12.75/12.63 MAYBE 12.75/12.63 12.75/12.63 DP problem for innermost termination. 12.75/12.63 P = 12.75/12.63 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 12.75/12.63 f11#(I0, I1, I2, I3, I4, I5) -> f11#(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 f11#(I11, I12, I13, I14, I15, I16) -> f11#(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 f11#(I28, I29, I30, I31, I32, I33) -> f11#(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 f10#(I41, I42, I43, I44, I45, I46) -> f4#(I47, I42, I44 + 1, I48, I49, I50) [-1 <= I51 - 1 /\ I44 <= I51 - 1 /\ I47 <= I41 /\ I47 <= I43 /\ 0 <= I41 - 1 /\ 0 <= I43 - 1 /\ 0 <= I47 - 1] 12.75/12.63 f6#(I52, I53, I54, I55, I56, I57) -> f4#(I58, I53, I55 + 1, I59, I60, I61) [-1 <= I62 - 1 /\ I55 <= I62 - 1 /\ I58 <= I52 /\ I58 <= I54 /\ 0 <= I52 - 1 /\ 0 <= I54 - 1 /\ 0 <= I58 - 1] 12.75/12.63 f5#(I63, I64, I65, I66, I67, I68) -> f11#(I69, 12, I70, I71, I72, I73) [I74 <= I64 /\ -1 <= I74 - 1 /\ I69 <= I63 /\ 0 <= I63 - 1 /\ 0 <= I69 - 1 /\ I74 - 1 = I70] 12.75/12.63 f9#(I75, I76, I77, I78, I79, I80) -> f10#(I81, I76, I82, I78, I83, I84) [-1 <= I82 - 1 /\ 0 <= I81 - 1 /\ -1 <= I77 - 1 /\ 0 <= I75 - 1 /\ I82 <= I77 /\ I81 - 1 <= I77 /\ I80 <= I79 - 1 /\ I81 <= I75] 12.75/12.63 f9#(I85, I86, I87, I88, I89, I90) -> f10#(I91, I86, I92, I88, I93, I94) [-1 <= I92 - 1 /\ 0 <= I91 - 1 /\ -1 <= I87 - 1 /\ 0 <= I85 - 1 /\ I92 <= I87 /\ I91 - 1 <= I87 /\ I89 <= I90 /\ I91 <= I85] 12.75/12.63 f7#(I95, I96, I97, I98, I99, I100) -> f9#(I101, I95, I102, I97, I98, I103) [I95 <= 7 /\ I99 <= I104 - 1 /\ -1 <= I97 - 1 /\ -1 <= I105 - 1 /\ I97 - I106 <= I105 - 1 /\ I101 <= I96 /\ I102 <= I96 /\ 0 <= I96 - 1 /\ 0 <= I101 - 1 /\ 0 <= I102 - 1 /\ I107 + I108 = I103] 12.75/12.63 f7#(I109, I110, I111, I112, I113, I114) -> f9#(I115, I109, I116, I111, I112, I117) [I109 <= 7 /\ I113 <= I118 - 1 /\ -1 <= I111 - 1 /\ -1 <= I119 - 1 /\ I111 - I120 <= I119 - 1 /\ I115 - 1 <= I110 /\ I116 <= I110 /\ -1 <= I110 - 1 /\ 0 <= I115 - 1 /\ -1 <= I116 - 1 /\ I121 + I122 = I117] 12.75/12.63 f8#(I123, I124, I125, I126, I127, I128) -> f8#(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 f8#(I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 f8#(I143, I144, I145, I146, I147, I148) -> f5#(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 f5#(I154, I155, I156, I157, I158, I159) -> f8#(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 f4#(I165, I166, I167, I168, I169, I170) -> f7#(I166, I171, I167, I172, I166 - 1, I173) [I166 <= 7 /\ I167 <= 12 /\ -1 <= I167 - 1 /\ 0 <= I167 - I174 /\ I166 <= I175 - 1 /\ 0 <= I166 - 1 /\ I166 - 1 <= I175 - 1 /\ -1 <= I176 - 1 /\ I167 <= I176 - 1 /\ I171 <= I165 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1] 12.75/12.63 f4#(I177, I178, I179, I180, I181, I182) -> f7#(I178, I183, I179, I184, I178 - 1, I185) [I178 <= 7 /\ I179 <= 12 /\ -1 <= I179 - 1 /\ 0 <= I179 - I186 /\ I178 <= I187 - 1 /\ 0 <= I178 - 1 /\ I178 - 1 <= I187 - 1 /\ -1 <= I188 - 1 /\ I179 <= I188 - 1 /\ 0 <= I177 - 1 /\ -1 <= I183 - 1] 12.75/12.63 f4#(I189, I190, I191, I192, I193, I194) -> f6#(I195, I190, I196, I191, I197, I198) [I190 <= 7 /\ I191 <= 12 /\ -1 <= I191 - 1 /\ I191 - I199 <= -1 /\ I190 <= I200 - 1 /\ 0 <= I190 - 1 /\ I190 - 1 <= I200 - 1 /\ I191 <= I201 - 1 /\ -1 <= I201 - 1 /\ I195 <= I189 /\ I196 <= I189 /\ 0 <= I189 - 1 /\ 0 <= I195 - 1 /\ 0 <= I196 - 1] 12.75/12.63 f4#(I202, I203, I204, I205, I206, I207) -> f6#(I208, I203, I209, I204, I210, I211) [I203 <= 