/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) -> f1#(rnd1, rnd2) 
  f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3#(I2, I3) -> f2#(I2 - 1, I4) [I2 <= I3]
  f2#(I5, I6) -> f3#(I5, 1) [-1 <= I5 - 1]
  f1#(I7, I8) -> f2#(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f3(I0, I1) -> f3(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3(I2, I3) -> f2(I2 - 1, I4) [I2 <= I3]
  f2(I5, I6) -> f3(I5, 1) [-1 <= I5 - 1]
  f1(I7, I8) -> f2(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]

The dependency graph for this problem is:
  0 -> 4
  1 -> 1, 2
  2 -> 3
  3 -> 1, 2
  4 -> 3
Where:
  0) init#(x1, x2) -> f1#(rnd1, rnd2) 
  1) f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  2) f3#(I2, I3) -> f2#(I2 - 1, I4) [I2 <= I3]
  3) f2#(I5, I6) -> f3#(I5, 1) [-1 <= I5 - 1]
  4) f1#(I7, I8) -> f2#(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]

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

DP problem for innermost termination.
P =
  f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3#(I2, I3) -> f2#(I2 - 1, I4) [I2 <= I3]
  f2#(I5, I6) -> f3#(I5, 1) [-1 <= I5 - 1]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f3(I0, I1) -> f3(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3(I2, I3) -> f2(I2 - 1, I4) [I2 <= I3]
  f2(I5, I6) -> f3(I5, 1) [-1 <= I5 - 1]
  f1(I7, I8) -> f2(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]

We use the reverse value criterion with the projection function NU:
  NU[f2#(z1,z2)] = z1
  NU[f3#(z1,z2)] = z1 - 1 - 1 + -1 * -1

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

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3#(I2, I3) -> f2#(I2 - 1, I4) [I2 <= I3]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f3(I0, I1) -> f3(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3(I2, I3) -> f2(I2 - 1, I4) [I2 <= I3]
  f2(I5, I6) -> f3(I5, 1) [-1 <= I5 - 1]
  f1(I7, I8) -> f2(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]

The dependency graph for this problem is:
  1 -> 1, 2
  2 -> 
Where:
  1) f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  2) f3#(I2, I3) -> f2#(I2 - 1, I4) [I2 <= I3]

We have the following SCCs.
  { 1 }

DP problem for innermost termination.
P =
  f3#(I0, I1) -> f3#(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
R = 
  init(x1, x2) -> f1(rnd1, rnd2) 
  f3(I0, I1) -> f3(I0, 2 * I1) [I1 <= I0 - 1 /\ 0 <= I1 - 1]
  f3(I2, I3) -> f2(I2 - 1, I4) [I2 <= I3]
  f2(I5, I6) -> f3(I5, 1) [-1 <= I5 - 1]
  f1(I7, I8) -> f2(I9, I10) [0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I8 - 1]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2)] = z1 - 1 + -1 * z2

This gives the following inequalities:
  I1 <= I0 - 1 /\ 0 <= I1 - 1  ==>  I0 - 1 + -1 * I1 > I0 - 1 + -1 * (2 * I1)  with  I0 - 1 + -1 * I1 >= 0

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