13.80/14.01 MAYBE 13.80/14.01 13.80/14.01 DP problem for innermost termination. 13.80/14.01 P = 13.80/14.01 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12#(I10, I11, I12, I13, I14, I15) -> f11#(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11#(I21, I22, I23, I24, I25, I26) -> f12#(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5#(I32, I33, I34, I35, I36, I37) -> f11#(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10#(I44, I45, I46, I47, I48, I49) -> f9#(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10#(I53, I54, I55, I56, I57, I58) -> f9#(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10#(I62, I63, I64, I65, I66, I67) -> f10#(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9#(I70, I71, I72, I73, I74, I75) -> f10#(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8#(I80, I81, I82, I83, I84, I85) -> f9#(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6#(I93, I94, I95, I96, I97, I98) -> f8#(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5#(I105, I106, I107, I108, I109, I110) -> f8#(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7#(I135, I136, I137, I138, I139, I140) -> f2#(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2#(I144, I145, I146, I147, I148, I149) -> f7#(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6#(I153, I154, I155, I156, I157, I158) -> f5#(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5#(I164, I165, I166, I167, I168, I169) -> f6#(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5#(I176, I177, I178, I179, I180, I181) -> f6#(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3#(I188, I189, I190, I191, I192, I193) -> f5#(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1#(I201, I202, I203, I204, I205, I206) -> f5#(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4#(I212, I213, I214, I215, I216, I217) -> f3#(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1#(I222, I223, I224, I225, I226, I227) -> f3#(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1#(I233, I234, I235, I236, I237, I238) -> f2#(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 R = 13.80/14.01 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12(I0, I1, I2, I3, I4, I5) -> f12(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12(I10, I11, I12, I13, I14, I15) -> f11(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11(I21, I22, I23, I24, I25, I26) -> f12(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5(I32, I33, I34, I35, I36, I37) -> f11(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10(I44, I45, I46, I47, I48, I49) -> f9(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10(I53, I54, I55, I56, I57, I58) -> f9(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10(I62, I63, I64, I65, I66, I67) -> f10(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9(I70, I71, I72, I73, I74, I75) -> f10(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8(I80, I81, I82, I83, I84, I85) -> f9(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6(I93, I94, I95, I96, I97, I98) -> f8(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5(I105, I106, I107, I108, I109, I110) -> f8(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7(I118, I119, I120, I121, I122, I123) -> f7(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7(I127, I128, I129, I130, I131, I132) -> f7(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7(I135, I136, I137, I138, I139, I140) -> f2(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2(I144, I145, I146, I147, I148, I149) -> f7(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6(I153, I154, I155, I156, I157, I158) -> f5(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5(I164, I165, I166, I167, I168, I169) -> f6(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5(I176, I177, I178, I179, I180, I181) -> f6(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3(I188, I189, I190, I191, I192, I193) -> f5(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1(I201, I202, I203, I204, I205, I206) -> f5(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4(I212, I213, I214, I215, I216, I217) -> f3(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1(I222, I223, I224, I225, I226, I227) -> f3(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1(I233, I234, I235, I236, I237, I238) -> f2(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/14.01 The dependency graph for this problem is: 13.80/14.01 0 -> 20, 22, 23 13.80/14.01 1 -> 1, 2 13.80/14.01 2 -> 3 13.80/14.01 3 -> 1, 2 13.80/14.01 4 -> 3 13.80/14.01 5 -> 8 13.80/14.01 6 -> 8 13.80/14.01 7 -> 5, 6, 7 13.80/14.01 8 -> 5, 7 13.80/14.01 9 -> 8 13.80/14.01 10 -> 9 13.80/14.01 11 -> 9 13.80/14.01 12 -> 12, 13, 14 13.80/14.01 13 -> 12, 13, 14 13.80/14.01 14 -> 15 13.80/14.01 15 -> 12, 13, 14 13.80/14.01 16 -> 4, 11, 17, 18 13.80/14.01 17 -> 10, 16 13.80/14.01 18 -> 10, 16 13.80/14.01 19 -> 4, 11, 17, 18 13.80/14.01 20 -> 4, 11, 17, 18 13.80/14.01 21 -> 19 13.80/14.01 22 -> 19 13.80/14.01 23 -> 15 13.80/14.01 Where: 13.80/14.01 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 1) f12#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 2) f12#(I10, I11, I12, I13, I14, I15) -> f11#(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 3) f11#(I21, I22, I23, I24, I25, I26) -> f12#(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 4) f5#(I32, I33, I34, I35, I36, I37) -> f11#(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 5) f10#(I44, I45, I46, I47, I48, I49) -> f9#(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 6) f10#(I53, I54, I55, I56, I57, I58) -> f9#(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 7) f10#(I62, I63, I64, I65, I66, I67) -> f10#(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 8) f9#(I70, I71, I72, I73, I74, I75) -> f10#(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 9) f8#(I80, I81, I82, I83, I84, I85) -> f9#(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 10) f6#(I93, I94, I95, I96, I97, I98) -> f8#(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 11) f5#(I105, I106, I107, I108, I109, I110) -> f8#(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 