7 /\ I204 <= 12 /\ -1 <= I204 - 1 /\ I204 - I212 <= -1 /\ I203 <= I213 - 1 /\ 0 <= I203 - 1 /\ I203 - 1 <= I213 - 1 /\ I204 <= I214 - 1 /\ -1 <= I214 - 1 /\ I208 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I208 - 1 /\ -1 <= I209 - 1] 12.75/12.63 f3#(I215, I216, I217, I218, I219, I220) -> f5#(I221, 0, I222, I223, I224, I225) [I221 <= I215 /\ I226 <= I216 /\ 0 <= I215 - 1 /\ 0 <= I221 - 1] 12.75/12.63 f4#(I227, I228, I229, I230, I231, I232) -> f3#(I233, I228 + 1, I234, I235, I236, I237) [0 <= I233 - 1 /\ 0 <= I227 - 1 /\ 12 <= I229 - 1 /\ I233 <= I227] 12.75/12.63 f3#(I238, I239, I240, I241, I242, I243) -> f4#(I244, I239, 0, I245, I246, I247) [I244 <= I238 /\ I239 <= I248 - 1 /\ 0 <= I238 - 1 /\ 0 <= I244 - 1] 12.75/12.63 f2#(I249, I250, I251, I252, I253, I254) -> f3#(I255, 1, I256, I257, I258, I259) [0 <= I255 - 1 /\ 0 <= I249 - 1 /\ 12 <= I250 - 1 /\ I255 <= I249] 12.75/12.63 f2#(I260, I261, I262, I263, I264, I265) -> f2#(I266, I261 + 1, I267, I268, I269, I270) [1 <= I261 - 1 /\ I261 <= 12 /\ 0 <= I271 - 1 /\ I261 <= I272 - 1 /\ -1 <= I272 - 1 /\ I266 <= I260 /\ 0 <= I260 - 1 /\ 0 <= I266 - 1] 12.75/12.63 f2#(I273, I274, I275, I276, I277, I278) -> f2#(I279, I274 + 1, I280, I281, I282, I283) [I274 <= 1 /\ I274 <= 12 /\ 0 <= I284 - 1 /\ I274 <= I285 - 1 /\ -1 <= I285 - 1 /\ I279 <= I273 /\ 0 <= I273 - 1 /\ 0 <= I279 - 1] 12.75/12.63 f1#(I286, I287, I288, I289, I290, I291) -> f2#(I292, 0, I293, I294, I295, I296) [0 <= I292 - 1 /\ 0 <= I286 - 1 /\ -1 <= I287 - 1 /\ I292 <= I286] 12.75/12.63 R = 12.75/12.63 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 12.75/12.63 f11(I0, I1, I2, I3, I4, I5) -> f11(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 f11(I11, I12, I13, I14, I15, I16) -> f11(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 f11(I28, I29, I30, I31, I32, I33) -> f11(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 f10(I41, I42, I43, I44, I45, I46) -> f4(I47, I42, I44 + 1, I48, I49, I50) [-1 <= I51 - 1 /\ I44 <= I51 - 1 /\ I47 <= I41 /\ I47 <= I43 /\ 0 <= I41 - 1 /\ 0 <= I43 - 1 /\ 0 <= I47 - 1] 12.75/12.63 f6(I52, I53, I54, I55, I56, I57) -> f4(I58, I53, I55 + 1, I59, I60, I61) [-1 <= I62 - 1 /\ I55 <= I62 - 1 /\ I58 <= I52 /\ I58 <= I54 /\ 0 <= I52 - 1 /\ 0 <= I54 - 1 /\ 0 <= I58 - 1] 12.75/12.63 f5(I63, I64, I65, I66, I67, I68) -> f11(I69, 12, I70, I71, I72, I73) [I74 <= I64 /\ -1 <= I74 - 1 /\ I69 <= I63 /\ 0 <= I63 - 1 /\ 0 <= I69 - 1 /\ I74 - 1 = I70] 12.75/12.63 f9(I75, I76, I77, I78, I79, I80) -> f10(I81, I76, I82, I78, I83, I84) [-1 <= I82 - 1 /\ 0 <= I81 - 1 /\ -1 <= I77 - 1 /\ 0 <= I75 - 1 /\ I82 <= I77 /\ I81 - 1 <= I77 /\ I80 <= I79 - 1 /\ I81 <= I75] 12.75/12.63 f9(I85, I86, I87, I88, I89, I90) -> f10(I91, I86, I92, I88, I93, I94) [-1 <= I92 - 1 /\ 0 <= I91 - 1 /\ -1 <= I87 - 1 /\ 0 <= I85 - 1 /\ I92 <= I87 /\ I91 - 1 <= I87 /\ I89 <= I90 /\ I91 <= I85] 12.75/12.63 f7(I95, I96, I97, I98, I99, I100) -> f9(I101, I95, I102, I97, I98, I103) [I95 <= 7 /\ I99 <= I104 - 1 /\ -1 <= I97 - 1 /\ -1 <= I105 - 1 /\ I97 - I106 <= I105 - 1 /\ I101 <= I96 /\ I102 <= I96 /\ 0 <= I96 - 1 /\ 0 <= I101 - 1 /\ 0 <= I102 - 1 /\ I107 + I108 = I103] 12.75/12.63 f7(I109, I110, I111, I112, I113, I114) -> f9(I115, I109, I116, I111, I112, I117) [I109 <= 7 /\ I113 <= I118 - 1 /\ -1 <= I111 - 1 /\ -1 <= I119 - 1 /\ I111 - I120 <= I119 - 1 /\ I115 - 1 <= I110 /\ I116 <= I110 /\ -1 <= I110 - 1 /\ 0 <= I115 - 1 /\ -1 <= I116 - 1 /\ I121 + I122 = I117] 12.75/12.63 