/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files


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YES

DP problem for innermost termination.
P =
  f8#(x1, x2, x3, x4) -> f1#(x1, x2, x3, x4) 
  f7#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
  f2#(I4, I5, I6, I7) -> f7#(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  f6#(I8, I9, I10, I11) -> f2#(I8, I9, I10, I11) 
  f2#(I12, I13, I14, I15) -> f6#(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
  f3#(I20, I21, I22, I23) -> f4#(I20, I21, I22, I23) [I21 = I21]
  f2#(I24, I25, I26, I27) -> f3#(I24, I25, I26, I27) [-1 * I26 + I27 <= 0 /\ -1 * I26 + I27 <= 0]
  f1#(I28, I29, I30, I31) -> f2#(I28, I29, I30, I31) 
R = 
  f8(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
  f7(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
  f2(I4, I5, I6, I7) -> f7(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  f6(I8, I9, I10, I11) -> f2(I8, I9, I10, I11) 
  f2(I12, I13, I14, I15) -> f6(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
  f4(I16, I17, I18, I19) -> f5(rnd1, I17, I18, I19) [rnd1 = rnd1]
  f3(I20, I21, I22, I23) -> f4(I20, I21, I22, I23) [I21 = I21]
  f2(I24, I25, I26, I27) -> f3(I24, I25, I26, I27) [-1 * I26 + I27 <= 0 /\ -1 * I26 + I27 <= 0]
  f1(I28, I29, I30, I31) -> f2(I28, I29, I30, I31) 

The dependency graph for this problem is:
  0 -> 7
  1 -> 2, 4, 6
  2 -> 1
  3 -> 2, 4, 6
  4 -> 3
  5 -> 
  6 -> 5
  7 -> 2, 4, 6
Where:
  0) f8#(x1, x2, x3, x4) -> f1#(x1, x2, x3, x4) 
  1) f7#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
  2) f2#(I4, I5, I6, I7) -> f7#(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  3) f6#(I8, I9, I10, I11) -> f2#(I8, I9, I10, I11) 
  4) f2#(I12, I13, I14, I15) -> f6#(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
  5) f3#(I20, I21, I22, I23) -> f4#(I20, I21, I22, I23) [I21 = I21]
  6) f2#(I24, I25, I26, I27) -> f3#(I24, I25, I26, I27) [-1 * I26 + I27 <= 0 /\ -1 * I26 + I27 <= 0]
  7) f1#(I28, I29, I30, I31) -> f2#(I28, I29, I30, I31) 

We have the following SCCs.
  { 1, 2, 3, 4 }

DP problem for innermost termination.
P =
  f7#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
  f2#(I4, I5, I6, I7) -> f7#(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  f6#(I8, I9, I10, I11) -> f2#(I8, I9, I10, I11) 
  f2#(I12, I13, I14, I15) -> f6#(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
R = 
  f8(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
  f7(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
  f2(I4, I5, I6, I7) -> f7(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  f6(I8, I9, I10, I11) -> f2(I8, I9, I10, I11) 
  f2(I12, I13, I14, I15) -> f6(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
  f4(I16, I17, I18, I19) -> f5(rnd1, I17, I18, I19) [rnd1 = rnd1]
  f3(I20, I21, I22, I23) -> f4(I20, I21, I22, I23) [I21 = I21]
  f2(I24, I25, I26, I27) -> f3(I24, I25, I26, I27) [-1 * I26 + I27 <= 0 /\ -1 * I26 + I27 <= 0]
  f1(I28, I29, I30, I31) -> f2(I28, I29, I30, I31) 

We use the reverse value criterion with the projection function NU:
  NU[f6#(z1,z2,z3,z4)] = z4 + -1 * z3
  NU[f2#(z1,z2,z3,z4)] = z4 + -1 * z3
  NU[f7#(z1,z2,z3,z4)] = z4 + -1 * z3

This gives the following inequalities:
    ==>  I3 + -1 * I2 >= I3 + -1 * I2
  0 <= -1 - I6 + I7  ==>  I7 + -1 * I6 > I7 + -1 * (1 + I6)  with  I7 + -1 * I6 >= 0
    ==>  I11 + -1 * I10 >= I11 + -1 * I10
  I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0  ==>  I15 + -1 * I14 > I15 + -1 * (1 + I14)  with  I15 + -1 * I14 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f7#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
  f6#(I8, I9, I10, I11) -> f2#(I8, I9, I10, I11) 
R = 
  f8(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
  f7(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
  f2(I4, I5, I6, I7) -> f7(I4, I5, 1 + I6, I7) [0 <= -1 - I6 + I7]
  f6(I8, I9, I10, I11) -> f2(I8, I9, I10, I11) 
  f2(I12, I13, I14, I15) -> f6(I12, I13, 1 + I14, I15) [I15 <= I14 /\ I14 <= I15 /\ -1 * I14 + I15 <= 0 /\ -1 * I14 + I15 <= 0]
  f4(I16, I17, I18, I19) -> f5(rnd1, I17, I18, I19) [rnd1 = rnd1]
  f3(I20, I21, I22, I23) -> f4(I20, I21, I22, I23) [I21 = I21]
  f2(I24, I25, I26, I27) -> f3(I24, I25, I26, I27) [-1 * I26 + I27 <= 0 /\ -1 * I26 + I27 <= 0]
  f1(I28, I29, I30, I31) -> f2(I28, I29, I30, I31) 

The dependency graph for this problem is:
  1 -> 
  3 -> 
Where:
  1) f7#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
  3) f6#(I8, I9, I10, I11) -> f2#(I8, I9, I10, I11) 

We have the following SCCs.