/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 =
  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  f15#(I0, I1, I2) -> f15#(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14#(I5, I6, I7) -> f15#(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14#(I10, I11, I12) -> f14#(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13#(I13, I14, I15) -> f14#(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13#(I16, I17, I18) -> f13#(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12#(I19, I20, I21) -> f13#(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12#(I22, I23, I24) -> f12#(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11#(I25, I26, I27) -> f12#(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11#(I28, I29, I30) -> f11#(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10#(I31, I32, I33) -> f11#(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10#(I34, I35, I36) -> f10#(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9#(I37, I38, I39) -> f10#(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9#(I40, I41, I42) -> f9#(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8#(I43, I44, I45) -> f9#(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8#(I46, I47, I48) -> f8#(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7#(I49, I50, I51) -> f8#(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7#(I52, I53, I54) -> f7#(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6#(I55, I56, I57) -> f7#(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6#(I58, I59, I60) -> f6#(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5#(I61, I62, I63) -> f6#(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5#(I64, I65, I66) -> f5#(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4#(I67, I68, I69) -> f5#(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4#(I70, I71, I72) -> f4#(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3#(I73, I74, I75) -> f4#(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3#(I79, I80, I81) -> f2#(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2#(I84, I85, I86) -> f3#(I84, I84, I84) 
  f1#(I87, I88, I89) -> f2#(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

The dependency graph for this problem is:
  0 -> 28
  1 -> 1
  2 -> 1
  3 -> 2, 3
  4 -> 2, 3
  5 -> 4, 5
  6 -> 4, 5
  7 -> 6, 7
  8 -> 6, 7
  9 -> 8, 9
  10 -> 8, 9
  11 -> 10, 11
  12 -> 10, 11
  13 -> 12, 13
  14 -> 12, 13
  15 -> 14, 15
  16 -> 14, 15
  17 -> 16, 17
  18 -> 16, 17
  19 -> 18, 19
  20 -> 18, 19
  21 -> 20, 21
  22 -> 20, 21
  23 -> 22, 23
  24 -> 23
  25 -> 24, 25, 26
  26 -> 27
  27 -> 24, 25, 26
  28 -> 27
Where:
  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
  1) f15#(I0, I1, I2) -> f15#(I0 - 1, I3, I4) [0 <= I0 - 1]
  2) f14#(I5, I6, I7) -> f15#(I5, I8, I9) [0 = I7 /\ 0 = I6]
  3) f14#(I10, I11, I12) -> f14#(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  4) f13#(I13, I14, I15) -> f14#(I13, I13, I13) [0 = I15 /\ 0 = I14]
  5) f13#(I16, I17, I18) -> f13#(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  6) f12#(I19, I20, I21) -> f13#(I19, I19, I19) [0 = I21 /\ 0 = I20]
  7) f12#(I22, I23, I24) -> f12#(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  8) f11#(I25, I26, I27) -> f12#(I25, I25, I25) [0 = I27 /\ 0 = I26]
  9) f11#(I28, I29, I30) -> f11#(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  10) f10#(I31, I32, I33) -> f11#(I31, I31, I31) [0 = I33 /\ 0 = I32]
  11) f10#(I34, I35, I36) -> f10#(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  12) f9#(I37, I38, I39) -> f10#(I37, I37, I37) [0 = I39 /\ 0 = I38]
  13) f9#(I40, I41, I42) -> f9#(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  14) f8#(I43, I44, I45) -> f9#(I43, I43, I43) [0 = I45 /\ 0 = I44]
  15) f8#(I46, I47, I48) -> f8#(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  16) f7#(I49, I50, I51) -> f8#(I49, I49, I49) [0 = I51 /\ 0 = I50]
  17) f7#(I52, I53, I54) -> f7#(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  18) f6#(I55, I56, I57) -> f7#(I55, I55, I55) [0 = I57 /\ 0 = I56]
  19) f6#(I58, I59, I60) -> f6#(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  20) f5#(I61, I62, I63) -> f6#(I61, I61, I61) [0 = I63 /\ 0 = I62]
  21) f5#(I64, I65, I66) -> f5#(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  22) f4#(I67, I68, I69) -> f5#(I67, I67, I67) [0 = I69 /\ 0 = I68]
  23) f4#(I70, I71, I72) -> f4#(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  24) f3#(I73, I74, I75) -> f4#(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  25) f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  26) f3#(I79, I80, I81) -> f2#(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  27) f2#(I84, I85, I86) -> f3#(I84, I84, I84) 
  28) f1#(I87, I88, I89) -> f2#(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We have the following SCCs.
  { 25, 26, 27 }
  { 23 }
  { 21 }
  { 19 }
  { 17 }
  { 15 }
  { 13 }
  { 11 }
  { 9 }
  { 7 }
  { 5 }
  { 3 }
  { 1 }

