52.79/52.52	MAYBE
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f14#(x1, x2, x3, x4) -> f1#(x1, x2, x3, x4) 
52.79/52.52	  f13#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
52.79/52.52	  f12#(I4, I5, I6, I7) -> f13#(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11#(I8, I9, I10, I11) -> f12#(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11#(I12, I13, I14, I15) -> f12#(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2#(I16, I17, I18, I19) -> f11#(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f3#(I63, I64, I65, I66) -> f4#(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3#(I67, I68, I69, I70) -> f4#(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2#(I71, I72, I73, I74) -> f3#(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1#(I75, I76, I77, I78) -> f2#(I75, I76, I77, I78) 
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	The dependency graph for this problem is:
52.79/52.52	  0 -> 18
52.79/52.52	  1 -> 5, 7, 12, 14, 17
52.79/52.52	  2 -> 1
52.79/52.52	  3 -> 2
52.79/52.52	  4 -> 2
52.79/52.52	  5 -> 3, 4
52.79/52.52	  6 -> 5, 7, 12, 14, 17
52.79/52.52	  7 -> 6
52.79/52.52	  8 -> 5, 7, 12, 14, 17
52.79/52.52	  9 -> 8
52.79/52.52	  10 -> 9
52.79/52.52	  11 -> 9
52.79/52.52	  12 -> 10, 11
52.79/52.52	  13 -> 5, 7, 12, 14, 17
52.79/52.52	  14 -> 13
52.79/52.52	  15 -> 
52.79/52.52	  16 -> 
52.79/52.52	  17 -> 15
52.79/52.52	  18 -> 5, 7, 12, 14, 17
52.79/52.52	Where:
52.79/52.52	  0) f14#(x1, x2, x3, x4) -> f1#(x1, x2, x3, x4) 
52.79/52.52	  1) f13#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
52.79/52.52	  2) f12#(I4, I5, I6, I7) -> f13#(I4, I5, 1 + I6, I7) 
52.79/52.52	  3) f11#(I8, I9, I10, I11) -> f12#(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  4) f11#(I12, I13, I14, I15) -> f12#(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  5) f2#(I16, I17, I18, I19) -> f11#(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  6) f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  7) f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  8) f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  9) f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  10) f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  11) f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  12) f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  13) f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  14) f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  15) f3#(I63, I64, I65, I66) -> f4#(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  16) f3#(I67, I68, I69, I70) -> f4#(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  17) f2#(I71, I72, I73, I74) -> f3#(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  18) f1#(I75, I76, I77, I78) -> f2#(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	We have the following SCCs.
52.79/52.52	  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 }
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f13#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
52.79/52.52	  f12#(I4, I5, I6, I7) -> f13#(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11#(I8, I9, I10, I11) -> f12#(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11#(I12, I13, I14, I15) -> f12#(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2#(I16, I17, I18, I19) -> f11#(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	We use the extended value criterion with the projection function NU:
52.79/52.52	  NU[f6#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f7#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f8#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f9#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f10#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f11#(x0,x1,x2,x3)] = -x2 + x3 - 1
52.79/52.52	  NU[f12#(x0,x1,x2,x3)] = -x2 + x3 - 1
52.79/52.52	  NU[f2#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f13#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	
52.79/52.52	This gives the following inequalities:
52.79/52.52	    ==>  -I2 + I3 >= -I2 + I3
52.79/52.52	    ==>  -I6 + I7 - 1 >= -(1 + I6) + I7
52.79/52.52	  1 <= I9  ==>  -I10 + I11 - 1 >= -I10 + I11 - 1
52.79/52.52	  1 + I13 <= 0  ==>  -I14 + I15 - 1 >= -I14 + I15 - 1
52.79/52.52	  rnd2 = rnd2 /\ 0 <= -1 - I18 + I19  ==>  -I18 + I19 > -I18 + I19 - 1  with  -I18 + I19 >= 0
52.79/52.52	    ==>  -I22 + I23 >= -I22 + I23
52.79/52.52	  0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27  ==>  -I26 + I27 >= -I26 + I27
52.79/52.52	    ==>  -I31 + I32 >= -I31 + I32
52.79/52.52	    ==>  -I35 + I36 >= -(1 + I35) + I36
52.79/52.52	  1 <= I38  ==>  -I39 + I40 >= -I39 + I40
52.79/52.52	  1 + I42 <= 0  ==>  -I43 + I44 >= -I43 + I44
52.79/52.52	  I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0  ==>  -I47 + I48 >= -I47 + I48
52.79/52.52	    ==>  -I52 + I53 >= -I52 + I53
52.79/52.52	  0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0  ==>  -I56 + I57 >= -I56 + I57
52.79/52.52	
52.79/52.52	We remove all the strictly oriented dependency pairs.
