19.42/19.14	MAYBE
19.42/19.14	
19.42/19.14	DP problem for innermost termination.
19.42/19.14	P =
19.42/19.14	  f14#(x1, x2, x3, x4) -> f13#(x1, x2, x3, x4) 
19.42/19.14	  f13#(I0, I1, I2, I3) -> f1#(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
19.42/19.14	  f3#(I4, I5, I6, I7) -> f12#(I4, I5, I6, I7) [I4 <= I5]
19.42/19.14	  f3#(I8, I9, I10, I11) -> f11#(I8, I9, I10, I11) [1 + I9 <= I8]
19.42/19.14	  f12#(I12, I13, I14, I15) -> f4#(I12, I13, I14, I15) [1 <= I15]
19.42/19.14	  f12#(I16, I17, I18, I19) -> f11#(I16, I17, I18, I19) [I19 <= 0]
19.42/19.14	  f11#(I20, I21, I22, I23) -> f2#(1 + I20, I21, I22, I23) [I20 <= I21]
19.42/19.14	  f11#(I24, I25, I26, I27) -> f2#(1 + I24, I25, I26, I27) [1 + I25 <= I24]
19.42/19.14	  f10#(I28, I29, I30, I31) -> f9#(I28, I29, I30, I31) 
19.42/19.14	  f9#(I32, I33, I34, I35) -> f10#(I32, I33, I34, I35) 
19.42/19.14	  f5#(I36, I37, I38, I39) -> f1#(I36, I37, I38, I39) [I36 <= 2]
19.42/19.14	  f5#(I40, I41, I42, I43) -> f4#(-1 + I40, I41, I42, I43) [3 <= I40]
19.42/19.14	  f8#(I44, I45, I46, I47) -> f9#(I44, I45, I46, I47) 
19.42/19.14	  f4#(I52, I53, I54, I55) -> f5#(I52, I53, I54, I55) 
19.42/19.14	  f2#(I56, I57, I58, I59) -> f3#(I56, I57, I58, rnd4) [rnd4 = rnd4]
19.42/19.14	  f1#(I60, I61, I62, I63) -> f2#(I60, I61, I62, I63) 
19.42/19.14	R = 
19.42/19.14	  f14(x1, x2, x3, x4) -> f13(x1, x2, x3, x4) 
19.42/19.14	  f13(I0, I1, I2, I3) -> f1(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
19.42/19.14	  f3(I4, I5, I6, I7) -> f12(I4, I5, I6, I7) [I4 <= I5]
19.42/19.14	  f3(I8, I9, I10, I11) -> f11(I8, I9, I10, I11) [1 + I9 <= I8]
19.42/19.14	  f12(I12, I13, I14, I15) -> f4(I12, I13, I14, I15) [1 <= I15]
19.42/19.14	  f12(I16, I17, I18, I19) -> f11(I16, I17, I18, I19) [I19 <= 0]
19.42/19.14	  f11(I20, I21, I22, I23) -> f2(1 + I20, I21, I22, I23) [I20 <= I21]
19.42/19.14	  f11(I24, I25, I26, I27) -> f2(1 + I24, I25, I26, I27) [1 + I25 <= I24]
19.42/19.14	  f10(I28, I29, I30, I31) -> f9(I28, I29, I30, I31) 
19.42/19.14	  f9(I32, I33, I34, I35) -> f10(I32, I33, I34, I35) 
19.42/19.14	  f5(I36, I37, I38, I39) -> f1(I36, I37, I38, I39) [I36 <= 2]
19.42/19.14	  f5(I40, I41, I42, I43) -> f4(-1 + I40, I41, I42, I43) [3 <= I40]
19.42/19.14	  f8(I44, I45, I46, I47) -> f9(I44, I45, I46, I47) 
19.42/19.14	  f6(I48, I49, I50, I51) -> f7(I48, I49, I50, I51) 
19.42/19.14	  f4(I52, I53, I54, I55) -> f5(I52, I53, I54, I55) 
19.42/19.14	  f2(I56, I57, I58, I59) -> f3(I56, I57, I58, rnd4) [rnd4 = rnd4]
19.42/19.14	  f1(I60, I61, I62, I63) -> f2(I60, I61, I62, I63) 
19.42/19.14	
19.42/19.14	The dependency graph for this problem is:
19.42/19.14	  0 -> 1
19.42/19.14	  1 -> 15
19.42/19.14	  2 -> 4, 5
19.42/19.14	  3 -> 7
19.42/19.14	  4 -> 13
19.42/19.14	  5 -> 6, 7
19.42/19.14	  6 -> 14
19.42/19.14	  7 -> 14
19.42/19.14	  8 -> 9
19.42/19.14	  9 -> 8
19.42/19.14	  10 -> 15
19.42/19.14	  11 -> 13
19.42/19.14	  12 -> 9
19.42/19.14	  13 -> 10, 11
19.42/19.14	  14 -> 2, 3
19.42/19.14	  15 -> 14
19.42/19.14	Where:
19.42/19.14	  0) f14#(x1, x2, x3, x4) -> f13#(x1, x2, x3, x4) 
19.42/19.14	  1) f13#(I0, I1, I2, I3) -> f1#(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
19.42/19.14	  2) f3#(I4, I5, I6, I7) -> f12#(I4, I5, I6, I7) [I4 <= I5]
19.42/19.14	  3) f3#(I8, I9, I10, I11) -> f11#(I8, I9, I10, I11) [1 + I9 <= I8]
19.42/19.14	  4) f12#(I12, I13, I14, I15) -> f4#(I12, I13, I14, I15) [1 <= I15]
19.42/19.14	  5) f12#(I16, I17, I18, I19) -> f11#(I16, I17, I18, I19) [I19 <= 0]
19.42/19.14	  6) f11#(I20, I21, I22, I23) -> f2#(1 + I20, I21, I22, I23) [I20 <= I21]
19.42/19.14	  7) f11#(I24, I25, I26, I27) -> f2#(1 + I24, I25, I26, I27) [1 + I25 <= I24]
19.42/19.14	  8) f10#(I28, I29, I30, I31) -> f9#(I28, I29, I30, I31) 
19.42/19.14	  9) f9#(I32, I33, I34, I35) -> f10#(I32, I33, I34, I35) 
19.42/19.14	  10) f5#(I36, I37, I38, I39) -> f1#(I36, I37, I38, I39) [I36 <= 2]
19.42/19.14	  11) f5#(I40, I41, I42, I43) -> f4#(-1 + I40, I41, I42, I43) [3 <= I40]
19.42/19.14	  12) f8#(I44, I45, I46, I47) -> f9#(I44, I45, I46, I47) 
19.42/19.14	  13) f4#(I52, I53, I54, I55) -> f5#(I52, I53, I54, I55) 
19.42/19.14	  14) f2#(I56, I57, I58, I59) -> f3#(I56, I57, I58, rnd4) [rnd4 = rnd4]
19.42/19.14	  15) f1#(I60, I61, I62, I63) -> f2#(I60, I61, I62, I63) 
19.42/19.14	
19.42/19.14	We have the following SCCs.
