2.57/2.81	MAYBE
2.57/2.81	
2.57/2.81	DP problem for innermost termination.
2.57/2.81	P =
2.57/2.81	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
2.57/2.81	  f2#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0]
2.57/2.81	  f2#(I8, I9, I10, I11) -> f2#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8]
2.57/2.81	  f5#(I16, I17, I18, I19) -> f5#(I20, I21, I18 - 1, I19 + 1) [0 <= I18 - 1 /\ 0 <= y1 - 1 /\ -1 <= I19 - 1 /\ I20 - 2 <= I16 /\ I20 - 2 <= I17 /\ I21 - 2 <= I16 /\ I21 - 2 <= I17 /\ 2 <= I16 - 1 /\ 2 <= I17 - 1 /\ 4 <= I20 - 1 /\ 4 <= I21 - 1]
2.57/2.81	  f5#(I22, I23, I24, I25) -> f5#(I26, I27, I24 - 1, I25 + 1) [4 <= I27 - 1 /\ 4 <= I26 - 1 /\ 2 <= I23 - 1 /\ 2 <= I22 - 1 /\ I27 - 2 <= I23 /\ I27 - 2 <= I22 /\ I26 - 2 <= I23 /\ I26 - 2 <= I22 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1]
2.57/2.81	  f5#(I28, I29, I30, I31) -> f5#(I32, I33, I30 - 1, I31 + 1) [2 <= I33 - 1 /\ 2 <= I32 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1]
2.57/2.81	  f5#(I34, I35, I36, I37) -> f5#(I38, I39, I36 - 1, I37 + 1) [0 <= I36 - 1 /\ 0 <= I40 - 1 /\ -1 <= I37 - 1 /\ 2 <= I34 - 1 /\ 1 <= I35 - 1 /\ 2 <= I38 - 1 /\ 2 <= I39 - 1]
2.57/2.81	  f5#(I41, I42, I43, I44) -> f5#(I45, I46, I43 - 1, I44 + 1) [0 <= I43 - 1 /\ 0 <= I47 - 1 /\ -1 <= I44 - 1 /\ I45 <= I41 /\ I46 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I45 - 1 /\ 0 <= I46 - 1]
2.57/2.81	  f5#(I48, I49, I50, I51) -> f5#(I52, I53, I50 - 1, I51 + 1) [0 <= I53 - 1 /\ 2 <= I52 - 1 /\ 2 <= I49 - 1 /\ 2 <= I48 - 1 /\ I53 + 2 <= I49 /\ I52 <= I48 /\ 0 <= I50 - 1 /\ -1 <= I51 - 1]
2.57/2.81	  f1#(I54, I55, I56, I57) -> f5#(I58, I59, I60, 1) [2 <= I59 - 1 /\ 2 <= I58 - 1 /\ 0 <= I54 - 1 /\ I59 - 2 <= I54 /\ I58 - 2 <= I54 /\ -1 <= I55 - 1 /\ 0 <= I60 - 1]
2.57/2.81	  f3#(I61, I62, I63, I64) -> f2#(I65, I66, I67, I68) [I65 <= I62 /\ 0 <= I69 - 1 /\ 0 <= I61 - 1 /\ 2 <= I62 - 1 /\ 2 <= I65 - 1 /\ I63 + 2 <= I62]
2.57/2.81	  f4#(I70, I71, I72, I73) -> f3#(I74, I75, I72, I76) [I72 + 2 <= I71 /\ 2 <= I75 - 1 /\ 0 <= I74 - 1 /\ 2 <= I71 - 1 /\ 0 <= I70 - 1 /\ I75 <= I71 /\ I74 + 2 <= I71 /\ I74 <= I70]
2.57/2.81	  f1#(I77, I78, I79, I80) -> f3#(I81, I82, I83, I84) [2 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I77 - 1 /\ I81 <= I77]
2.57/2.81	  f1#(I85, I86, I87, I88) -> f2#(I89, I90, I91, I92) [-1 <= I89 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I89 + 1 <= I85]
2.57/2.81	R = 
2.57/2.81	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
2.57/2.81	  f2(I0, I1, I2, I3) -> f2(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0]
