2.61/2.62	MAYBE
2.61/2.62	
2.61/2.62	DP problem for innermost termination.
2.61/2.62	P =
2.61/2.62	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
2.61/2.62	  f5#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [2 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 - 2 <= I1 /\ I5 - 2 <= I0 /\ I4 - 2 <= I1 /\ I4 - 2 <= I0]
2.61/2.62	  f5#(I8, I9, I10, I11) -> f5#(I12, I13, I14, I15) [-1 <= I13 - 1 /\ -1 <= I12 - 1 /\ 1 <= I9 - 1 /\ 1 <= I8 - 1 /\ I13 + 2 <= I9 /\ I13 + 2 <= I8 /\ I12 + 2 <= I9 /\ I12 + 2 <= I8]
2.61/2.62	  f2#(I16, I17, I18, I19) -> f5#(I20, I21, I22, I23) [I20 <= I17 /\ 0 <= y1 - 1 /\ I21 <= I17 /\ 0 <= I16 - 1 /\ 0 <= I17 - 1 /\ 0 <= I20 - 1 /\ 0 <= I21 - 1 /\ I18 + 2 <= I17]
2.61/2.62	  f1#(I24, I25, I26, I27) -> f5#(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I24 - 1 /\ I29 + 1 <= I24 /\ 0 <= I25 - 1 /\ I28 + 1 <= I24]
2.61/2.62	  f4#(I32, I33, I34, I35) -> f4#(I36, I37, I34 - 1, I35 + 1) [0 <= I34 - 1 /\ 0 <= I38 - 1 /\ -1 <= I35 - 1 /\ I36 - 2 <= I32 /\ I36 - 2 <= I33 /\ I37 - 2 <= I32 /\ I37 - 2 <= I33 /\ 1 <= I32 - 1 /\ 1 <= I33 - 1 /\ 3 <= I36 - 1 /\ 3 <= I37 - 1]
2.61/2.62	  f4#(I39, I40, I41, I42) -> f4#(I43, I44, I41 - 1, I42 + 1) [3 <= I44 - 1 /\ 3 <= I43 - 1 /\ 1 <= I40 - 1 /\ 1 <= I39 - 1 /\ I44 - 2 <= I40 /\ I44 - 2 <= I39 /\ I43 - 2 <= I40 /\ I43 - 2 <= I39 /\ 0 <= I41 - 1 /\ -1 <= I42 - 1]
2.61/2.62	  f4#(I45, I46, I47, I48) -> f4#(I49, I50, I47 - 1, I48 + 1) [0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 1 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I47 - 1 /\ -1 <= I48 - 1]
2.61/2.62	  f4#(I51, I52, I53, I54) -> f4#(I55, I56, I53 - 1, I54 + 1) [0 <= I53 - 1 /\ 0 <= I57 - 1 /\ -1 <= I54 - 1 /\ 0 <= I51 - 1 /\ 1 <= I52 - 1 /\ 0 <= I55 - 1 /\ 0 <= I56 - 1]
2.61/2.62	  f4#(I58, I59, I60, I61) -> f4#(I62, I63, I60 - 1, I61 + 1) [0 <= I60 - 1 /\ 0 <= I64 - 1 /\ -1 <= I61 - 1 /\ I62 <= I58 /\ I63 + 2 <= I59 /\ 0 <= I58 - 1 /\ 2 <= I59 - 1 /\ 0 <= I62 - 1 /\ 0 <= I63 - 1]
2.61/2.62	  f4#(I65, I66, I67, I68) -> f4#(I69, I70, I67 - 1, I68 + 1) [0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 2 <= I66 - 1 /\ 0 <= I65 - 1 /\ I70 + 2 <= I66 /\ I69 <= I65 /\ 0 <= I67 - 1 /\ -1 <= I68 - 1]
2.61/2.62	  f1#(I71, I72, I73, I74) -> f4#(I75, I76, I77, 1) [1 <= I76 - 1 /\ 1 <= I75 - 1 /\ 0 <= I71 - 1 /\ I76 - 1 <= I71 /\ I75 - 1 <= I71 /\ -1 <= I72 - 1 /\ 0 <= I77 - 1]
2.61/2.62	  f3#(I78, I79, I80, I81) -> f2#(I82, I83, I80, I84) [I80 + 2 <= I79 /\ 1 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ I83 <= I79 /\ I82 + 1 <= I79 /\ I82 <= I78]
2.61/2.62	  f1#(I85, I86, I87, I88) -> f2#(I89, I90, I91, I92) [0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 0 <= I85 - 1 /\ I89 <= I85]
2.61/2.62	R = 
2.61/2.62	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
2.61/2.62	  f5(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [2 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 - 2 <= I1 /\ I5 - 2 <= I0 /\ I4 - 2 <= I1 /\ I4 - 2 <= I0]