19.42/19.14	  { 8, 9 }
19.42/19.14	  { 2, 3, 4, 5, 6, 7, 10, 11, 13, 14, 15 }
19.42/19.14	
19.42/19.14	DP problem for innermost termination.
19.42/19.14	P =
19.42/19.14	  f3#(I4, I5, I6, I7) -> f12#(I4, I5, I6, I7) [I4 <= I5]
19.42/19.14	  f3#(I8, I9, I10, I11) -> f11#(I8, I9, I10, I11) [1 + I9 <= I8]
19.42/19.14	  f12#(I12, I13, I14, I15) -> f4#(I12, I13, I14, I15) [1 <= I15]
19.42/19.14	  f12#(I16, I17, I18, I19) -> f11#(I16, I17, I18, I19) [I19 <= 0]
19.42/19.14	  f11#(I20, I21, I22, I23) -> f2#(1 + I20, I21, I22, I23) [I20 <= I21]
19.42/19.14	  f11#(I24, I25, I26, I27) -> f2#(1 + I24, I25, I26, I27) [1 + I25 <= I24]
19.42/19.14	  f5#(I36, I37, I38, I39) -> f1#(I36, I37, I38, I39) [I36 <= 2]
19.42/19.14	  f5#(I40, I41, I42, I43) -> f4#(-1 + I40, I41, I42, I43) [3 <= I40]
19.42/19.14	  f4#(I52, I53, I54, I55) -> f5#(I52, I53, I54, I55) 
19.42/19.14	  f2#(I56, I57, I58, I59) -> f3#(I56, I57, I58, rnd4) [rnd4 = rnd4]
19.42/19.14	  f1#(I60, I61, I62, I63) -> f2#(I60, I61, I62, I63) 
19.42/19.14	R = 
19.42/19.14	  f14(x1, x2, x3, x4) -> f13(x1, x2, x3, x4) 
19.42/19.14	  f13(I0, I1, I2, I3) -> f1(rnd1, I1, rnd3, I3) [y1 = y1 /\ rnd3 = rnd3 /\ rnd1 = rnd3]
19.42/19.14	  f3(I4, I5, I6, I7) -> f12(I4, I5, I6, I7) [I4 <= I5]
19.42/19.14	  f3(I8, I9, I10, I11) -> f11(I8, I9, I10, I11) [1 + I9 <= I8]
19.42/19.14	  f12(I12, I13, I14, I15) -> f4(I12, I13, I14, I15) [1 <= I15]
19.42/19.14	  f12(I16, I17, I18, I19) -> f11(I16, I17, I18, I19) [I19 <= 0]
19.42/19.14	  f11(I20, I21, I22, I23) -> f2(1 + I20, I21, I22, I23) [I20 <= I21]
19.42/19.14	  f11(I24, I25, I26, I27) -> f2(1 + I24, I25, I26, I27) [1 + I25 <= I24]
19.42/19.14	  f10(I28, I29, I30, I31) -> f9(I28, I29, I30, I31) 
19.42/19.14	  f9(I32, I33, I34, I35) -> f10(I32, I33, I34, I35) 
19.42/19.14	  f5(I36, I37, I38, I39) -> f1(I36, I37, I38, I39) [I36 <= 2]
19.42/19.14	  f5(I40, I41, I42, I43) -> f4(-1 + I40, I41, I42, I43) [3 <= I40]
19.42/19.14	  f8(I44, I45, I46, I47) -> f9(I44, I45, I46, I47) 
19.42/19.14	  f6(I48, I49, I50, I51) -> f7(I48, I49, I50, I51) 
19.42/19.14	  f4(I52, I53, I54, I55) -> f5(I52, I53, I54, I55) 
19.42/19.14	  f2(I56, I57, I58, I59) -> f3(I56, I57, I58, rnd4) [rnd4 = rnd4]
19.42/19.14	  f1(I60, I61, I62, I63) -> f2(I60, I61, I62, I63) 
19.42/19.14	
19.42/22.11	EOF