2.57/2.81	  f2(I8, I9, I10, I11) -> f2(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8]
2.57/2.81	  f5(I16, I17, I18, I19) -> f5(I20, I21, I18 - 1, I19 + 1) [0 <= I18 - 1 /\ 0 <= y1 - 1 /\ -1 <= I19 - 1 /\ I20 - 2 <= I16 /\ I20 - 2 <= I17 /\ I21 - 2 <= I16 /\ I21 - 2 <= I17 /\ 2 <= I16 - 1 /\ 2 <= I17 - 1 /\ 4 <= I20 - 1 /\ 4 <= I21 - 1]
2.57/2.81	  f5(I22, I23, I24, I25) -> f5(I26, I27, I24 - 1, I25 + 1) [4 <= I27 - 1 /\ 4 <= I26 - 1 /\ 2 <= I23 - 1 /\ 2 <= I22 - 1 /\ I27 - 2 <= I23 /\ I27 - 2 <= I22 /\ I26 - 2 <= I23 /\ I26 - 2 <= I22 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1]
2.57/2.81	  f5(I28, I29, I30, I31) -> f5(I32, I33, I30 - 1, I31 + 1) [2 <= I33 - 1 /\ 2 <= I32 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1]
2.57/2.81	  f5(I34, I35, I36, I37) -> f5(I38, I39, I36 - 1, I37 + 1) [0 <= I36 - 1 /\ 0 <= I40 - 1 /\ -1 <= I37 - 1 /\ 2 <= I34 - 1 /\ 1 <= I35 - 1 /\ 2 <= I38 - 1 /\ 2 <= I39 - 1]
2.57/2.81	  f5(I41, I42, I43, I44) -> f5(I45, I46, I43 - 1, I44 + 1) [0 <= I43 - 1 /\ 0 <= I47 - 1 /\ -1 <= I44 - 1 /\ I45 <= I41 /\ I46 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I45 - 1 /\ 0 <= I46 - 1]
2.57/2.81	  f5(I48, I49, I50, I51) -> f5(I52, I53, I50 - 1, I51 + 1) [0 <= I53 - 1 /\ 2 <= I52 - 1 /\ 2 <= I49 - 1 /\ 2 <= I48 - 1 /\ I53 + 2 <= I49 /\ I52 <= I48 /\ 0 <= I50 - 1 /\ -1 <= I51 - 1]
2.57/2.81	  f1(I54, I55, I56, I57) -> f5(I58, I59, I60, 1) [2 <= I59 - 1 /\ 2 <= I58 - 1 /\ 0 <= I54 - 1 /\ I59 - 2 <= I54 /\ I58 - 2 <= I54 /\ -1 <= I55 - 1 /\ 0 <= I60 - 1]
2.57/2.81	  f3(I61, I62, I63, I64) -> f2(I65, I66, I67, I68) [I65 <= I62 /\ 0 <= I69 - 1 /\ 0 <= I61 - 1 /\ 2 <= I62 - 1 /\ 2 <= I65 - 1 /\ I63 + 2 <= I62]
2.57/2.81	  f4(I70, I71, I72, I73) -> f3(I74, I75, I72, I76) [I72 + 2 <= I71 /\ 2 <= I75 - 1 /\ 0 <= I74 - 1 /\ 2 <= I71 - 1 /\ 0 <= I70 - 1 /\ I75 <= I71 /\ I74 + 2 <= I71 /\ I74 <= I70]
2.57/2.81	  f1(I77, I78, I79, I80) -> f3(I81, I82, I83, I84) [2 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I77 - 1 /\ I81 <= I77]
2.57/2.81	  f1(I85, I86, I87, I88) -> f2(I89, I90, I91, I92) [-1 <= I89 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I89 + 1 <= I85]
2.57/2.81	
2.57/2.81	The dependency graph for this problem is:
2.57/2.81	  0 -> 9, 12, 13
2.57/2.81	  1 -> 1, 2
2.57/2.81	  2 -> 1, 2
2.57/2.81	  3 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  4 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  5 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  6 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  7 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  8 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  9 -> 3, 4, 5, 6, 7, 8
