2.41/2.70	MAYBE
2.41/2.70	
2.41/2.70	DP problem for innermost termination.
2.41/2.70	P =
2.41/2.70	  f18#(x1, x2, x3, x4) -> f17#(x1, x2, x3, x4) 
2.41/2.70	  f17#(I0, I1, I2, I3) -> f16#(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
2.41/2.70	  f16#(I4, I5, I6, I7) -> f1#(I4, I5, I6, I7) [1 + I4 <= 0]
2.41/2.70	  f16#(I8, I9, I10, I11) -> f3#(I8, I9, I10, I11) [0 <= I8]
2.41/2.70	  f15#(I12, I13, I14, I15) -> f3#(I12, I13, I14, I15) 
2.41/2.70	  f5#(I16, I17, I18, I19) -> f14#(I16, I17, I18, I19) [I16 <= I17]
2.41/2.70	  f5#(I20, I21, I22, I23) -> f13#(I20, I21, I22, I23) [1 + I21 <= I20]
2.41/2.70	  f14#(I24, I25, I26, I27) -> f10#(I24, I25, I26, I27) [1 <= I27]
2.41/2.70	  f14#(I28, I29, I30, I31) -> f13#(I28, I29, I30, I31) [I31 <= 0]
2.41/2.70	  f13#(I32, I33, I34, I35) -> f4#(1 + I32, I33, I34, I35) [I32 <= I33]
2.41/2.70	  f13#(I36, I37, I38, I39) -> f4#(1 + I36, I37, I38, I39) [1 + I37 <= I36]
2.41/2.70	  f12#(I40, I41, I42, I43) -> f9#(I40, I41, I42, I43) 
2.41/2.70	  f9#(I44, I45, I46, I47) -> f12#(I44, I45, I46, I47) 
2.41/2.70	  f11#(I48, I49, I50, I51) -> f3#(I48, I49, I50, I51) [I48 <= 2]
2.41/2.70	  f11#(I52, I53, I54, I55) -> f10#(-1 + I52, I53, I54, I55) [3 <= I52]
2.41/2.70	  f10#(I56, I57, I58, I59) -> f11#(I56, I57, I58, I59) 
2.41/2.70	  f8#(I60, I61, I62, I63) -> f9#(I60, I61, I62, I63) 
2.41/2.70	  f4#(I68, I69, I70, I71) -> f5#(I68, I69, I70, rnd4) [rnd4 = rnd4]
2.41/2.70	  f3#(I72, I73, I74, I75) -> f4#(I72, I73, I74, I75) 
2.41/2.70	  f2#(I76, I77, I78, I79) -> f1#(I76, I77, I78, I79) 
2.41/2.70	  f1#(I80, I81, I82, I83) -> f2#(I80, I81, I82, I83) 
2.41/2.70	R = 
2.41/2.70	  f18(x1, x2, x3, x4) -> f17(x1, x2, x3, x4) 
2.41/2.70	  f17(I0, I1, I2, I3) -> f16(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
2.41/2.70	  f16(I4, I5, I6, I7) -> f1(I4, I5, I6, I7) [1 + I4 <= 0]
2.41/2.70	  f16(I8, I9, I10, I11) -> f3(I8, I9, I10, I11) [0 <= I8]
2.41/2.70	  f15(I12, I13, I14, I15) -> f3(I12, I13, I14, I15) 
2.41/2.70	  f5(I16, I17, I18, I19) -> f14(I16, I17, I18, I19) [I16 <= I17]
2.41/2.70	  f5(I20, I21, I22, I23) -> f13(I20, I21, I22, I23) [1 + I21 <= I20]
2.41/2.70	  f14(I24, I25, I26, I27) -> f10(I24, I25, I26, I27) [1 <= I27]
2.41/2.70	  f14(I28, I29, I30, I31) -> f13(I28, I29, I30, I31) [I31 <= 0]
2.41/2.70	  f13(I32, I33, I34, I35) -> f4(1 + I32, I33, I34, I35) [I32 <= I33]
2.41/2.70	  f13(I36, I37, I38, I39) -> f4(1 + I36, I37, I38, I39) [1 + I37 <= I36]
2.41/2.70	  f12(I40, I41, I42, I43) -> f9(I40, I41, I42, I43) 
2.41/2.70	  f9(I44, I45, I46, I47) -> f12(I44, I45, I46, I47) 
2.41/2.70	  f11(I48, I49, I50, I51) -> f3(I48, I49, I50, I51) [I48 <= 2]