f8(I123, I124, I125, I126, I127, I128) -> f8(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 f8(I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 f8(I143, I144, I145, I146, I147, I148) -> f5(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 f5(I154, I155, I156, I157, I158, I159) -> f8(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 f4(I165, I166, I167, I168, I169, I170) -> f7(I166, I171, I167, I172, I166 - 1, I173) [I166 <= 7 /\ I167 <= 12 /\ -1 <= I167 - 1 /\ 0 <= I167 - I174 /\ I166 <= I175 - 1 /\ 0 <= I166 - 1 /\ I166 - 1 <= I175 - 1 /\ -1 <= I176 - 1 /\ I167 <= I176 - 1 /\ I171 <= I165 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1] 12.75/12.63 f4(I177, I178, I179, I180, I181, I182) -> f7(I178, I183, I179, I184, I178 - 1, I185) [I178 <= 7 /\ I179 <= 12 /\ -1 <= I179 - 1 /\ 0 <= I179 - I186 /\ I178 <= I187 - 1 /\ 0 <= I178 - 1 /\ I178 - 1 <= I187 - 1 /\ -1 <= I188 - 1 /\ I179 <= I188 - 1 /\ 0 <= I177 - 1 /\ -1 <= I183 - 1] 12.75/12.63 f4(I189, I190, I191, I192, I193, I194) -> f6(I195, I190, I196, I191, I197, I198) [I190 <= 7 /\ I191 <= 12 /\ -1 <= I191 - 1 /\ I191 - I199 <= -1 /\ I190 <= I200 - 1 /\ 0 <= I190 - 1 /\ I190 - 1 <= I200 - 1 /\ I191 <= I201 - 1 /\ -1 <= I201 - 1 /\ I195 <= I189 /\ I196 <= I189 /\ 0 <= I189 - 1 /\ 0 <= I195 - 1 /\ 0 <= I196 - 1] 12.75/12.63 f4(I202, I203, I204, I205, I206, I207) -> f6(I208, I203, I209, I204, I210, I211) [I203 <= 7 /\ I204 <= 12 /\ -1 <= I204 - 1 /\ I204 - I212 <= -1 /\ I203 <= I213 - 1 /\ 0 <= I203 - 1 /\ I203 - 1 <= I213 - 1 /\ I204 <= I214 - 1 /\ -1 <= I214 - 1 /\ I208 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I208 - 1 /\ -1 <= I209 - 1] 12.75/12.63 f3(I215, I216, I217, I218, I219, I220) -> f5(I221, 0, I222, I223, I224, I225) [I221 <= I215 /\ I226 <= I216 /\ 0 <= I215 - 1 /\ 0 <= I221 - 1] 12.75/12.63 f4(I227, I228, I229, I230, I231, I232) -> f3(I233, I228 + 1, I234, I235, I236, I237) [0 <= I233 - 1 /\ 0 <= I227 - 1 /\ 12 <= I229 - 1 /\ I233 <= I227] 12.75/12.63 f3(I238, I239, I240, I241, I242, I243) -> f4(I244, I239, 0, I245, I246, I247) [I244 <= I238 /\ I239 <= I248 - 1 /\ 0 <= I238 - 1 /\ 0 <= I244 - 1] 12.75/12.63 f2(I249, I250, I251, I252, I253, I254) -> f3(I255, 1, I256, I257, I258, I259) [0 <= I255 - 1 /\ 0 <= I249 - 1 /\ 12 <= I250 - 1 /\ I255 <= I249] 12.75/12.63 f2(I260, I261, I262, I263, I264, I265) -> f2(I266, I261 + 1, I267, I268, I269, I270) [1 <= I261 - 1 /\ I261 <= 12 /\ 0 <= I271 - 1 /\ I261 <= I272 - 1 /\ -1 <= I272 - 1 /\ I266 <= I260 /\ 0 <= I260 - 1 /\ 0 <= I266 - 1] 12.75/12.63 f2(I273, I274, I275, I276, I277, I278) -> f2(I279, I274 + 1, I280, I281, I282, I283) [I274 <= 1 /\ I274 <= 12 /\ 0 <= I284 - 1 /\ I274 <= I285 - 1 /\ -1 <= I285 - 1 /\ I279 <= I273 /\ 0 <= I273 - 1 /\ 0 <= I279 - 1] 12.75/12.63 f1(I286, I287, I288, I289, I290, I291) -> f2(I292, 0, I293, I294, I295, I296) [0 <= I292 - 1 /\ 0 <= I286 - 1 /\ -1 <= I287 - 1 /\ I292 <= I286] 12.75/12.63 12.75/12.63 The dependency graph for this problem is: 12.75/12.63 0 -> 25 12.75/12.63 1 -> 1, 2, 3 12.75/12.63 2 -> 1, 2, 3 12.75/12.63 3 -> 1, 2, 3 12.75/12.63 4 -> 15, 16, 17, 18, 20 12.75/12.63 5 -> 15, 16, 17, 18, 20 12.75/12.63 6 -> 1, 2, 3 12.75/12.63 7 -> 4 12.75/12.63 8 -> 4 12.75/12.63 9 -> 7, 8 12.75/12.63 10 -> 7, 8 12.75/12.63 11 -> 13 12.75/12.63 12 -> 11, 12 12.75/12.63 13 -> 6, 14 12.75/12.63 14 -> 12 12.75/12.63 15 -> 9, 10 12.75/12.63 16 -> 9, 10 12.75/12.63 17 -> 5 12.75/12.63 18 -> 5 12.75/12.63 19 -> 6, 14 12.75/12.63 20 -> 19, 