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


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YES

DP problem for innermost termination.
P =
  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  f3#(I0, I1, I2) -> f3#(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
  f2#(I6, I7, I8) -> f3#(I9, I10, 0) [I6 <= 1 /\ 3 <= I10 - 1 /\ 1 <= I9 - 1]
  f2#(I11, I12, I13) -> f2#(I11 - 1, 1, I14) [1 <= I11 - 1]
  f2#(I15, I16, I17) -> f2#(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
  f1#(I20, I21, I22) -> f2#(I23, 0, I24) [0 <= I20 - 1 /\ -1 <= I23 - 1 /\ 0 <= I21 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f3(I0, I1, I2) -> f3(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
  f2(I6, I7, I8) -> f3(I9, I10, 0) [I6 <= 1 /\ 3 <= I10 - 1 /\ 1 <= I9 - 1]
  f2(I11, I12, I13) -> f2(I11 - 1, 1, I14) [1 <= I11 - 1]
  f2(I15, I16, I17) -> f2(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
  f1(I20, I21, I22) -> f2(I23, 0, I24) [0 <= I20 - 1 /\ -1 <= I23 - 1 /\ 0 <= I21 - 1]

The dependency graph for this problem is:
  0 -> 5
  1 -> 1
  2 -> 1
  3 -> 2, 3, 4
  4 -> 2, 3, 4
  5 -> 2, 3
Where:
  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  1) f3#(I0, I1, I2) -> f3#(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
  2) f2#(I6, I7, I8) -> f3#(I9, I10, 0) [I6 <= 1 /\ 3 <= I10 - 1 /\ 1 <= I9 - 1]
  3) f2#(I11, I12, I13) -> f2#(I11 - 1, 1, I14) [1 <= I11 - 1]
  4) f2#(I15, I16, I17) -> f2#(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
  5) f1#(I20, I21, I22) -> f2#(I23, 0, I24) [0 <= I20 - 1 /\ -1 <= I23 - 1 /\ 0 <= I21 - 1]

We have the following SCCs.
  { 3, 4 }
  { 1 }

DP problem for innermost termination.
P =
  f3#(I0, I1, I2) -> f3#(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f3(I0, I1, I2) -> f3(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
  f2(I6, I7, I8) -> f3(I9, I10, 0) [I6 <= 1 /\ 3 <= I10 - 1 /\ 1 <= I9 - 1]
  f2(I11, I12, I13) -> f2(I11 - 1, 1, I14) [1 <= I11 - 1]
  f2(I15, I16, I17) -> f2(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
  f1(I20, I21, I22) -> f2(I23, 0, I24) [0 <= I20 - 1 /\ -1 <= I23 - 1 /\ 0 <= I21 - 1]

We use the basic value criterion with the projection function NU:
  NU[f3#(z1,z2,z3)] = z2

This gives the following inequalities:
  I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1  ==>  I1 >! I4

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

DP problem for innermost termination.
P =
  f2#(I11, I12, I13) -> f2#(I11 - 1, 1, I14) [1 <= I11 - 1]
  f2#(I15, I16, I17) -> f2#(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f3(I0, I1, I2) -> f3(I3, I4, I5) [I5 + 2 <= I1 /\ I2 + 2 <= I0 /\ -1 <= I4 - 1 /\ 1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I4 + 1 <= I1 /\ I3 - 1 <= I1]
  f2(I6, I7, I8) -> f3(I9, I10, 0) [I6 <= 1 /\ 3 <= I10 - 1 /\ 1 <= I9 - 1]
  f2(I11, I12, I13) -> f2(I11 - 1, 1, I14) [1 <= I11 - 1]
  f2(I15, I16, I17) -> f2(I15 - 1, I18, I19) [0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1]
  f1(I20, I21, I22) -> f2(I23, 0, I24) [0 <= I20 - 1 /\ -1 <= I23 - 1 /\ 0 <= I21 - 1]

We use the basic value criterion with the projection function NU:
  NU[f2#(z1,z2,z3)] = z1

This gives the following inequalities:
  1 <= I11 - 1  ==>  I11 >! I11 - 1
  0 <= I16 - 1 /\ 1 <= I15 - 1 /\ I16 <= I18 - 1  ==>  I15 >! I15 - 1

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