2.61/2.62	  f5(I8, I9, I10, I11) -> f5(I12, I13, I14, I15) [-1 <= I13 - 1 /\ -1 <= I12 - 1 /\ 1 <= I9 - 1 /\ 1 <= I8 - 1 /\ I13 + 2 <= I9 /\ I13 + 2 <= I8 /\ I12 + 2 <= I9 /\ I12 + 2 <= I8]
2.61/2.62	  f2(I16, I17, I18, I19) -> f5(I20, I21, I22, I23) [I20 <= I17 /\ 0 <= y1 - 1 /\ I21 <= I17 /\ 0 <= I16 - 1 /\ 0 <= I17 - 1 /\ 0 <= I20 - 1 /\ 0 <= I21 - 1 /\ I18 + 2 <= I17]
2.61/2.62	  f1(I24, I25, I26, I27) -> f5(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I24 - 1 /\ I29 + 1 <= I24 /\ 0 <= I25 - 1 /\ I28 + 1 <= I24]
2.61/2.62	  f4(I32, I33, I34, I35) -> f4(I36, I37, I34 - 1, I35 + 1) [0 <= I34 - 1 /\ 0 <= I38 - 1 /\ -1 <= I35 - 1 /\ I36 - 2 <= I32 /\ I36 - 2 <= I33 /\ I37 - 2 <= I32 /\ I37 - 2 <= I33 /\ 1 <= I32 - 1 /\ 1 <= I33 - 1 /\ 3 <= I36 - 1 /\ 3 <= I37 - 1]
2.61/2.62	  f4(I39, I40, I41, I42) -> f4(I43, I44, I41 - 1, I42 + 1) [3 <= I44 - 1 /\ 3 <= I43 - 1 /\ 1 <= I40 - 1 /\ 1 <= I39 - 1 /\ I44 - 2 <= I40 /\ I44 - 2 <= I39 /\ I43 - 2 <= I40 /\ I43 - 2 <= I39 /\ 0 <= I41 - 1 /\ -1 <= I42 - 1]
2.61/2.62	  f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48 + 1) [0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 1 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I47 - 1 /\ -1 <= I48 - 1]
2.61/2.62	  f4(I51, I52, I53, I54) -> f4(I55, I56, I53 - 1, I54 + 1) [0 <= I53 - 1 /\ 0 <= I57 - 1 /\ -1 <= I54 - 1 /\ 0 <= I51 - 1 /\ 1 <= I52 - 1 /\ 0 <= I55 - 1 /\ 0 <= I56 - 1]
2.61/2.62	  f4(I58, I59, I60, I61) -> f4(I62, I63, I60 - 1, I61 + 1) [0 <= I60 - 1 /\ 0 <= I64 - 1 /\ -1 <= I61 - 1 /\ I62 <= I58 /\ I63 + 2 <= I59 /\ 0 <= I58 - 1 /\ 2 <= I59 - 1 /\ 0 <= I62 - 1 /\ 0 <= I63 - 1]
2.61/2.62	  f4(I65, I66, I67, I68) -> f4(I69, I70, I67 - 1, I68 + 1) [0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 2 <= I66 - 1 /\ 0 <= I65 - 1 /\ I70 + 2 <= I66 /\ I69 <= I65 /\ 0 <= I67 - 1 /\ -1 <= I68 - 1]
2.61/2.62	  f1(I71, I72, I73, I74) -> f4(I75, I76, I77, 1) [1 <= I76 - 1 /\ 1 <= I75 - 1 /\ 0 <= I71 - 1 /\ I76 - 1 <= I71 /\ I75 - 1 <= I71 /\ -1 <= I72 - 1 /\ 0 <= I77 - 1]
2.61/2.62	  f3(I78, I79, I80, I81) -> f2(I82, I83, I80, I84) [I80 + 2 <= I79 /\ 1 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ I83 <= I79 /\ I82 + 1 <= I79 /\ I82 <= I78]
2.61/2.62	  f1(I85, I86, I87, I88) -> f2(I89, I90, I91, I92) [0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 0 <= I85 - 1 /\ I89 <= I85]
2.61/2.62	
2.61/2.62	The dependency graph for this problem is:
2.61/2.62	  0 -> 4, 11, 13
2.61/2.62	  1 -> 1, 2
2.61/2.62	  2 -> 1, 2
2.61/2.62	  3 -> 1, 2
2.61/2.62	  4 -> 1, 2
2.61/2.62	  5 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  6 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  7 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  8 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  9 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  10 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  11 -> 5, 6, 7, 8, 9, 10