12) f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 13) f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 14) f7#(I135, I136, I137, I138, I139, I140) -> f2#(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 15) f2#(I144, I145, I146, I147, I148, I149) -> f7#(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 16) f6#(I153, I154, I155, I156, I157, I158) -> f5#(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 17) f5#(I164, I165, I166, I167, I168, I169) -> f6#(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 18) f5#(I176, I177, I178, I179, I180, I181) -> f6#(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 19) f3#(I188, I189, I190, I191, I192, I193) -> f5#(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 20) f1#(I201, I202, I203, I204, I205, I206) -> f5#(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 21) f4#(I212, I213, I214, I215, I216, I217) -> f3#(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 22) f1#(I222, I223, I224, I225, I226, I227) -> f3#(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 23) f1#(I233, I234, I235, I236, I237, I238) -> f2#(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/14.01 We have the following SCCs. 13.80/14.01 { 16, 17, 18 } 13.80/14.01 { 5, 6, 7, 8 } 13.80/14.01 { 1, 2, 3 } 13.80/14.01 { 12, 13, 14, 15 } 13.80/14.01 13.80/14.01 DP problem for innermost termination. 13.80/14.01 P = 13.80/14.01 f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7#(I135, I136, I137, I138, I139, I140) -> f2#(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2#(I144, I145, I146, I147, I148, I149) -> f7#(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 R = 13.80/14.01 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12(I0, I1, I2, I3, I4, I5) -> f12(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12(I10, I11, I12, I13, I14, I15) -> f11(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11(I21, I22, I23, I24, I25, I26) -> f12(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5(I32, I33, I34, I35, I36, I37) -> f11(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10(I44, I45, I46, I47, I48, I49) -> f9(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10(I53, I54, I55, I56, I57, I58) -> f9(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10(I62, I63, I64, I65, I66, I67) -> f10(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9(I70, I71, I72, I73, I74, I75) -> f10(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8(I80, I81, I82, I83, I84, I85) -> f9(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6(I93, I94, I95, I96, I97, I98) -> f8(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5(I105, I106, I107, I108, I109, I110) -> f8(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7(I118, I119, I120, I121, I122, I123) -> f7(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7(I127, I128, I129, I130, I131, I132) -> f7(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7(I135, I136, I137, I138, I139, I140) -> f2(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2(I144, I145, I146, I147, I148, I149) -> f7(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6(I153, I154, I155, I156, I157, I158) -> f5(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5(I164, I165, I166, I167, I168, I169) -> f6(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5(I176, I177, I178, I179, I180, I181) -> f6(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3(I188, I189, I190, I191, I192, I193) -> f5(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1(I201, I202, I203, I204, I205, I206) -> f5(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4(I212, I213, I214, I215, I216, I217) -> f3(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1(I222, I223, I224, I225, I226, I227) -> f3(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1(I233, I234, I235, I236, I237, I238) -> f2(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/14.01 We use the basic value criterion with the projection function NU: 13.80/14.01 NU[f2#(z1,z2,z3,z4,z5,z6)] = z1 13.80/14.01 NU[f7#(z1,z2,z3,z4,z5,z6)] = z1 13.80/14.01 13.80/14.01 This gives the following inequalities: 13.80/14.01 1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1 ==> I118 (>! \union =) I118 13.80/14.01 1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1 ==> I127 (>! \union =) 1 13.80/14.01 1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1 ==> I135 >! I135 - 1 13.80/14.01 -1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1 ==> I144 (>! \union =) I144 13.80/14.01 13.80/14.01 We remove all the strictly oriented dependency pairs. 13.80/14.01 13.80/14.01 DP problem for innermost termination. 13.80/14.01 P = 13.80/14.01 f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f2#(I144, I145, I146, I147, I148, I149) -> f7#(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 R = 13.80/14.01 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12(I0, I1, I2, I3, I4, I5) -> f12(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12(I10, I11, I12, I13, I14, I15) -> f11(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11(I21, I22, I23, I24, I25, I26) -> f12(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5(I32, I33, I34, I35, I36, I37) -> f11(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10(I44, I45, I46, I47, I48, I49) -> f9(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10(I53, I54, I55, I56, I57, I58) -> f9(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10(I62, I63, I64, I65, I66, I67) -> f10(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9(I70, I71, I72, I73, I74, I75) -> f10(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8(I80, I81, I82, I83, I84, I85) -> f9(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6(I93, I94, I95, I96, I97, I98) -> f8(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5(I105, I106, I107, I108, I109, I110) -> f8(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7(I118, I119, I120, I121, I122, I123) -> f7(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7(I127, I128, I129, I130, I131, I132