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f13#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
52.79/52.52	  f12#(I4, I5, I6, I7) -> f13#(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11#(I8, I9, I10, I11) -> f12#(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11#(I12, I13, I14, I15) -> f12#(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	The dependency graph for this problem is:
52.79/52.52	  1 -> 7, 12, 14
52.79/52.52	  2 -> 1
52.79/52.52	  3 -> 2
52.79/52.52	  4 -> 2
52.79/52.52	  6 -> 7, 12, 14
52.79/52.52	  7 -> 6
52.79/52.52	  8 -> 7, 12, 14
52.79/52.52	  9 -> 8
52.79/52.52	  10 -> 9
52.79/52.52	  11 -> 9
52.79/52.52	  12 -> 10, 11
52.79/52.52	  13 -> 7, 12, 14
52.79/52.52	  14 -> 13
52.79/52.52	Where:
52.79/52.52	  1) f13#(I0, I1, I2, I3) -> f2#(I0, I1, I2, I3) 
52.79/52.52	  2) f12#(I4, I5, I6, I7) -> f13#(I4, I5, 1 + I6, I7) 
52.79/52.52	  3) f11#(I8, I9, I10, I11) -> f12#(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  4) f11#(I12, I13, I14, I15) -> f12#(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  6) f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  7) f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  8) f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  9) f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  10) f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  11) f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  12) f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  13) f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  14) f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	
52.79/52.52	We have the following SCCs.
52.79/52.52	  { 6, 7, 8, 9, 10, 11, 12, 13, 14 }
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2#(I45, I46, I47, I48) -> f7#(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	We use the extended value criterion with the projection function NU:
52.79/52.52	  NU[f6#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f7#(x0,x1,x2,x3)] = -x2 + x3 - 1
52.79/52.52	  NU[f8#(x0,x1,x2,x3)] = -x2 + x3 - 1
52.79/52.52	  NU[f9#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f2#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	  NU[f10#(x0,x1,x2,x3)] = -x2 + x3
52.79/52.52	
52.79/52.52	This gives the following inequalities:
52.79/52.52	    ==>  -I22 + I23 >= -I22 + I23
52.79/52.52	  0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27  ==>  -I26 + I27 >= -I26 + I27
52.79/52.52	    ==>  -I31 + I32 >= -I31 + I32
52.79/52.52	    ==>  -I35 + I36 - 1 >= -(1 + I35) + I36
52.79/52.52	  1 <= I38  ==>  -I39 + I40 - 1 >= -I39 + I40 - 1
52.79/52.52	  1 + I42 <= 0  ==>  -I43 + I44 - 1 >= -I43 + I44 - 1
52.79/52.52	  I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0  ==>  -I47 + I48 > -I47 + I48 - 1  with  -I47 + I48 >= 0
52.79/52.52	    ==>  -I52 + I53 >= -I52 + I53
52.79/52.52	  0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0  ==>  -I56 + I57 >= -I56 + I57
52.79/52.52	
52.79/52.52	We remove all the strictly oriented dependency pairs.