DP problem for innermost termination.
P =
  f15#(I0, I1, I2) -> f15#(I0 - 1, I3, I4) [0 <= I0 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f15#(z1,z2,z3)] = z1

This gives the following inequalities:
  0 <= I0 - 1  ==>  I0 >! I0 - 1

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

DP problem for innermost termination.
P =
  f14#(I10, I11, I12) -> f14#(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f14#(z1,z2,z3)] = z3

This gives the following inequalities:
  I11 = I12 /\ 0 <= I11 - 1  ==>  I12 >! I11 - 1

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

DP problem for innermost termination.
P =
  f13#(I16, I17, I18) -> f13#(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f13#(z1,z2,z3)] = z3

This gives the following inequalities:
  I17 = I18 /\ 0 <= I17 - 1  ==>  I18 >! I17 - 1

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

DP problem for innermost termination.
P =
  f12#(I22, I23, I24) -> f12#(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f12#(z1,z2,z3)] = z3

This gives the following inequalities:
  I23 = I24 /\ 0 <= I23 - 1  ==>  I24 >! I23 - 1

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

DP problem for innermost termination.
P =
  f11#(I28, I29, I30) -> f11#(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f11#(z1,z2,z3)] = z3

This gives the following inequalities:
  I29 = I30 /\ 0 <= I29 - 1  ==>  I30 >! I29 - 1

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

DP problem for innermost termination.
P =
  f10#(I34, I35, I36) -> f10#(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f10#(z1,z2,z3)] = z3

This gives the following inequalities:
  I35 = I36 /\ 0 <= I35 - 1  ==>  I36 >! I35 - 1

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

DP problem for innermost termination.
P =
  f9#(I40, I41, I42) -> f9#(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f9#(z1,z2,z3)] = z3

This gives the following inequalities:
  I41 = I42 /\ 0 <= I41 - 1  ==>  I42 >! I41 - 1

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

DP problem for innermost termination.
P =
  f8#(I46, I47, I48) -> f8#(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f8#(z1,z2,z3)] = z3

This gives the following inequalities:
  I47 = I48 /\ 0 <= I47 - 1  ==>  I48 >! I47 - 1

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

DP problem for innermost termination.
P =
  f7#(I52, I53, I54) -> f7#(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f7#(z1,z2,z3)] = z3

This gives the following inequalities:
  I53 = I54 /\ 0 <= I53 - 1  ==>  I54 >! I53 - 1

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

DP problem for innermost termination.
P =
  f6#(I58, I59, I60) -> f6#(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f6#(z1,z2,z3)] = z3

This gives the following inequalities:
  I59 = I60 /\ 0 <= I59 - 1  ==>  I60 >! I59 - 1

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

DP problem for innermost termination.
P =
  f5#(I64, I65, I66) -> f5#(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f5#(z1,z2,z3)] = z3

This gives the following inequalities:
  I65 = I66 /\ 0 <= I65 - 1  ==>  I66 >! I65 - 1

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

DP problem for innermost termination.
P =
  f4#(I70, I71, I72) -> f4#(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f4#(z1,z2,z3)] = z3

This gives the following inequalities:
  I71 = I72 /\ 0 <= I71 - 1  ==>  I72 >! I71 - 1

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

DP problem for innermost termination.
P =
  f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3#(I79, I80, I81) -> f2#(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2#(I84, I85, I86) -> f3#(I84, I84, I84) 
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the basic value criterion with the projection function NU:
  NU[f2#(z1,z2,z3)] = z1
  NU[f3#(z1,z2,z3)] = z1

This gives the following inequalities:
  I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1  ==>  I76 (>! \union =) I76
  I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1  ==>  I79 >! I79 - 1
    ==>  I84 (>! \union =) I84

