3.55/3.93	MAYBE
3.55/3.93	
3.55/3.93	DP problem for innermost termination.
3.55/3.93	P =
3.55/3.93	  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
3.55/3.93	  f7#(I0, I1, I2) -> f6#(1, I1 + 1, I0) [0 = I2]
3.55/3.93	  f7#(I3, I4, I5) -> f6#(0, I4 + 1, I3) [1 = I5]
3.55/3.93	  f6#(I6, I7, I8) -> f6#(0, I7 + 1, I8) [0 = I6 /\ I7 <= I8 - 1]
3.55/3.93	  f6#(I9, I10, I11) -> f7#(I11, I10, 0) [0 <= I11 - 1 /\ 0 <= y1 - 1 /\ 0 <= I9 - 1 /\ I10 <= y1 - 1 /\ I10 <= I11 - 1]
3.55/3.93	  f6#(I12, I13, I14) -> f7#(I14, I13, 1) [0 <= I14 - 1 /\ 0 <= I15 - 1 /\ 0 <= I12 - 1 /\ I13 <= I15 - 1 /\ I13 <= I14 - 1]
3.55/3.93	  f3#(I16, I17, I18) -> f6#(1, 0, I16) [I17 <= I19 - 1 /\ 0 <= I19 - 1]
3.55/3.93	  f5#(I20, I21, I22) -> f5#(I20, I21 + 1, I23) [I21 <= I24 - 1 /\ I20 <= I24 - 1]
3.55/3.93	  f5#(I25, I26, I27) -> f5#(I25, I26 + 1, I28) [I26 <= I29 - 1 /\ I26 <= y2 - 1 /\ I25 <= y2 - 1]
3.55/3.93	  f5#(I30, I31, I32) -> f5#(I30, I31 + 1, I33) [I34 <= I31 - 1 /\ I31 <= I35 - 1 /\ I30 <= I35 - 1]
3.55/3.93	  f5#(I36, I37, I38) -> f4#(I36 + 1, I39, I40) [I41 <= I37]
3.55/3.93	  f4#(I42, I43, I44) -> f5#(I42, 0, I45) [I42 <= I46 - 1]
3.55/3.93	  f2#(I47, I48, I49) -> f4#(0, I50, I51) [I52 <= I47]
3.55/3.93	  f3#(I53, I54, I55) -> f3#(I53, I54 + 1, I56) [0 <= I57 - 1 /\ I54 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I53 - 1 /\ I53 <= I57 - 1 /\ I53 <= I53 + 1 - 1]
3.55/3.93	  f3#(I59, I60, I61) -> f2#(I59 + 1, I62, I63) [0 <= I64 - 1 /\ I60 <= I64 - 1 /\ 0 <= I65 - 1 /\ -1 <= I59 - 1 /\ I59 <= I64 - 1 /\ I59 <= I59 + 1 - 1]
3.55/3.93	  f3#(I66, I67, I68) -> f3#(I66, I67 + 1, I69) [I67 <= I70 - 1 /\ 0 <= I70 - 1]
3.55/3.93	  f2#(I71, I72, I73) -> f3#(I71, 0, I74) [I71 <= I75 - 1]
3.55/3.93	  f1#(I76, I77, I78) -> f2#(0, I79, I80) [-1 <= I77 - 1 /\ 0 <= I76 - 1]
3.55/3.93	R = 
3.55/3.93	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.55/3.93	  f7(I0, I1, I2) -> f6(1, I1 + 1, I0) [0 = I2]
3.55/3.93	  f7(I3, I4, I5) -> f6(0, I4 + 1, I3) [1 = I5]
3.55/3.93	  f6(I6, I7, I8) -> f6(0, I7 + 1, I8) [0 = I6 /\ I7 <= I8 - 1]
3.55/3.93	  f6(I9, I10, I11) -> f7(I11, I10, 0) [0 <= I11 - 1 /\ 0 <= y1 - 1 /\ 0 <= I9 - 1 /\ I10 <= y1 - 1 /\ I10 <= I11 - 1]
3.55/3.93	  f6(I12, I13, I14) -> f7(I14, I13, 1) [0 <= I14 - 1 /\ 0 <= I15 - 1 /\ 0 <= I12 - 1 /\ I13 <= I15 - 1 /\ I13 <= I14 - 1]
3.55/3.93	  f3(I16, I17, I18) -> f6(1, 0, I16) [I17 <= I19 - 1 /\ 0 <= I19 - 1]
3.55/3.93	  f5(I20, I21, I22) -> f5(I20, I21 + 1, I23) [I21 <= I24 - 1 /\ I20 <= I24 - 1]
3.55/3.93	  f5(I25, I26, I27) -> f5(I25, I26 + 1, I28) [I26 <= I29 - 1 /\ I26 <= y2 - 1 /\ I25 <= y2 - 1]
3.55/3.93	  f5(I30, I31, I32) -> f5(I30, I31 + 1, I33) [I34 <= I31 - 1 /\ I31 <= I35 - 1 /\ I30 <= I35 - 1]
3.55/3.93	  f5(I36, I37, I38) -> f4(I36 + 1, I39, I40) [I41 <= I37]
3.55/3.93	  f4(I42, I43, I44) -> f5(I42, 0, I45) [I42 <= I46 - 1]
3.55/3.93	  f2(I47, I48, I49) -> f4(0, I50, I51) [I52 <= I47]