2.57/2.81	  10 -> 1, 2
2.57/2.81	  11 -> 10
2.57/2.81	  12 -> 10
2.57/2.81	  13 -> 1, 2
2.57/2.81	Where:
2.57/2.81	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
2.57/2.81	  1) f2#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0]
2.57/2.81	  2) f2#(I8, I9, I10, I11) -> f2#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8]
2.57/2.81	  3) f5#(I16, I17, I18, I19) -> f5#(I20, I21, I18 - 1, I19 + 1) [0 <= I18 - 1 /\ 0 <= y1 - 1 /\ -1 <= I19 - 1 /\ I20 - 2 <= I16 /\ I20 - 2 <= I17 /\ I21 - 2 <= I16 /\ I21 - 2 <= I17 /\ 2 <= I16 - 1 /\ 2 <= I17 - 1 /\ 4 <= I20 - 1 /\ 4 <= I21 - 1]
2.57/2.81	  4) f5#(I22, I23, I24, I25) -> f5#(I26, I27, I24 - 1, I25 + 1) [4 <= I27 - 1 /\ 4 <= I26 - 1 /\ 2 <= I23 - 1 /\ 2 <= I22 - 1 /\ I27 - 2 <= I23 /\ I27 - 2 <= I22 /\ I26 - 2 <= I23 /\ I26 - 2 <= I22 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1]
2.57/2.81	  5) f5#(I28, I29, I30, I31) -> f5#(I32, I33, I30 - 1, I31 + 1) [2 <= I33 - 1 /\ 2 <= I32 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1]
2.57/2.81	  6) f5#(I34, I35, I36, I37) -> f5#(I38, I39, I36 - 1, I37 + 1) [0 <= I36 - 1 /\ 0 <= I40 - 1 /\ -1 <= I37 - 1 /\ 2 <= I34 - 1 /\ 1 <= I35 - 1 /\ 2 <= I38 - 1 /\ 2 <= I39 - 1]
2.57/2.81	  7) f5#(I41, I42, I43, I44) -> f5#(I45, I46, I43 - 1, I44 + 1) [0 <= I43 - 1 /\ 0 <= I47 - 1 /\ -1 <= I44 - 1 /\ I45 <= I41 /\ I46 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I45 - 1 /\ 0 <= I46 - 1]
2.57/2.81	  8) f5#(I48, I49, I50, I51) -> f5#(I52, I53, I50 - 1, I51 + 1) [0 <= I53 - 1 /\ 2 <= I52 - 1 /\ 2 <= I49 - 1 /\ 2 <= I48 - 1 /\ I53 + 2 <= I49 /\ I52 <= I48 /\ 0 <= I50 - 1 /\ -1 <= I51 - 1]
2.57/2.81	  9) f1#(I54, I55, I56, I57) -> f5#(I58, I59, I60, 1) [2 <= I59 - 1 /\ 2 <= I58 - 1 /\ 0 <= I54 - 1 /\ I59 - 2 <= I54 /\ I58 - 2 <= I54 /\ -1 <= I55 - 1 /\ 0 <= I60 - 1]
2.57/2.81	  10) f3#(I61, I62, I63, I64) -> f2#(I65, I66, I67, I68) [I65 <= I62 /\ 0 <= I69 - 1 /\ 0 <= I61 - 1 /\ 2 <= I62 - 1 /\ 2 <= I65 - 1 /\ I63 + 2 <= I62]
2.57/2.81	  11) f4#(I70, I71, I72, I73) -> f3#(I74, I75, I72, I76) [I72 + 2 <= I71 /\ 2 <= I75 - 1 /\ 0 <= I74 - 1 /\ 2 <= I71 - 1 /\ 0 <= I70 - 1 /\ I75 <= I71 /\ I74 + 2 <= I71 /\ I74 <= I70]
2.57/2.81	  12) f1#(I77, I78, I79, I80) -> f3#(I81, I82, I83, I84) [2 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I77 - 1 /\ I81 <= I77]
2.57/2.81	  13) f1#(I85, I86, I87, I88) -> f2#(I89, I90, I91, I92) [-1 <= I89 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I89 + 1 <= I85]
2.57/2.81	
2.57/2.81	We have the following SCCs.