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f2#(I84, I85, I86) -> f3#(I84, I84, I84) 
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

The dependency graph for this problem is:
  25 -> 25
  27 -> 25
Where:
  25) f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  27) f2#(I84, I85, I86) -> f3#(I84, I84, I84) 

We have the following SCCs.
  { 25 }

DP problem for innermost termination.
P =
  f3#(I76, I77, I78) -> f3#(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
R = 
  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
  f15(I0, I1, I2) -> f15(I0 - 1, I3, I4) [0 <= I0 - 1]
  f14(I5, I6, I7) -> f15(I5, I8, I9) [0 = I7 /\ 0 = I6]
  f14(I10, I11, I12) -> f14(I10, I11 - 1, I11 - 1) [I11 = I12 /\ 0 <= I11 - 1]
  f13(I13, I14, I15) -> f14(I13, I13, I13) [0 = I15 /\ 0 = I14]
  f13(I16, I17, I18) -> f13(I16, I17 - 1, I17 - 1) [I17 = I18 /\ 0 <= I17 - 1]
  f12(I19, I20, I21) -> f13(I19, I19, I19) [0 = I21 /\ 0 = I20]
  f12(I22, I23, I24) -> f12(I22, I23 - 1, I23 - 1) [I23 = I24 /\ 0 <= I23 - 1]
  f11(I25, I26, I27) -> f12(I25, I25, I25) [0 = I27 /\ 0 = I26]
  f11(I28, I29, I30) -> f11(I28, I29 - 1, I29 - 1) [I29 = I30 /\ 0 <= I29 - 1]
  f10(I31, I32, I33) -> f11(I31, I31, I31) [0 = I33 /\ 0 = I32]
  f10(I34, I35, I36) -> f10(I34, I35 - 1, I35 - 1) [I35 = I36 /\ 0 <= I35 - 1]
  f9(I37, I38, I39) -> f10(I37, I37, I37) [0 = I39 /\ 0 = I38]
  f9(I40, I41, I42) -> f9(I40, I41 - 1, I41 - 1) [I41 = I42 /\ 0 <= I41 - 1]
  f8(I43, I44, I45) -> f9(I43, I43, I43) [0 = I45 /\ 0 = I44]
  f8(I46, I47, I48) -> f8(I46, I47 - 1, I47 - 1) [I47 = I48 /\ 0 <= I47 - 1]
  f7(I49, I50, I51) -> f8(I49, I49, I49) [0 = I51 /\ 0 = I50]
  f7(I52, I53, I54) -> f7(I52, I53 - 1, I53 - 1) [I53 = I54 /\ 0 <= I53 - 1]
  f6(I55, I56, I57) -> f7(I55, I55, I55) [0 = I57 /\ 0 = I56]
  f6(I58, I59, I60) -> f6(I58, I59 - 1, I59 - 1) [I59 = I60 /\ 0 <= I59 - 1]
  f5(I61, I62, I63) -> f6(I61, I61, I61) [0 = I63 /\ 0 = I62]
  f5(I64, I65, I66) -> f5(I64, I65 - 1, I65 - 1) [I65 = I66 /\ 0 <= I65 - 1]
  f4(I67, I68, I69) -> f5(I67, I67, I67) [0 = I69 /\ 0 = I68]
  f4(I70, I71, I72) -> f4(I70, I71 - 1, I71 - 1) [I71 = I72 /\ 0 <= I71 - 1]
  f3(I73, I74, I75) -> f4(I74, I74, I74) [I74 = I75 /\ I74 <= 99 /\ 0 <= I74 - 1]
  f3(I76, I77, I78) -> f3(I76, I77 + 1, I77 + 1) [I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1]
  f3(I79, I80, I81) -> f2(I79 - 1, I82, I83) [I80 = I81 /\ 99 <= I80 - 1 /\ 0 <= I79 - 1]
  f2(I84, I85, I86) -> f3(I84, I84, I84) 
  f1(I87, I88, I89) -> f2(I88, I90, I91) [-1 <= I88 - 1 /\ 0 <= I87 - 1]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3)] = 99 + -1 * z2

This gives the following inequalities:
  I77 = I78 /\ I77 <= 99 /\ 0 <= I77 - 1  ==>  99 + -1 * I77 > 99 + -1 * (I77 + 1)  with  99 + -1 * I77 >= 0

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