21 12.75/12.63 21 -> 15, 16, 17, 18 12.75/12.63 22 -> 19, 21 12.75/12.63 23 -> 22, 23 12.75/12.63 24 -> 23, 24 12.75/12.63 25 -> 24 12.75/12.63 Where: 12.75/12.63 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 12.75/12.63 1) f11#(I0, I1, I2, I3, I4, I5) -> f11#(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 2) f11#(I11, I12, I13, I14, I15, I16) -> f11#(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 3) f11#(I28, I29, I30, I31, I32, I33) -> f11#(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 4) f10#(I41, I42, I43, I44, I45, I46) -> f4#(I47, I42, I44 + 1, I48, I49, I50) [-1 <= I51 - 1 /\ I44 <= I51 - 1 /\ I47 <= I41 /\ I47 <= I43 /\ 0 <= I41 - 1 /\ 0 <= I43 - 1 /\ 0 <= I47 - 1] 12.75/12.63 5) f6#(I52, I53, I54, I55, I56, I57) -> f4#(I58, I53, I55 + 1, I59, I60, I61) [-1 <= I62 - 1 /\ I55 <= I62 - 1 /\ I58 <= I52 /\ I58 <= I54 /\ 0 <= I52 - 1 /\ 0 <= I54 - 1 /\ 0 <= I58 - 1] 12.75/12.63 6) f5#(I63, I64, I65, I66, I67, I68) -> f11#(I69, 12, I70, I71, I72, I73) [I74 <= I64 /\ -1 <= I74 - 1 /\ I69 <= I63 /\ 0 <= I63 - 1 /\ 0 <= I69 - 1 /\ I74 - 1 = I70] 12.75/12.63 7) f9#(I75, I76, I77, I78, I79, I80) -> f10#(I81, I76, I82, I78, I83, I84) [-1 <= I82 - 1 /\ 0 <= I81 - 1 /\ -1 <= I77 - 1 /\ 0 <= I75 - 1 /\ I82 <= I77 /\ I81 - 1 <= I77 /\ I80 <= I79 - 1 /\ I81 <= I75] 12.75/12.63 8) f9#(I85, I86, I87, I88, I89, I90) -> f10#(I91, I86, I92, I88, I93, I94) [-1 <= I92 - 1 /\ 0 <= I91 - 1 /\ -1 <= I87 - 1 /\ 0 <= I85 - 1 /\ I92 <= I87 /\ I91 - 1 <= I87 /\ I89 <= I90 /\ I91 <= I85] 12.75/12.63 9) f7#(I95, I96, I97, I98, I99, I100) -> f9#(I101, I95, I102, I97, I98, I103) [I95 <= 7 /\ I99 <= I104 - 1 /\ -1 <= I97 - 1 /\ -1 <= I105 - 1 /\ I97 - I106 <= I105 - 1 /\ I101 <= I96 /\ I102 <= I96 /\ 0 <= I96 - 1 /\ 0 <= I101 - 1 /\ 0 <= I102 - 1 /\ I107 + I108 = I103] 12.75/12.63 10) f7#(I109, I110, I111, I112, I113, I114) -> f9#(I115, I109, I116, I111, I112, I117) [I109 <= 7 /\ I113 <= I118 - 1 /\ -1 <= I111 - 1 /\ -1 <= I119 - 1 /\ I111 - I120 <= I119 - 1 /\ I115 - 1 <= I110 /\ I116 <= I110 /\ -1 <= I110 - 1 /\ 0 <= I115 - 1 /\ -1 <= I116 - 1 /\ I121 + I122 = I117] 12.75/12.63 11) f8#(I123, I124, I125, I126, I127, I128) -> f8#(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 12) f8#(I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 13) f8#(I143, I144, I145, I146, I147, I148) -> f5#(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 14) f5#(I154, I155, I156, I157, I158, I159) -> f8#(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 15) f4#(I165, I166, I167, I168, I169, I170) -> f7#(I166, I171, I167, I172, I166 - 1, I173) [I166 <= 7 /\ I167 <= 12 /\ -1 <= I167 - 1 /\ 0 <= I167 - I174 /\ I166 <= I175 - 1 /\ 0 <= I166 - 1 /\ I166 - 1 <= I175 - 1 /\ -1 <= I176 - 1 /\ I167 <= I176 - 1 /\ I171 <= I165 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1] 12.75/12.63 16) f4#(I177, I178, I179, I180, I181, I182) -> f7#(I178, I183, I179, I184, I178 - 1, I185) [I178 <= 7 /\ I179 <= 12 /\ -1 <= I179 - 1 /\ 0 <= I179 - I186 /\ I178 <= I187 - 1 /\ 0 <= I178 - 1 /\ I178 - 1 <= I187 - 1 /\ -1 <= I188 - 1 /\ I179 <= I188 - 1 /\ 0 <= I177 - 1 /\ -1 <= I183 - 1] 12.75/12.63 17) f4#(I189, I190, I191, I192, I193, I194) -> f6#(I195, I190, I196, I191, I197, I198) [I190 <= 7 /\ I191 <= 12 /\ -1 <= I191 - 1 /\ I191 - I199 <= -1 /\ I190 <= I200 - 1 /\ 0 <= I190 - 1 /\ I190 - 1 <= I200 - 1 /\ I191 <= I201 - 1 /\ -1 <= I201 - 1 /\ I195 <= I189 /\ I196 <= I189 /\ 0 <= I189 - 1 /\ 0 <= I195 - 1 /\ 0 <= I196 - 1] 12.75/12.63 18) f4#(I202, I203, I204, I205, I206, I207) -> f6#(I208, I203, I209, I204, I210, I211) [I203 <= 7 /\ I204 <= 12 /\ -1 <= I204 - 1 /\ I204 - I212 <= -1 /\ I203 <= I213 - 1 /\ 0 <= I203 - 1 /\ I203 - 1 <= I213 - 1 /\ I204 <= I214 - 1 /\ -1 <= I214 - 1 /\ I208 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I208 - 1 /\ -1 <= I209 - 1] 12.75/12.63 19) f3#(I215, I216, I217, I218, I219, I220) -> f5#(I221, 0, I222, I223, I224, I225) [I221 <= I215 /\ I226 <= I216 /\ 0 <= I215 - 1 /\ 0 <= I221 - 1] 12.75/12.63 20) f4#(I227, I228, I229, I230, I231, I232) -> f3#(I233, I228 + 1, I234, I235, I236, I237) [0 <= I233 - 1 /\ 0 <= I227 - 1 /\ 12 <= I229 - 1 /\ I233 <= I227] 12.75/12.63 21) f3#(I238, I239, I240, I241, I242, I243) -> f4#(I244, I239, 0, I245, I246, I247) [I244 <= I238 /\ I239 <= I248 - 1 /\ 0 <= I238 - 1 /\ 0 <= I244 - 1] 12.75/12.63 22) f2#(I249, I250, I251, I252, I253, I254) -> f3#(I255, 1, I256, I257, I258, I259) [0 <= I255 - 1 /\ 0 <= I249 - 1 /\ 12 <= I250 - 1 /\ I255 <= I249] 12.75/12.63 23) f2#(I260, I261, I262, I263, I264, I265) -> f2#(I266, I261 + 1, I267, I268, I269, I270) [1 <= I261 - 1 /\ I261 <= 12 /\ 0 <= I271 - 1 /\ I261 <= I272 - 1 /\ -1 <= I272 - 1 /\ I266 <= I260 /\ 0 <= I260 - 1 /\ 0 <= I266 - 1] 12.75/12.63 24) f2#(I273, I274, I275, I276, I277, I278) -> f2#(I279, I274 + 1, I280, I281, I282, I283) [I274 <= 1 /\ I274 <= 12 /\ 0 <= I284 - 1 /\ I274 <= I285 - 1 /\ -1 <= I285 - 1 /\ I279 <= I273 /\ 0 <= I273 - 1 /\ 0 <= I279 - 1] 12.75/12.63 25) f1#(I286, I287, I288, I289, I290, I291) -> f2#(I292, 0, I293, I294, I295, I296) [0 <= I292 - 1 /\ 0 <= I286 - 1 /\ -1 <= I287 - 1 /\ I292 <= I286] 12.75/12.63 12.75/12.63 We have the following SCCs. 12.75/12.63 { 24 } 12.75/12.63 { 23 } 12.75/12.63 { 4, 5, 7, 8, 9, 10, 15, 16, 17, 18, 20, 21 } 12.75/12.63 { 11, 12, 13, 14 } 12.75/12.63 { 1, 2, 3 } 12.75/12.63 12.75/12.63 DP problem for innermost termination. 12.75/12.63 P = 12.75/12.63 f11#(I0, I1, I2, I3, I4, I5) -> f11#(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 f11#(I11, I12, I13, I14, I15, I16) -> f11#(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 f11#(I28, I29, I30, I31, I32, I33) -> f11#(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 R = 12.75/12.63 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 12.75/12.63 f11(I0, I1, I2, I3, I4, I5) -> f11(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 f11(I11, I12, I13, I14, I15, I16) -> f11(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 f11(I28, I29, I30, I31, I32, I33) -> f11(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 f10(I41, I42, I43, I44, I45, I46) -> f4(I47, I42, I44 + 1, I48, I49, I50) [-1 <= I51 - 1 /\ I44 <= I51 - 1 /\ I47 <= I41 /\ I47 <= I43 /\ 0 <= I41 - 1 /\ 0 <= I43 - 1 /\ 0 <= I47 - 1] 12.75/12.63 f6(I52, I53, I54, I55, I56, I57) -> f4(I58, I53, I55 + 1, I59, I60, I61) [-1 <= I62 - 1 /\ I55 <= I62 - 1 /\ I58 <= I52 /\ I58 <= I54 /\ 0 <= I52 - 1 /\ 0 <= I54 - 1 /\ 0 <= I58 - 1] 12.75/12.63 f5(I63, I64, I65, I66, I67, I68) -> f11(I69, 12, I70, I71, I72, I73) [I74 <= I64 /\ -1 <= I74 - 1 /\ I69 <= I63 /\ 0 <= I63 - 1 /\ 0 <= I69 - 1 /\ I74 - 1 = I70] 12.75/12.63 f9(I75, I76, I77, I78, I79, I80) -> f10(I81, I76, I82, I78, I83, I84) [-1 <= I82 - 1 /\ 0 <= I81 - 1 /\ -1 <= I77 - 1 /\ 0 <= I75 - 1 /\ I82 <= I77 /\ I81 - 1 <= I77 /\ I80 <= I79 - 1 /\ I81 <= I75] 12.75/12.63 f9(I85, I86, I87, I88, I89, I90) -> f10(I91, I86, I92, I88, I93, I94) [-1 <= I92 - 1 /\ 