2.61/2.62	  12 -> 3
2.61/2.62	  13 -> 3
2.61/2.62	Where:
2.61/2.62	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
2.61/2.62	  1) f5#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [2 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 - 2 <= I1 /\ I5 - 2 <= I0 /\ I4 - 2 <= I1 /\ I4 - 2 <= I0]
2.61/2.62	  2) f5#(I8, I9, I10, I11) -> f5#(I12, I13, I14, I15) [-1 <= I13 - 1 /\ -1 <= I12 - 1 /\ 1 <= I9 - 1 /\ 1 <= I8 - 1 /\ I13 + 2 <= I9 /\ I13 + 2 <= I8 /\ I12 + 2 <= I9 /\ I12 + 2 <= I8]
2.61/2.62	  3) f2#(I16, I17, I18, I19) -> f5#(I20, I21, I22, I23) [I20 <= I17 /\ 0 <= y1 - 1 /\ I21 <= I17 /\ 0 <= I16 - 1 /\ 0 <= I17 - 1 /\ 0 <= I20 - 1 /\ 0 <= I21 - 1 /\ I18 + 2 <= I17]
2.61/2.62	  4) f1#(I24, I25, I26, I27) -> f5#(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I24 - 1 /\ I29 + 1 <= I24 /\ 0 <= I25 - 1 /\ I28 + 1 <= I24]
2.61/2.62	  5) f4#(I32, I33, I34, I35) -> f4#(I36, I37, I34 - 1, I35 + 1) [0 <= I34 - 1 /\ 0 <= I38 - 1 /\ -1 <= I35 - 1 /\ I36 - 2 <= I32 /\ I36 - 2 <= I33 /\ I37 - 2 <= I32 /\ I37 - 2 <= I33 /\ 1 <= I32 - 1 /\ 1 <= I33 - 1 /\ 3 <= I36 - 1 /\ 3 <= I37 - 1]
2.61/2.62	  6) f4#(I39, I40, I41, I42) -> f4#(I43, I44, I41 - 1, I42 + 1) [3 <= I44 - 1 /\ 3 <= I43 - 1 /\ 1 <= I40 - 1 /\ 1 <= I39 - 1 /\ I44 - 2 <= I40 /\ I44 - 2 <= I39 /\ I43 - 2 <= I40 /\ I43 - 2 <= I39 /\ 0 <= I41 - 1 /\ -1 <= I42 - 1]
2.61/2.62	  7) f4#(I45, I46, I47, I48) -> f4#(I49, I50, I47 - 1, I48 + 1) [0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 1 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I47 - 1 /\ -1 <= I48 - 1]
2.61/2.62	  8) f4#(I51, I52, I53, I54) -> f4#(I55, I56, I53 - 1, I54 + 1) [0 <= I53 - 1 /\ 0 <= I57 - 1 /\ -1 <= I54 - 1 /\ 0 <= I51 - 1 /\ 1 <= I52 - 1 /\ 0 <= I55 - 1 /\ 0 <= I56 - 1]
2.61/2.62	  9) f4#(I58, I59, I60, I61) -> f4#(I62, I63, I60 - 1, I61 + 1) [0 <= I60 - 1 /\ 0 <= I64 - 1 /\ -1 <= I61 - 1 /\ I62 <= I58 /\ I63 + 2 <= I59 /\ 0 <= I58 - 1 /\ 2 <= I59 - 1 /\ 0 <= I62 - 1 /\ 0 <= I63 - 1]
2.61/2.62	  10) f4#(I65, I66, I67, I68) -> f4#(I69, I70, I67 - 1, I68 + 1) [0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 2 <= I66 - 1 /\ 0 <= I65 - 1 /\ I70 + 2 <= I66 /\ I69 <= I65 /\ 0 <= I67 - 1 /\ -1 <= I68 - 1]
2.61/2.62	  11) f1#(I71, I72, I73, I74) -> f4#(I75, I76, I77, 1) [1 <= I76 - 1 /\ 1 <= I75 - 1 /\ 0 <= I71 - 1 /\ I76 - 1 <= I71 /\ I75 - 1 <= I71 /\ -1 <= I72 - 1 /\ 0 <= I77 - 1]
2.61/2.62	  12) f3#(I78, I79, I80, I81) -> f2#(I82, I83, I80, I84) [I80 + 2 <= I79 /\ 1 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ I83 <= I79 /\ I82 + 1 <= I79 /\ I82 <= I78]
2.61/2.62	  13) f1#(I85, I86, I87, I88) -> f2#(I89, I90, I91, I92) [0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 0 <= I85 - 1 /\ I89 <= I85]
2.61/2.62	
2.61/2.62	We have the following SCCs.
2.61/2.62	  { 5, 6, 7, 8, 9, 10 }
2.61/2.62	  { 1, 2 }
2.61/2.62	
2.61/2.62	DP problem for innermost termination.