3.55/3.93	  f3(I53, I54, I55) -> f3(I53, I54 + 1, I56) [0 <= I57 - 1 /\ I54 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I53 - 1 /\ I53 <= I57 - 1 /\ I53 <= I53 + 1 - 1]
3.55/3.93	  f3(I59, I60, I61) -> f2(I59 + 1, I62, I63) [0 <= I64 - 1 /\ I60 <= I64 - 1 /\ 0 <= I65 - 1 /\ -1 <= I59 - 1 /\ I59 <= I64 - 1 /\ I59 <= I59 + 1 - 1]
3.55/3.93	  f3(I66, I67, I68) -> f3(I66, I67 + 1, I69) [I67 <= I70 - 1 /\ 0 <= I70 - 1]
3.55/3.93	  f2(I71, I72, I73) -> f3(I71, 0, I74) [I71 <= I75 - 1]
3.55/3.93	  f1(I76, I77, I78) -> f2(0, I79, I80) [-1 <= I77 - 1 /\ 0 <= I76 - 1]
3.55/3.93	
3.55/3.93	The dependency graph for this problem is:
3.55/3.93	  0 -> 17
3.55/3.93	  1 -> 4, 5
3.55/3.93	  2 -> 3
3.55/3.93	  3 -> 3
3.55/3.93	  4 -> 1
3.55/3.93	  5 -> 2
3.55/3.93	  6 -> 4, 5
3.55/3.93	  7 -> 7, 8, 9, 10
3.55/3.93	  8 -> 7, 8, 9, 10
3.55/3.93	  9 -> 7, 8, 9, 10
3.55/3.93	  10 -> 11
3.55/3.93	  11 -> 7, 8, 9, 10
3.55/3.93	  12 -> 11
3.55/3.93	  13 -> 6, 13, 14, 15
3.55/3.93	  14 -> 12, 16
3.55/3.93	  15 -> 6, 13, 14, 15
3.55/3.93	  16 -> 6, 13, 14, 15
3.55/3.93	  17 -> 12, 16
3.55/3.93	Where:
3.55/3.93	  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
3.55/3.93	  1) f7#(I0, I1, I2) -> f6#(1, I1 + 1, I0) [0 = I2]
3.55/3.93	  2) f7#(I3, I4, I5) -> f6#(0, I4 + 1, I3) [1 = I5]
3.55/3.93	  3) f6#(I6, I7, I8) -> f6#(0, I7 + 1, I8) [0 = I6 /\ I7 <= I8 - 1]
3.55/3.93	  4) f6#(I9, I10, I11) -> f7#(I11, I10, 0) [0 <= I11 - 1 /\ 0 <= y1 - 1 /\ 0 <= I9 - 1 /\ I10 <= y1 - 1 /\ I10 <= I11 - 1]
3.55/3.93	  5) f6#(I12, I13, I14) -> f7#(I14, I13, 1) [0 <= I14 - 1 /\ 0 <= I15 - 1 /\ 0 <= I12 - 1 /\ I13 <= I15 - 1 /\ I13 <= I14 - 1]
3.55/3.93	  6) f3#(I16, I17, I18) -> f6#(1, 0, I16) [I17 <= I19 - 1 /\ 0 <= I19 - 1]
3.55/3.93	  7) f5#(I20, I21, I22) -> f5#(I20, I21 + 1, I23) [I21 <= I24 - 1 /\ I20 <= I24 - 1]
3.55/3.93	  8) f5#(I25, I26, I27) -> f5#(I25, I26 + 1, I28) [I26 <= I29 - 1 /\ I26 <= y2 - 1 /\ I25 <= y2 - 1]
3.55/3.93	  9) f5#(I30, I31, I32) -> f5#(I30, I31 + 1, I33) [I34 <= I31 - 1 /\ I31 <= I35 - 1 /\ I30 <= I35 - 1]
3.55/3.93	  10) f5#(I36, I37, I38) -> f4#(I36 + 1, I39, I40) [I41 <= I37]
3.55/3.93	  11) f4#(I42, I43, I44) -> f5#(I42, 0, I45) [I42 <= I46 - 1]
3.55/3.93	  12) f2#(I47, I48, I49) -> f4#(0, I50, I51) [I52 <= I47]
3.55/3.93	  13) f3#(I53, I54, I55) -> f3#(I53, I54 + 1, I56) [0 <= I57 - 1 /\ I54 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I53 - 1 /\ I53 <= I57 - 1 /\ I53 <= I53 + 1 - 1]
3.55/3.93	  14) f3#(I59, I60, I61) -> f2#(I59 + 1, I62, I63) [0 <= I64 - 1 /\ I60 <= I64 - 1 /\ 0 <= I65 - 1 /\ -1 <= I59 - 1 /\ I59 <= I64 - 1 /\ I59 <= I59 + 1 - 1]
3.55/3.93	  15) f3#(I66, I67, I68) -> f3#(I66, I67 + 1, I69) [I67 <= I70 - 1 /\ 0 <= I70 - 1]
3.55/3.93	  16) f2#(I71, I72, I73) -> f3#(I71, 0, I74) [I71 <= I75 - 1]
3.55/3.93	  17) f1#(I76, I77, I78) -> f2#(0, I79, I80) [-1 <= I77 - 1 /\ 0 <= I76 - 1]
3.55/3.93	
3.55/3.93	We have the following SCCs.