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/52.52	The dependency graph for this problem is:
52.79/52.52	  6 -> 7, 14
52.79/52.52	  7 -> 6
52.79/52.52	  8 -> 7, 14
52.79/52.52	  9 -> 8
52.79/52.52	  10 -> 9
52.79/52.52	  11 -> 9
52.79/52.52	  13 -> 7, 14
52.79/52.52	  14 -> 13
52.79/52.52	Where:
52.79/52.52	  6) f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  7) f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  8) f9#(I29, I30, I31, I32) -> f2#(I29, I30, I31, I32) 
52.79/52.52	  9) f8#(I33, I34, I35, I36) -> f9#(I33, I34, 1 + I35, I36) 
52.79/52.52	  10) f7#(I37, I38, I39, I40) -> f8#(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  11) f7#(I41, I42, I43, I44) -> f8#(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  13) f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  14) f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	
52.79/52.52	We have the following SCCs.
52.79/52.52	  { 6, 7, 13, 14 }
52.79/52.52	
52.79/52.52	DP problem for innermost termination.
52.79/52.52	P =
52.79/52.52	  f10#(I20, I21, I22, I23) -> f2#(I20, I21, I22, I23) 
52.79/52.52	  f2#(I24, I25, I26, I27) -> f10#(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f6#(I50, I51, I52, I53) -> f2#(I50, I51, I52, I53) 
52.79/52.52	  f2#(I54, I55, I56, I57) -> f6#(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	R = 
52.79/52.52	  f14(x1, x2, x3, x4) -> f1(x1, x2, x3, x4) 
52.79/52.52	  f13(I0, I1, I2, I3) -> f2(I0, I1, I2, I3) 
52.79/52.52	  f12(I4, I5, I6, I7) -> f13(I4, I5, 1 + I6, I7) 
52.79/52.52	  f11(I8, I9, I10, I11) -> f12(I8, I9, I10, I11) [1 <= I9]
52.79/52.52	  f11(I12, I13, I14, I15) -> f12(I12, I13, I14, I15) [1 + I13 <= 0]
52.79/52.52	  f2(I16, I17, I18, I19) -> f11(I16, rnd2, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
52.79/52.52	  f10(I20, I21, I22, I23) -> f2(I20, I21, I22, I23) 
52.79/52.52	  f2(I24, I25, I26, I27) -> f10(I24, I28, I26, I27) [0 <= I28 /\ I28 <= 0 /\ I28 = I28 /\ 0 <= -1 - I26 + I27]
52.79/52.52	  f9(I29, I30, I31, I32) -> f2(I29, I30, I31, I32) 
52.79/52.52	  f8(I33, I34, I35, I36) -> f9(I33, I34, 1 + I35, I36) 
52.79/52.52	  f7(I37, I38, I39, I40) -> f8(I37, I38, I39, I40) [1 <= I38]
52.79/52.52	  f7(I41, I42, I43, I44) -> f8(I41, I42, I43, I44) [1 + I42 <= 0]
52.79/52.52	  f2(I45, I46, I47, I48) -> f7(I45, I49, I47, I48) [I49 = I49 /\ I48 <= I47 /\ I47 <= I48 /\ -1 * I47 + I48 <= 0 /\ -1 * I47 + I48 <= 0]
52.79/52.52	  f6(I50, I51, I52, I53) -> f2(I50, I51, I52, I53) 
52.79/52.52	  f2(I54, I55, I56, I57) -> f6(I54, I58, I56, I57) [0 <= I58 /\ I58 <= 0 /\ I58 = I58 /\ I57 <= I56 /\ I56 <= I57 /\ -1 * I56 + I57 <= 0 /\ -1 * I56 + I57 <= 0]
52.79/52.52	  f4(I59, I60, I61, I62) -> f5(rnd1, I60, I61, I62) [rnd1 = rnd1]
52.79/52.52	  f3(I63, I64, I65, I66) -> f4(I63, I64, I65, I66) [1 + I66 <= I65]
52.79/52.52	  f3(I67, I68, I69, I70) -> f4(I67, I68, I69, I70) [1 + I69 <= I70]
52.79/52.52	  f2(I71, I72, I73, I74) -> f3(I71, I72, I73, I74) [-1 * I73 + I74 <= 0 /\ -1 * I73 + I74 <= 0]
52.79/52.52	  f1(I75, I76, I77, I78) -> f2(I75, I76, I77, I78) 
52.79/52.52	
52.79/55.50	EOF