14.34/14.21	MAYBE
14.34/14.21	
14.34/14.21	DP problem for innermost termination.
14.34/14.21	P =
14.34/14.21	  f9#(x1, x2, x3, x4) -> f8#(x1, x2, x3, x4) 
14.34/14.21	  f8#(I0, I1, I2, I3) -> f2#(I0, I1, 1 + I0, I3) [I0 <= I1 /\ 0 <= I0]
14.34/14.21	  f2#(I8, I9, I10, I11) -> f6#(I8, I9, I10, I11) 
14.34/14.21	  f6#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [1 + I14 <= I12]
14.34/14.21	  f6#(I16, I17, I18, I19) -> f5#(I16, I17, I18, I19) [1 + I16 <= I18]
14.34/14.21	  f6#(I20, I21, I22, I23) -> f4#(I20, I21, I22, I23) [I20 <= I22 /\ I22 <= I20]
14.34/14.21	  f5#(I24, I25, I26, I27) -> f3#(I24, I25, I26, rnd4) [rnd4 = rnd4]
14.34/14.21	  f3#(I28, I29, I30, I31) -> f1#(I28, I29, I30, I31) [1 + I31 <= 0]
14.34/14.21	  f3#(I32, I33, I34, I35) -> f1#(I32, I33, I34, I35) [1 <= I35]
14.34/14.21	  f3#(I36, I37, I38, I39) -> f4#(I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0]
14.34/14.21	  f1#(I40, I41, I42, I43) -> f2#(I40, I41, 1 + I42, I43) [I42 <= I41]
14.34/14.21	  f1#(I44, I45, I46, I47) -> f2#(I44, I45, 0, I47) [1 + I45 <= I46]
14.34/14.21	R = 
14.34/14.21	  f9(x1, x2, x3, x4) -> f8(x1, x2, x3, x4) 
14.34/14.21	  f8(I0, I1, I2, I3) -> f2(I0, I1, 1 + I0, I3) [I0 <= I1 /\ 0 <= I0]
14.34/14.21	  f4(I4, I5, I6, I7) -> f7(I4, I5, I6, I7) 
14.34/14.21	  f2(I8, I9, I10, I11) -> f6(I8, I9, I10, I11) 
14.34/14.21	  f6(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [1 + I14 <= I12]
14.34/14.21	  f6(I16, I17, I18, I19) -> f5(I16, I17, I18, I19) [1 + I16 <= I18]
14.34/14.21	  f6(I20, I21, I22, I23) -> f4(I20, I21, I22, I23) [I20 <= I22 /\ I22 <= I20]
14.34/14.21	  f5(I24, I25, I26, I27) -> f3(I24, I25, I26, rnd4) [rnd4 = rnd4]
14.34/14.21	  f3(I28, I29, I30, I31) -> f1(I28, I29, I30, I31) [1 + I31 <= 0]
14.34/14.21	  f3(I32, I33, I34, I35) -> f1(I32, I33, I34, I35) [1 <= I35]
14.34/14.21	  f3(I36, I37, I38, I39) -> f4(I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0]
14.34/14.21	  f1(I40, I41, I42, I43) -> f2(I40, I41, 1 + I42, I43) [I42 <= I41]
14.34/14.21	  f1(I44, I45, I46, I47) -> f2(I44, I45, 0, I47) [1 + I45 <= I46]
14.34/14.21	
14.34/14.21	The dependency graph for this problem is:
14.34/14.21	  0 -> 1
14.34/14.21	  1 -> 2
14.34/14.21	  2 -> 3, 4, 5
14.34/14.21	  3 -> 6
14.34/14.21	  4 -> 6
14.34/14.21	  5 -> 
14.34/14.21	  6 -> 7, 8, 9
14.34/14.21	  7 -> 10, 11
14.34/14.21	  8 -> 10, 11
14.34/14.21	  9 -> 
14.34/14.21	  10 -> 2
14.34/14.21	  11 -> 2
14.34/14.21	Where:
14.34/14.21	  0) f9#(x1, x2, x3, x4) -> f8#(x1, x2, x3, x4) 
14.34/14.21	  1) f8#(I0, I1, I2, I3) -> f2#(I0, I1, 1 + I0, I3) [I0 <= I1 /\ 0 <= I0]
14.34/14.21	  2) f2#(I8, I9, I10, I11) -> f6#(I8, I9, I10, I11) 
