 <= -1]
  f2(I6, I7) -> f2(-5, I8) [-5 = I6]
  f1(I9, I10) -> f2(-1 * I10, I11) [0 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 * I10 <= 0]

The dependency graph for this problem is:
  0 -> 4
  1 -> 1
  2 -> 2, 3
  3 -> 3
  4 -> 1, 2, 3
Where:
  0) init#(x1, x2) -> f1#(rnd1, rnd2) 
  1) f2#(I0, I1) -> f2#(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
  2) f2#(I3, I4) -> f2#(I3 + 1, I5) [I3 <= -5 - 1 /\ I3 <= 0 /\ I3 <= -1]
  3) f2#(I6, I7) -> f2#(-5, I8) [-5 = I6]
  4) f1#(I9, I10) -> f2#(-1 * I10, I11) [0 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 * I10 <= 0]

We have the following SCCs.
  { 2 }
  { 3 }
  { 1 }

DP problem for innermost termination.
P =
  f2#(I0, I1) -> f2#(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f2(I0, I1) -> f2(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
  f2(I3, I4) -> f2(I3 + 1, I5) [I3 <= -5 - 1 /\ I3 <= 0 /\ I3 <= -1]
  f2(I6, I7) -> f2(-5, I8) [-5 = I6]
  f1(I9, I10) -> f2(-1 * I10, I11) [0 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 * I10 <= 0]

We use the reverse value criterion with the projection function NU:
  NU[f2#(z1,z2)] = 0 + -1 * z1

This gives the following inequalities:
  -5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1  ==>  0 + -1 * I0 > 0 + -1 * (I0 + 1)  with  0 + -1 * I0 >= 0

All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.

DP problem for innermost termination.
P =
  f2#(I6, I7) -> f2#(-5, I8) [-5 = I6]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f2(I0, I1) -> f2(I0 + 1, I2) [-5 <= I0 - 1 /\ I0 <= 0 /\ I0 <= -1]
  f2(I3, I4) -> f2(I3 + 1, I5) [I3 <= -5 - 1 /\ I3 <= 0 /\ I3 <= -1]
  f2(I6, I7) -> f2(-5, I8) [-5 = I6]
  f1(I9, I10) -> f2(-1 * I10, I11) [0 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 * I10 <= 0]