MAYBE

DP problem for innermost termination.
P =
  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  f3#(I0, I1, I2) -> f3#(I3, I4, I5) [-1 <= I3 - 1 /\ 0 <= I0 - 1]
  f2#(I6, I7, I8) -> f3#(I9, I10, I11) [2 <= I9 - 1 /\ 1 <= I7 - 1 /\ I8 <= 0 /\ I9 - 1 <= I7]
  f2#(I12, I13, I14) -> f3#(I15, I16, I17) [0 <= I15 - 1 /\ I14 <= 0 /\ 0 <= I13 - 1]
  f2#(I18, I19, I20) -> f2#(I18 - 1, I21, I18) [2 <= I21 - 1 /\ 0 <= I19 - 1 /\ 0 <= I20 - 1 /\ I21 - 2 <= I19]
  f1#(I22, I23, I24) -> f2#(I23 - 1, I25, I23) [1 <= I25 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ I25 - 1 <= I22]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f3(I0, I1, I2) -> f3(I3, I4, I5) [-1 <= I3 - 1 /\ 0 <= I0 - 1]
  f2(I6, I7, I8) -> f3(I9, I10, I11) [2 <= I9 - 1 /\ 1 <= I7 - 1 /\ I8 <= 0 /\ I9 - 1 <= I7]
  f2(I12, I13, I14) -> f3(I15, I16, I17) [0 <= I15 - 1 /\ I14 <= 0 /\ 0 <= I13 - 1]
  f2(I18, I19, I20) -> f2(I18 - 1, I21, I18) [2 <= I21 - 1 /\ 0 <= I19 - 1 /\ 0 <= I20 - 1 /\ I21 - 2 <= I19]
  f1(I22, I23, I24) -> f2(I23 - 1, I25, I23) [1 <= I25 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ I25 - 1 <= I22]

The dependency graph for this problem is:
  0 -> 5
  1 -> 1
  2 -> 1
  3 -> 1
  4 -> 2, 3, 4
  5 -> 2, 3, 4
Where:
  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  1) f3#(I0, I1, I2) -> f3#(I3, I4, I5) [-1 <= I3 - 1 /\ 0 <= I0 - 1]
  2) f2#(I6, I7, I8) -> f3#(I9, I10, I11) [2 <= I9 - 1 /\ 1 <= I7 - 1 /\ I8 <= 0 /\ I9 - 1 <= I7]
  3) f2#(I12, I13, I14) -> f3#(I15, I16, I17) [0 <= I15 - 1 /\ I14 <= 0 /\ 0 <= I13 - 1]
  4) f2#(I18, I19, I20) -> f2#(I18 - 1, I21, I18) [2 <= I21 - 1 /\ 0 <= I19 - 1 /\ 0 <= I20 - 1 /\ I21 - 2 <= I19]
  5) f1#(I22, I23, I24) -> f2#(I23 - 1, I25, I23) [1 <= I25 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ I25 - 1 <= I22]

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

DP problem for innermost termination.
P =
  f3#(I0, I1, I2) -> f3#(I3, I4, I5) [-1 <= I3 - 1 /\ 0 <= I0 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f3(I0, I1, I2) -> f3(I3, I4, I5) [-1 <= I3 - 1 /\ 0 <= I0 - 1]
  f2(I6, I7, I8) -> f3(I9, I10, I11) [2 <= I9 - 1 /\ 1 <= I7 - 1 /\ I8 <= 0 /\ I9 - 1 <= I7]
  f2(I12, I13, I14) -> f3(I15, I16, I17) [0 <= I15 - 1 /\ I14 <= 0 /\ 0 <= I13 - 1]
  f2(I18, I19, I20) -> f2(I18 - 1, I21, I18) [2 <= I21 - 1 /\ 0 <= I19 - 1 /\ 0 <= I20 - 1 /\ I21 - 2 <= I19]
  f1(I22, I23, I24) -> f2(I23 - 1, I25, I23) [1 <= I25 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ I25 - 1 <= I22]