0 <= I91 - 1 /\ -1 <= I87 - 1 /\ 0 <= I85 - 1 /\ I92 <= I87 /\ I91 - 1 <= I87 /\ I89 <= I90 /\ I91 <= I85] 12.75/12.63 f7(I95, I96, I97, I98, I99, I100) -> f9(I101, I95, I102, I97, I98, I103) [I95 <= 7 /\ I99 <= I104 - 1 /\ -1 <= I97 - 1 /\ -1 <= I105 - 1 /\ I97 - I106 <= I105 - 1 /\ I101 <= I96 /\ I102 <= I96 /\ 0 <= I96 - 1 /\ 0 <= I101 - 1 /\ 0 <= I102 - 1 /\ I107 + I108 = I103] 12.75/12.63 f7(I109, I110, I111, I112, I113, I114) -> f9(I115, I109, I116, I111, I112, I117) [I109 <= 7 /\ I113 <= I118 - 1 /\ -1 <= I111 - 1 /\ -1 <= I119 - 1 /\ I111 - I120 <= I119 - 1 /\ I115 - 1 <= I110 /\ I116 <= I110 /\ -1 <= I110 - 1 /\ 0 <= I115 - 1 /\ -1 <= I116 - 1 /\ I121 + I122 = I117] 12.75/12.63 f8(I123, I124, I125, I126, I127, I128) -> f8(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 f8(I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 f8(I143, I144, I145, I146, I147, I148) -> f5(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 f5(I154, I155, I156, I157, I158, I159) -> f8(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 f4(I165, I166, I167, I168, I169, I170) -> f7(I166, I171, I167, I172, I166 - 1, I173) [I166 <= 7 /\ I167 <= 12 /\ -1 <= I167 - 1 /\ 0 <= I167 - I174 /\ I166 <= I175 - 1 /\ 0 <= I166 - 1 /\ I166 - 1 <= I175 - 1 /\ -1 <= I176 - 1 /\ I167 <= I176 - 1 /\ I171 <= I165 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1] 12.75/12.63 f4(I177, I178, I179, I180, I181, I182) -> f7(I178, I183, I179, I184, I178 - 1, I185) [I178 <= 7 /\ I179 <= 12 /\ -1 <= I179 - 1 /\ 0 <= I179 - I186 /\ I178 <= I187 - 1 /\ 0 <= I178 - 1 /\ I178 - 1 <= I187 - 1 /\ -1 <= I188 - 1 /\ I179 <= I188 - 1 /\ 0 <= I177 - 1 /\ -1 <= I183 - 1] 12.75/12.63 f4(I189, I190, I191, I192, I193, I194) -> f6(I195, I190, I196, I191, I197, I198) [I190 <= 7 /\ I191 <= 12 /\ -1 <= I191 - 1 /\ I191 - I199 <= -1 /\ I190 <= I200 - 1 /\ 0 <= I190 - 1 /\ I190 - 1 <= I200 - 1 /\ I191 <= I201 - 1 /\ -1 <= I201 - 1 /\ I195 <= I189 /\ I196 <= I189 /\ 0 <= I189 - 1 /\ 0 <= I195 - 1 /\ 0 <= I196 - 1] 12.75/12.63 f4(I202, I203, I204, I205, I206, I207) -> f6(I208, I203, I209, I204, I210, I211) [I203 <= 7 /\ I204 <= 12 /\ -1 <= I204 - 1 /\ I204 - I212 <= -1 /\ I203 <= I213 - 1 /\ 0 <= I203 - 1 /\ I203 - 1 <= I213 - 1 /\ I204 <= I214 - 1 /\ -1 <= I214 - 1 /\ I208 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I208 - 1 /\ -1 <= I209 - 1] 12.75/12.63 f3(I215, I216, I217, I218, I219, I220) -> f5(I221, 0, I222, I223, I224, I225) [I221 <= I215 /\ I226 <= I216 /\ 0 <= I215 - 1 /\ 0 <= I221 - 1] 12.75/12.63 f4(I227, I228, I229, I230, I231, I232) -> f3(I233, I228 + 1, I234, I235, I236, I237) [0 <= I233 - 1 /\ 0 <= I227 - 1 /\ 12 <= I229 - 1 /\ I233 <= I227] 12.75/12.63 f3(I238, I239, I240, I241, I242, I243) -> f4(I244, I239, 0, I245, I246, I247) [I244 <= I238 /\ I239 <= I248 - 1 /\ 0 <= I238 - 1 /\ 0 <= I244 - 1] 12.75/12.63 f2(I249, I250, I251, I252, I253, I254) -> f3(I255, 1, I256, I257, I258, I259) [0 <= I255 - 1 /\ 0 <= I249 - 1 /\ 12 <= I250 - 1 /\ I255 <= I249] 12.75/12.63 f2(I260, I261, I262, I263, I264, I265) -> f2(I266, I261 + 1, I267, I268, I269, I270) [1 <= I261 - 1 /\ I261 <= 12 /\ 0 <= I271 - 1 /\ I261 <= I272 - 1 /\ -1 <= I272 - 1 /\ I266 <= I260 /\ 0 <= I260 - 1 /\ 0 <= I266 - 1] 12.75/12.63 f2(I273, I274, I275, I276, I277, I278) -> f2(I279, I274 + 1, I280, I281, I282, I283) [I274 <= 1 /\ I274 <= 12 /\ 0 <= I284 - 1 /\ I274 <= I285 - 1 /\ -1 <= I285 - 1 /\ I279 <= I273 /\ 0 <= I273 - 1 /\ 0 <= I279 - 1] 12.75/12.63 