2.57/2.81	  { 3, 4, 5, 6, 7, 8 }
2.57/2.81	  { 1, 2 }
2.57/2.81	
2.57/2.81	DP problem for innermost termination.
2.57/2.81	P =
2.57/2.81	  f2#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0]
2.57/2.81	  f2#(I8, I9, I10, I11) -> f2#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8]
2.57/2.81	R = 
2.57/2.81	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
2.57/2.81	  f2(I0, I1, I2, I3) -> f2(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0]
2.57/2.81	  f2(I8, I9, I10, I11) -> f2(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8]
2.57/2.81	  f5(I16, I17, I18, I19) -> f5(I20, I21, I18 - 1, I19 + 1) [0 <= I18 - 1 /\ 0 <= y1 - 1 /\ -1 <= I19 - 1 /\ I20 - 2 <= I16 /\ I20 - 2 <= I17 /\ I21 - 2 <= I16 /\ I21 - 2 <= I17 /\ 2 <= I16 - 1 /\ 2 <= I17 - 1 /\ 4 <= I20 - 1 /\ 4 <= I21 - 1]
2.57/2.81	  f5(I22, I23, I24, I25) -> f5(I26, I27, I24 - 1, I25 + 1) [4 <= I27 - 1 /\ 4 <= I26 - 1 /\ 2 <= I23 - 1 /\ 2 <= I22 - 1 /\ I27 - 2 <= I23 /\ I27 - 2 <= I22 /\ I26 - 2 <= I23 /\ I26 - 2 <= I22 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1]
2.57/2.81	  f5(I28, I29, I30, I31) -> f5(I32, I33, I30 - 1, I31 + 1) [2 <= I33 - 1 /\ 2 <= I32 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1]
2.57/2.81	  f5(I34, I35, I36, I37) -> f5(I38, I39, I36 - 1, I37 + 1) [0 <= I36 - 1 /\ 0 <= I40 - 1 /\ -1 <= I37 - 1 /\ 2 <= I34 - 1 /\ 1 <= I35 - 1 /\ 2 <= I38 - 1 /\ 2 <= I39 - 1]
2.57/2.81	  f5(I41, I42, I43, I44) -> f5(I45, I46, I43 - 1, I44 + 1) [0 <= I43 - 1 /\ 0 <= I47 - 1 /\ -1 <= I44 - 1 /\ I45 <= I41 /\ I46 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I45 - 1 /\ 0 <= I46 - 1]
2.57/2.81	  f5(I48, I49, I50, I51) -> f5(I52, I53, I50 - 1, I51 + 1) [0 <= I53 - 1 /\ 2 <= I52 - 1 /\ 2 <= I49 - 1 /\ 2 <= I48 - 1 /\ I53 + 2 <= I49 /\ I52 <= I48 /\ 0 <= I50 - 1 /\ -1 <= I51 - 1]
2.57/2.81	  f1(I54, I55, I56, I57) -> f5(I58, I59, I60, 1) [2 <= I59 - 1 /\ 2 <= I58 - 1 /\ 0 <= I54 - 1 /\ I59 - 2 <= I54 /\ I58 - 2 <= I54 /\ -1 <= I55 - 1 /\ 0 <= I60 - 1]
2.57/2.81	  f3(I61, I62, I63, I64) -> f2(I65, I66, I67, I68) [I65 <= I62 /\ 0 <= I69 - 1 /\ 0 <= I61 - 1 /\ 2 <= I62 - 1 /\ 2 <= I65 - 1 /\ I63 + 2 <= I62]
2.57/2.81	  f4(I70, I71, I72, I73) -> f3(I74, I75, I72, I76) [I72 + 2 <= I71 /\ 2 <= I75 - 1 /\ 0 <= I74 - 1 /\ 2 <= I71 - 1 /\ 0 <= I70 - 1 /\ I75 <= I71 /\ I74 + 2 <= I71 /\ I74 <= I70]
2.57/2.81	  f1(I77, I78, I79, I80) -> f3(I81, I82, I83, I84) [2 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I77 - 1 /\ I81 <= I77]
2.57/2.81	  f1(I85, I86, I87, I88) -> f2(I89, I90, I91, I92) [-1 <= I89 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I89 + 1 <= I85]
2.57/2.81	
2.70/5.78	EOF