2.61/2.62	P =
2.61/2.62	  f5#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [2 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 - 2 <= I1 /\ I5 - 2 <= I0 /\ I4 - 2 <= I1 /\ I4 - 2 <= I0]
2.61/2.62	  f5#(I8, I9, I10, I11) -> f5#(I12, I13, I14, I15) [-1 <= I13 - 1 /\ -1 <= I12 - 1 /\ 1 <= I9 - 1 /\ 1 <= I8 - 1 /\ I13 + 2 <= I9 /\ I13 + 2 <= I8 /\ I12 + 2 <= I9 /\ I12 + 2 <= I8]
2.61/2.62	R = 
2.61/2.62	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
2.61/2.62	  f5(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [2 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 - 2 <= I1 /\ I5 - 2 <= I0 /\ I4 - 2 <= I1 /\ I4 - 2 <= I0]
2.61/2.62	  f5(I8, I9, I10, I11) -> f5(I12, I13, I14, I15) [-1 <= I13 - 1 /\ -1 <= I12 - 1 /\ 1 <= I9 - 1 /\ 1 <= I8 - 1 /\ I13 + 2 <= I9 /\ I13 + 2 <= I8 /\ I12 + 2 <= I9 /\ I12 + 2 <= I8]
2.61/2.62	  f2(I16, I17, I18, I19) -> f5(I20, I21, I22, I23) [I20 <= I17 /\ 0 <= y1 - 1 /\ I21 <= I17 /\ 0 <= I16 - 1 /\ 0 <= I17 - 1 /\ 0 <= I20 - 1 /\ 0 <= I21 - 1 /\ I18 + 2 <= I17]
2.61/2.62	  f1(I24, I25, I26, I27) -> f5(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I24 - 1 /\ I29 + 1 <= I24 /\ 0 <= I25 - 1 /\ I28 + 1 <= I24]
2.61/2.62	  f4(I32, I33, I34, I35) -> f4(I36, I37, I34 - 1, I35 + 1) [0 <= I34 - 1 /\ 0 <= I38 - 1 /\ -1 <= I35 - 1 /\ I36 - 2 <= I32 /\ I36 - 2 <= I33 /\ I37 - 2 <= I32 /\ I37 - 2 <= I33 /\ 1 <= I32 - 1 /\ 1 <= I33 - 1 /\ 3 <= I36 - 1 /\ 3 <= I37 - 1]
2.61/2.62	  f4(I39, I40, I41, I42) -> f4(I43, I44, I41 - 1, I42 + 1) [3 <= I44 - 1 /\ 3 <= I43 - 1 /\ 1 <= I40 - 1 /\ 1 <= I39 - 1 /\ I44 - 2 <= I40 /\ I44 - 2 <= I39 /\ I43 - 2 <= I40 /\ I43 - 2 <= I39 /\ 0 <= I41 - 1 /\ -1 <= I42 - 1]
2.61/2.62	  f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48 + 1) [0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 1 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I47 - 1 /\ -1 <= I48 - 1]
2.61/2.62	  f4(I51, I52, I53, I54) -> f4(I55, I56, I53 - 1, I54 + 1) [0 <= I53 - 1 /\ 0 <= I57 - 1 /\ -1 <= I54 - 1 /\ 0 <= I51 - 1 /\ 1 <= I52 - 1 /\ 0 <= I55 - 1 /\ 0 <= I56 - 1]
2.61/2.62	  f4(I58, I59, I60, I61) -> f4(I62, I63, I60 - 1, I61 + 1) [0 <= I60 - 1 /\ 0 <= I64 - 1 /\ -1 <= I61 - 1 /\ I62 <= I58 /\ I63 + 2 <= I59 /\ 0 <= I58 - 1 /\ 2 <= I59 - 1 /\ 0 <= I62 - 1 /\ 0 <= I63 - 1]
2.61/2.62	  f4(I65, I66, I67, I68) -> f4(I69, I70, I67 - 1, I68 + 1) [0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 2 <= I66 - 1 /\ 0 <= I65 - 1 /\ I70 + 2 <= I66 /\ I69 <= I65 /\ 0 <= I67 - 1 /\ -1 <= I68 - 1]
2.61/2.62	  f1(I71, I72, I73, I74) -> f4(I75, I76, I77, 1) [1 <= I76 - 1 /\ 1 <= I75 - 1 /\ 0 <= I71 - 1 /\ I76 - 1 <= I71 /\ I75 - 1 <= I71 /\ -1 <= I72 - 1 /\ 0 <= I77 - 1]
2.61/2.62	  f3(I78, I79, I80, I81) -> f2(I82, I83, I80, I84) [I80 + 2 <= I79 /\ 1 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ I83 <= I79 /\ I82 + 1 <= I79 /\ I82 <= I78]
2.61/2.62	  f1(I85, I86, I87, I88) -> f2(I89, I90, I91, I92) [0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 0 <= I85 - 1 /\ I89 <= I85]
2.61/2.62	
2.61/5.60	EOF