f1(I286, I287, I288, I289, I290, I291) -> f2(I292, 0, I293, I294, I295, I296) [0 <= I292 - 1 /\ 0 <= I286 - 1 /\ -1 <= I287 - 1 /\ I292 <= I286] 12.75/12.63 12.75/12.63 We use the basic value criterion with the projection function NU: 12.75/12.63 NU[f11#(z1,z2,z3,z4,z5,z6)] = z3 12.75/12.63 12.75/12.63 This gives the following inequalities: 12.75/12.63 I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7 ==> I2 >! I2 - 1 12.75/12.63 I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18 ==> I13 >! I13 - 1 12.75/12.63 I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1 ==> I30 >! I30 - 1 12.75/12.63 12.75/12.63 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 12.75/12.63 12.75/12.63 DP problem for innermost termination. 12.75/12.63 P = 12.75/12.63 f8#(I123, I124, I125, I126, I127, I128) -> f8#(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 f8#(I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 f8#(I143, I144, I145, I146, I147, I148) -> f5#(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 f5#(I154, I155, I156, I157, I158, I159) -> f8#(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 R = 12.75/12.63 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 12.75/12.63 f11(I0, I1, I2, I3, I4, I5) -> f11(I6, I7, I2 - 1, I8, I9, I10) [I2 <= y1 - 1 /\ 0 <= I2 - 1 /\ -1 <= y2 - 1 /\ I1 <= y2 - 1 /\ I2 - 1 <= y1 - 1 /\ -1 <= y3 - 1 /\ I1 <= y3 - 1 /\ y4 <= y5 - 1 /\ I2 <= 7 /\ -1 <= I1 - 1 /\ I6 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I6 - 1 /\ I1 - y6 = I7] 12.75/12.63 f11(I11, I12, I13, I14, I15, I16) -> f11(I17, I18, I13 - 1, I19, I20, I21) [I13 <= I22 - 1 /\ 0 <= I13 - 1 /\ -1 <= I23 - 1 /\ I12 <= I23 - 1 /\ I13 - 1 <= I22 - 1 /\ -1 <= I24 - 1 /\ I12 <= I24 - 1 /\ I25 <= I26 - 1 /\ I13 <= 7 /\ -1 <= I12 - 1 /\ I17 <= I11 /\ 0 <= I11 - 1 /\ 0 <= I17 - 1 /\ I12 - I27 = I18] 12.75/12.63 f11(I28, I29, I30, I31, I32, I33) -> f11(I34, I29, I30 - 1, I35, I36, I37) [I30 <= I38 - 1 /\ 0 <= I30 - 1 /\ -1 <= I39 - 1 /\ I29 <= I39 - 1 /\ I30 - 1 <= I38 - 1 /\ I29 <= I40 - 1 /\ -1 <= I40 - 1 /\ I34 <= I28 /\ 0 <= I28 - 1 /\ 0 <= I34 - 1] 12.75/12.63 f10(I41, I42, I43, I44, I45, I46) -> f4(I47, I42, I44 + 1, I48, I49, I50) [-1 <= I51 - 1 /\ I44 <= I51 - 1 /\ I47 <= I41 /\ I47 <= I43 /\ 0 <= I41 - 1 /\ 0 <= I43 - 1 /\ 0 <= I47 - 1] 12.75/12.63 f6(I52, I53, I54, I55, I56, I57) -> f4(I58, I53, I55 + 1, I59, I60, I61) [-1 <= I62 - 1 /\ I55 <= I62 - 1 /\ I58 <= I52 /\ I58 <= I54 /\ 0 <= I52 - 1 /\ 0 <= I54 - 1 /\ 0 <= I58 - 1] 12.75/12.63 f5(I63, I64, I65, I66, I67, I68) -> f11(I69, 12, I70, I71, I72, I73) [I74 <= I64 /\ -1 <= I74 - 1 /\ I69 <= I63 /\ 0 <= I63 - 1 /\ 0 <= I69 - 1 /\ I74 - 1 = I70] 12.75/12.63 f9(I75, I76, I77, I78, I79, I80) -> f10(I81, I76, I82, I78, I83, I84) [-1 <= I82 - 1 /\ 0 <= I81 - 1 /\ -1 <= I77 - 1 /\ 0 <= I75 - 1 /\ I82 <= I77 /\ I81 - 1 <= I77 /\ I80 <= I79 - 1 /\ I81 <= I75] 12.75/12.63 f9(I85, I86, I87, I88, I89, I90) -> f10(I91, I86, I92, I88, I93, I94) [-1 <= I92 - 1 /\ 0 <= I91 - 1 /\ -1 <= I87 - 1 /\ 0 <= I85 - 1 /\ I92 <= I87 /\ I91 - 1 <= I87 /\ I89 <= I90 /\ I91 <= I85] 12.75/12.63 f7(I95, I96, I97, I98, I99, I100) -> f9(I101, I95, I102, I97, I98, I103) [I95 <= 7 /\ I99 <= I104 - 1 /\ -1 <= I97 - 1 /\ -1 <= I105 - 1 /\ I97 - I106 <= I105 - 1 /\ I101 <= I96 /\ I102 <= I96 /\ 0 <= I96 - 1 /\ 0 <= I101 - 1 /\ 0 <= I102 - 1 /\ I107 + I108 = I103] 12.75/12.63 f7(I109, I110, I111, I112, I113, I114) -> f9(I115, I109, I116, I111, I112, I117) [I109 <= 7 /\ I113 <= I118 - 1 /\ -1 <= I111 - 1 /\ -1 <= I119 - 1 /\ I111 - I120 <= I119 - 1 /\ I115 - 1 <= I110 /\ I116 <= I110 /\ -1 <= I110 - 1 /\ 0 <= I115 - 1 /\ -1 <= I116 - 1 /\ I121 + I122 = I117] 12.75/12.63 f8(I123, I124, I125, I126, I127, I128) -> f8(I129, I124, 13, I130, I131, I132) [12 = I125 /\ 0 <= I129 - 1 /\ 0 <= I123 - 1 /\ I129 <= I123] 12.75/12.63 f8(I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I135 + 1, I140, I141, I142) [0 <= I139 - 1 /\ 0 <= I133 - 1 /\ I139 <= I133 /\ I135 <= 11 /\ I135 <= 12] 12.75/12.63 f8(I143, I144, I145, I146, I147, I148) -> f5(I149, I144 + 1, I150, I151, I152, I153) [0 <= I149 - 1 /\ 0 <= I143 - 1 /\ 12 <= I145 - 1 /\ I149 <= I143] 12.75/12.63 f5(I154, I155, I156, I157, I158, I159) -> f8(I160, I155, 0, I161, I162, I163) [I160 <= I154 /\ I155 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I160 - 1] 12.75/12.63 f4(I165, I166, I167, I168, I169, I170) -> f7(I166, I171, I167, I172, I166 - 1, I173) [I166 <= 7 /\ I167 <= 12 /\ -1 <= I167 - 1 /\ 0 <= I167 - I174 /\ I166 <= I175 - 1 /\ 0 <= I166 - 1 /\ I166 - 1 <= I175 - 1 /\ -1 <= I176 - 1 /\ I167 <= I176 - 1 /\ I171 <= I165 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1] 12.75/12.63 f4(I177, I178, I179, I180, I181, I182) -> f7(I178, I183, I179, I184, I178 - 1, I185) [I178 <= 7 /\ I179 <= 12 /\ -1 <= I179 - 1 /\ 0 <= I179 - I186 /\ I178 <= I187 - 1 /\ 0 <= I178 - 1 /\ I178 - 1 <= I187 - 1 /\ -1 <= I188 - 1 /\ I179 <= I188 - 1 /\ 0 <= I177 - 1 /\ -1 <= I183 - 1] 12.75/12.63 f4(I189, I190, I191, I192, I193, I194) -> f6(I195, I190, I196, I191, I197, I198) [I190 <= 7 /\ I191 <= 12 /\ -1 <= I191 - 1 /\ I191 - I199 <= -1 /\ I190 <= I200 - 1 /\ 0 <= I190 - 1 /\ I190 - 1 <= I200 - 1 /\ I191 <= I201 - 1 /\ -1 <= I201 - 1 /\ I195 <= I189 /\ I196 <= I189 /\ 0 <= I189 - 1 /\ 0 <= I195 - 1 /\ 0 <= I196 - 1] 12.75/12.63 f4(I202, I203, I204, I205, I206, I207) -> f6(I208, I203, I209, I204, I210, I211) [I203 <= 7 /\ I204 <= 12 /\ -1 <= I204 - 1 /\ I204 - I212 <= -1 /\ I203 <= I213 - 1 /\ 0 <= I203 - 1 /\ I203 - 1 <= I213 - 1 /\ I204 <= I214 - 1 /\ -1 <= I214 - 1 /\ I208 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I208 - 1 /\ -1 <= I209 - 1] 12.75/12.63 f3(I215, I216, I217, I218, I219, I220) -> f5(I221, 0, I222, I223, I224, I225) [I221 <= I215 /\ I226 <= I216 /\ 0 <= I215 - 1 /\ 0 <= I221 - 1] 12.75/12.63 f4(I227, I228, I229, I230, I231, I232) -> f3(I233, I228 + 1, I234, I235, I236, I237) [0 <= I233 - 1 /\ 0 <= I227 - 1 /\ 12 <= I229 - 1 /\ I233 <= I227] 12.75/12.63 f3(I238, I239, I240, I241, I242, I243) -> f4(I244, I239, 0, I245, I246, I247) [I244 <= I238 /\ I239 <= I248 - 1 /\ 0 <= I238 - 1 /\ 0 <= I244 - 1] 12.75/12.63 f2(I249, I250, I251, I252, I253, I254) -> f3(I255, 1, I256, I257, I258, I259) [0 <= I255 - 1 /\ 0 <= I249 - 1 /\ 12 <= I250 - 1 /\ I255 <= I249] 12.75/12.63 f2(I260, I261, I262, I263, I264, I265) -> f2(I266, I261 + 1, I267, I268, I269, I270) [1 <= I261 - 1 /\ I261 <= 12 /\ 0 <= I271 - 1 /\ I261 <= I272 - 1 /\ -1 <= I272 - 1 /\ I266 <= I260 /\ 0 <= I260 - 1 /\ 0 <= I266 - 1] 12.75/12.63 f2(I273, I274, I275, I276, I277, I278) -> f2(I279, I274 + 1, I280, I281, I282, I283) [I274 <= 1 /\ I274 <= 12 /\ 0 <= I284 - 1 /\ I274 <= I285 - 1 /\ -1 <= I285 - 1 /\ I279 <= I273 /\ 0 <= I273 - 1 /\ 0 <= I279 - 1] 12.75/12.63 f1(I286, I287, I288, I289, I290, I291) -> f2(I292, 0, I293, I294, I295, I296) [0 <= I292 - 1 /\ 0 <= I286 - 1 /\ -1 <= I287 - 1 /\ I292 <= I286] 12.75/12.63 12.75/15.61 EOF