3.55/3.93	  { 13, 14, 15, 16 }
3.55/3.93	  { 1, 4 }
3.55/3.93	  { 3 }
3.55/3.93	  { 7, 8, 9, 10, 11 }
3.55/3.93	
3.55/3.93	DP problem for innermost termination.
3.55/3.93	P =
3.55/3.93	  f5#(I20, I21, I22) -> f5#(I20, I21 + 1, I23) [I21 <= I24 - 1 /\ I20 <= I24 - 1]
3.55/3.93	  f5#(I25, I26, I27) -> f5#(I25, I26 + 1, I28) [I26 <= I29 - 1 /\ I26 <= y2 - 1 /\ I25 <= y2 - 1]
3.55/3.93	  f5#(I30, I31, I32) -> f5#(I30, I31 + 1, I33) [I34 <= I31 - 1 /\ I31 <= I35 - 1 /\ I30 <= I35 - 1]
3.55/3.93	  f5#(I36, I37, I38) -> f4#(I36 + 1, I39, I40) [I41 <= I37]
3.55/3.93	  f4#(I42, I43, I44) -> f5#(I42, 0, I45) [I42 <= I46 - 1]
3.55/3.93	R = 
3.55/3.93	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.55/3.93	  f7(I0, I1, I2) -> f6(1, I1 + 1, I0) [0 = I2]
3.55/3.93	  f7(I3, I4, I5) -> f6(0, I4 + 1, I3) [1 = I5]
3.55/3.93	  f6(I6, I7, I8) -> f6(0, I7 + 1, I8) [0 = I6 /\ I7 <= I8 - 1]
3.55/3.93	  f6(I9, I10, I11) -> f7(I11, I10, 0) [0 <= I11 - 1 /\ 0 <= y1 - 1 /\ 0 <= I9 - 1 /\ I10 <= y1 - 1 /\ I10 <= I11 - 1]
3.55/3.93	  f6(I12, I13, I14) -> f7(I14, I13, 1) [0 <= I14 - 1 /\ 0 <= I15 - 1 /\ 0 <= I12 - 1 /\ I13 <= I15 - 1 /\ I13 <= I14 - 1]
3.55/3.93	  f3(I16, I17, I18) -> f6(1, 0, I16) [I17 <= I19 - 1 /\ 0 <= I19 - 1]
3.55/3.93	  f5(I20, I21, I22) -> f5(I20, I21 + 1, I23) [I21 <= I24 - 1 /\ I20 <= I24 - 1]
3.55/3.93	  f5(I25, I26, I27) -> f5(I25, I26 + 1, I28) [I26 <= I29 - 1 /\ I26 <= y2 - 1 /\ I25 <= y2 - 1]
3.55/3.93	  f5(I30, I31, I32) -> f5(I30, I31 + 1, I33) [I34 <= I31 - 1 /\ I31 <= I35 - 1 /\ I30 <= I35 - 1]
3.55/3.93	  f5(I36, I37, I38) -> f4(I36 + 1, I39, I40) [I41 <= I37]
3.55/3.93	  f4(I42, I43, I44) -> f5(I42, 0, I45) [I42 <= I46 - 1]
3.55/3.93	  f2(I47, I48, I49) -> f4(0, I50, I51) [I52 <= I47]
3.55/3.93	  f3(I53, I54, I55) -> f3(I53, I54 + 1, I56) [0 <= I57 - 1 /\ I54 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I53 - 1 /\ I53 <= I57 - 1 /\ I53 <= I53 + 1 - 1]
3.55/3.93	  f3(I59, I60, I61) -> f2(I59 + 1, I62, I63) [0 <= I64 - 1 /\ I60 <= I64 - 1 /\ 0 <= I65 - 1 /\ -1 <= I59 - 1 /\ I59 <= I64 - 1 /\ I59 <= I59 + 1 - 1]
3.55/3.93	  f3(I66, I67, I68) -> f3(I66, I67 + 1, I69) [I67 <= I70 - 1 /\ 0 <= I70 - 1]
3.55/3.93	  f2(I71, I72, I73) -> f3(I71, 0, I74) [I71 <= I75 - 1]
3.55/3.93	  f1(I76, I77, I78) -> f2(0, I79, I80) [-1 <= I77 - 1 /\ 0 <= I76 - 1]
3.55/3.93	
3.64/3.94	EOF