14.34/14.21	  3) f6#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [1 + I14 <= I12]
14.34/14.21	  4) f6#(I16, I17, I18, I19) -> f5#(I16, I17, I18, I19) [1 + I16 <= I18]
14.34/14.21	  5) f6#(I20, I21, I22, I23) -> f4#(I20, I21, I22, I23) [I20 <= I22 /\ I22 <= I20]
14.34/14.21	  6) f5#(I24, I25, I26, I27) -> f3#(I24, I25, I26, rnd4) [rnd4 = rnd4]
14.34/14.21	  7) f3#(I28, I29, I30, I31) -> f1#(I28, I29, I30, I31) [1 + I31 <= 0]
14.34/14.21	  8) f3#(I32, I33, I34, I35) -> f1#(I32, I33, I34, I35) [1 <= I35]
14.34/14.21	  9) f3#(I36, I37, I38, I39) -> f4#(I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0]
14.34/14.21	  10) f1#(I40, I41, I42, I43) -> f2#(I40, I41, 1 + I42, I43) [I42 <= I41]
14.34/14.21	  11) f1#(I44, I45, I46, I47) -> f2#(I44, I45, 0, I47) [1 + I45 <= I46]
14.34/14.21	
14.34/14.21	We have the following SCCs.
14.34/14.21	  { 2, 3, 4, 6, 7, 8, 10, 11 }
14.34/14.21	
14.34/14.21	DP problem for innermost termination.
14.34/14.21	P =
14.34/14.21	  f2#(I8, I9, I10, I11) -> f6#(I8, I9, I10, I11) 
14.34/14.21	  f6#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [1 + I14 <= I12]
14.34/14.21	  f6#(I16, I17, I18, I19) -> f5#(I16, I17, I18, I19) [1 + I16 <= I18]
14.34/14.21	  f5#(I24, I25, I26, I27) -> f3#(I24, I25, I26, rnd4) [rnd4 = rnd4]
14.34/14.21	  f3#(I28, I29, I30, I31) -> f1#(I28, I29, I30, I31) [1 + I31 <= 0]
14.34/14.21	  f3#(I32, I33, I34, I35) -> f1#(I32, I33, I34, I35) [1 <= I35]
14.34/14.21	  f1#(I40, I41, I42, I43) -> f2#(I40, I41, 1 + I42, I43) [I42 <= I41]
14.34/14.21	  f1#(I44, I45, I46, I47) -> f2#(I44, I45, 0, I47) [1 + I45 <= I46]
14.34/14.21	R = 
14.34/14.21	  f9(x1, x2, x3, x4) -> f8(x1, x2, x3, x4) 
14.34/14.21	  f8(I0, I1, I2, I3) -> f2(I0, I1, 1 + I0, I3) [I0 <= I1 /\ 0 <= I0]
14.34/14.21	  f4(I4, I5, I6, I7) -> f7(I4, I5, I6, I7) 
14.34/14.21	  f2(I8, I9, I10, I11) -> f6(I8, I9, I10, I11) 
14.34/14.21	  f6(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [1 + I14 <= I12]
14.34/14.21	  f6(I16, I17, I18, I19) -> f5(I16, I17, I18, I19) [1 + I16 <= I18]
14.34/14.21	  f6(I20, I21, I22, I23) -> f4(I20, I21, I22, I23) [I20 <= I22 /\ I22 <= I20]
14.34/14.21	  f5(I24, I25, I26, I27) -> f3(I24, I25, I26, rnd4) [rnd4 = rnd4]
14.34/14.21	  f3(I28, I29, I30, I31) -> f1(I28, I29, I30, I31) [1 + I31 <= 0]
14.34/14.21	  f3(I32, I33, I34, I35) -> f1(I32, I33, I34, I35) [1 <= I35]
14.34/14.21	  f3(I36, I37, I38, I39) -> f4(I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0]
14.34/14.21	  f1(I40, I41, I42, I43) -> f2(I40, I41, 1 + I42, I43) [I42 <= I41]
14.34/14.21	  f1(I44, I45, I46, I47) -> f2(I44, I45, 0, I47) [1 + I45 <= I46]
14.34/14.21	
14.34/17.19	EOF