2.41/2.70	  f11(I52, I53, I54, I55) -> f10(-1 + I52, I53, I54, I55) [3 <= I52]
2.41/2.70	  f10(I56, I57, I58, I59) -> f11(I56, I57, I58, I59) 
2.41/2.70	  f8(I60, I61, I62, I63) -> f9(I60, I61, I62, I63) 
2.41/2.70	  f6(I64, I65, I66, I67) -> f7(I64, I65, I66, I67) 
2.41/2.70	  f4(I68, I69, I70, I71) -> f5(I68, I69, I70, rnd4) [rnd4 = rnd4]
2.41/2.70	  f3(I72, I73, I74, I75) -> f4(I72, I73, I74, I75) 
2.41/2.70	  f2(I76, I77, I78, I79) -> f1(I76, I77, I78, I79) 
2.41/2.70	  f1(I80, I81, I82, I83) -> f2(I80, I81, I82, I83) 
2.41/2.70	
2.41/2.70	The dependency graph for this problem is:
2.41/2.70	  0 -> 1
2.41/2.70	  1 -> 2, 3
2.41/2.70	  2 -> 20
2.41/2.70	  3 -> 18
2.41/2.70	  4 -> 18
2.41/2.70	  5 -> 7, 8
2.41/2.70	  6 -> 10
2.41/2.70	  7 -> 15
2.41/2.70	  8 -> 9, 10
2.41/2.70	  9 -> 17
2.41/2.70	  10 -> 17
2.41/2.70	  11 -> 12
2.41/2.70	  12 -> 11
2.41/2.70	  13 -> 18
2.41/2.70	  14 -> 15
2.41/2.70	  15 -> 13, 14
2.41/2.70	  16 -> 12
2.41/2.70	  17 -> 5, 6
2.41/2.70	  18 -> 17
2.41/2.70	  19 -> 20
2.41/2.70	  20 -> 19
2.41/2.70	Where:
2.41/2.70	  0) f18#(x1, x2, x3, x4) -> f17#(x1, x2, x3, x4) 
2.41/2.70	  1) f17#(I0, I1, I2, I3) -> f16#(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
2.41/2.70	  2) f16#(I4, I5, I6, I7) -> f1#(I4, I5, I6, I7) [1 + I4 <= 0]
2.41/2.70	  3) f16#(I8, I9, I10, I11) -> f3#(I8, I9, I10, I11) [0 <= I8]
2.41/2.70	  4) f15#(I12, I13, I14, I15) -> f3#(I12, I13, I14, I15) 
2.41/2.70	  5) f5#(I16, I17, I18, I19) -> f14#(I16, I17, I18, I19) [I16 <= I17]
2.41/2.70	  6) f5#(I20, I21, I22, I23) -> f13#(I20, I21, I22, I23) [1 + I21 <= I20]
2.41/2.70	  7) f14#(I24, I25, I26, I27) -> f10#(I24, I25, I26, I27) [1 <= I27]
2.41/2.70	  8) f14#(I28, I29, I30, I31) -> f13#(I28, I29, I30, I31) [I31 <= 0]
2.41/2.70	  9) f13#(I32, I33, I34, I35) -> f4#(1 + I32, I33, I34, I35) [I32 <= I33]
2.41/2.70	  10) f13#(I36, I37, I38, I39) -> f4#(1 + I36, I37, I38, I39) [1 + I37 <= I36]
2.41/2.70	  11) f12#(I40, I41, I42, I43) -> f9#(I40, I41, I42, I43) 
2.41/2.70	  12) f9#(I44, I45, I46, I47) -> f12#(I44, I45, I46, I47) 
2.41/2.70	  13) f11#(I48, I49, I50, I51) -> f3#(I48, I49, I50, I51) [I48 <= 2]
2.41/2.70	  14) f11#(I52, I53, I54, I55) -> f10#(-1 + I52, I53, I54, I55) [3 <= I52]
2.41/2.70	  15) f10#(I56, I57, I58, I59) -> f11#(I56, I57, I58, I59) 
2.41/2.70	  16) f8#(I60, I61, I62, I63) -> f9#(I60, I61, I62, I63) 
2.41/2.70	  17) f4#(I68, I69, I70, I71) -> f5#(I68, I69, I70, rnd4) [rnd4 = rnd4]
2.41/2.70	  18) f3#(I72, I73, I74, I75) -> f4#(I72, I73, I74, I75) 
2.41/2.70	  19) f2#(I76, I77, I78, I79) -> f1#(I76, I77, I78, I79) 
2.41/2.70	  20) f1#(I80, I81, I82, I83) -> f2#(I80, I81, I82, I83) 
2.41/2.70	
2.41/2.70	We have the following SCCs.
2.41/2.70	  { 11, 12 }
2.41/2.70	  { 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18 }
2.41/2.70	  { 19, 20 }
2.41/2.70	
2.41/2.70	DP problem for innermost termination.
2.41/2.70	P =
2.41/2.70	  f2#(I76, I77, I78, I79) -> f1#(I76, I77, I78, I79) 
2.41/2.70	  f1#(I80, I81, I82, I83) -> f2#(I80, I81, I82, I83) 
2.41/2.70	R = 
2.41/2.70	  f18(x1, x2, x3, x4) -> f17(x1, x2, x3, x4) 
2.41/2.70	  f17(I0, I1, I2, I3) -> f16(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
2.41/2.70	  f16(I4, I5, I6, I7) -> f1(I4, I5, I6, I7) [1 + I4 <= 0]
2.41/2.70	  f16(I8, I9, I10, I11) -> f3(I8, I9, I10, I11) [0 <= I8]
2.41/2.70	  f15(I12, I13, I14, I15) -> f3(I12, I13, I14, I15) 
2.41/2.70	  f5(I16, I17, I18, I19) -> f14(I16, I17, I18, I19) [I16 <= I17]
2.41/2.70	  f5(I20, I21, I22, I23) -> f13(I20, I21, I22, I23) [1 + I21 <= I20]
2.41/2.70	  f14(I24, I25, I26, I27) -> f10(I24, I25, I26, I27) [1 <= I27]
2.41/2.70	  f14(I28, I29, I30, I31) -> f13(I28, I29, I30, I31) [I31 <= 0]
2.41/2.70	  f13(I32, I33, I34, I35) -> f4(1 + I32, I33, I34, I35) [I32 <= I33]
2.41/2.70	  f13(I36, I37, I38, I39) -> f4(1 + I36, I37, I38, I39) [1 + I37 <= I36]
2.41/2.70	  f12(I40, I41, I42, I43) -> f9(I40, I41, I42, I43) 
2.41/2.70	  f9(I44, I45, I46, I47) -> f12(I44, I45, I46, I47) 
2.41/2.70	  f11(I48, I49, I50, I51) -> f3(I48, I49, I50, I51) [I48 <= 2]
2.41/2.70	  f11(I52, I53, I54, I55) -> f10(-1 + I52, I53, I54, I55) [3 <= I52]
2.41/2.70	  f10(I56, I57, I58, I59) -> f11(I56, I57, I58, I59) 
2.41/2.70	  f8(I60, I61, I62, I63) -> f9(I60, I61, I62, I63) 
2.41/2.70	  f6(I64, I65, I66, I67) -> f7(I64, I65, I66, I67) 
2.41/2.70	  f4(I68, I69, I70, I71) -> f5(I68, I69, I70, rnd4) [rnd4 = rnd4]
2.41/2.70	  f3(I72, I73, I74, I75) -> f4(I72, I73, I74, I75) 
2.41/2.70	  f2(I76, I77, I78, I79) -> f1(I76, I77, I78, I79) 
2.41/2.70	  f1(I80, I81, I82, I83) -> f2(I80, I81, I82, I83) 
2.41/2.70	
2.41/5.68	EOF