) -> f7(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7(I135, I136, I137, I138, I139, I140) -> f2(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2(I144, I145, I146, I147, I148, I149) -> f7(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6(I153, I154, I155, I156, I157, I158) -> f5(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5(I164, I165, I166, I167, I168, I169) -> f6(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5(I176, I177, I178, I179, I180, I181) -> f6(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3(I188, I189, I190, I191, I192, I193) -> f5(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1(I201, I202, I203, I204, I205, I206) -> f5(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4(I212, I213, I214, I215, I216, I217) -> f3(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1(I222, I223, I224, I225, I226, I227) -> f3(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1(I233, I234, I235, I236, I237, I238) -> f2(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/14.01 The dependency graph for this problem is: 13.80/14.01 12 -> 12, 13 13.80/14.01 13 -> 12, 13 13.80/14.01 15 -> 12, 13 13.80/14.01 Where: 13.80/14.01 12) f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 13) f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 15) f2#(I144, I145, I146, I147, I148, I149) -> f7#(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 13.80/14.01 We have the following SCCs. 13.80/14.01 { 12, 13 } 13.80/14.01 13.80/14.01 DP problem for innermost termination. 13.80/14.01 P = 13.80/14.01 f7#(I118, I119, I120, I121, I122, I123) -> f7#(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7#(I127, I128, I129, I130, I131, I132) -> f7#(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 R = 13.80/14.01 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12(I0, I1, I2, I3, I4, I5) -> f12(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12(I10, I11, I12, I13, I14, I15) -> f11(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11(I21, I22, I23, I24, I25, I26) -> f12(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5(I32, I33, I34, I35, I36, I37) -> f11(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10(I44, I45, I46, I47, I48, I49) -> f9(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10(I53, I54, I55, I56, I57, I58) -> f9(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10(I62, I63, I64, I65, I66, I67) -> f10(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9(I70, I71, I72, I73, I74, I75) -> f10(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8(I80, I81, I82, I83, I84, I85) -> f9(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6(I93, I94, I95, I96, I97, I98) -> f8(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5(I105, I106, I107, I108, I109, I110) -> f8(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7(I118, I119, I120, I121, I122, I123) -> f7(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7(I127, I128, I129, I130, I131, I132) -> f7(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7(I135, I136, I137, I138, I139, I140) -> f2(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2(I144, I145, I146, I147, I148, I149) -> f7(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6(I153, I154, I155, I156, I157, I158) -> f5(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5(I164, I165, I166, I167, I168, I169) -> f6(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5(I176, I177, I178, I179, I180, I181) -> f6(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3(I188, I189, I190, I191, I192, I193) -> f5(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1(I201, I202, I203, I204, I205, I206) -> f5(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4(I212, I213, I214, I215, I216, I217) -> f3(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1(I222, I223, I224, I225, I226, I227) -> f3(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1(I233, I234, I235, I236, I237, I238) -> f2(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/14.01 We use the basic value criterion with the projection function NU: 13.80/14.01 NU[f7#(z1,z2,z3,z4,z5,z6)] = z2 13.80/14.01 13.80/14.01 This gives the following inequalities: 13.80/14.01 1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1 ==> I119 >! I119 - 1 13.80/14.01 1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1 ==> I128 >! I128 - 1 13.80/14.01 13.80/14.01 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 13.80/14.01 13.80/14.01 DP problem for innermost termination. 13.80/14.01 P = 13.80/14.01 f12#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12#(I10, I11, I12, I13, I14, I15) -> f11#(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11#(I21, I22, I23, I24, I25, I26) -> f12#(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 R = 13.80/14.01 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 13.80/14.01 f12(I0, I1, I2, I3, I4, I5) -> f12(I0, I6, I2, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I1 - 1 /\ I6 + 1 <= I1] 13.80/14.01 f12(I10, I11, I12, I13, I14, I15) -> f11(I16, I10, I17, I18, I19, I20) [0 <= I16 - 1 /\ 0 <= I11 - 1] 13.80/14.01 f11(I21, I22, I23, I24, I25, I26) -> f12(I22, I27, I28, I29, I30, I31) [I22 = I23 /\ I22 + 2 <= I21 /\ I24 + 2 <= I21 /\ -1 <= I27 - 1 /\ 0 <= I21 - 1] 13.80/14.01 f5(I32, I33, I34, I35, I36, I37) -> f11(I38, I39, I40, I41, I42, I43) [0 <= y1 - 1 /\ I35 <= 0 /\ I38 <= I33 /\ 0 <= I32 - 1 /\ 0 <= I33 - 1 /\ 0 <= I38 - 1 /\ I41 + 2 <= I33 /\ I39 + 2 <= I33 /\ I39 = I40] 13.80/14.01 f10(I44, I45, I46, I47, I48, I49) -> f9(I44 - 1, I50, I44, I48, I51, I52) [-1 <= I50 - 1 /\ -1 <= I47 - 1 /\ 1 <= I46 - 1] 13.80/14.01 f10(I53, I54, I55, I56, I57, I58) -> f9(I53 - 1, I59, I53, I57, I60, I61) [-1 <= I59 - 1 /\ I56 <= -1 /\ 0 <= I55 - 1] 13.80/14.01 f10(I62, I63, I64, I65, I66, I67) -> f10(I62, I63 - 1, I68, I63, I66, I69) [0 <= I68 - 1 /\ 2 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 + 2 <= I64] 13.80/14.01 f9(I70, I71, I72, I73, I74, I75) -> f10(I70, I76, I77, I78, I73 + 1, I79) [I78 - 1 = I76 /\ 0 <= I77 - 1 /\ 2 <= I71 - 1 /\ I77 + 2 <= I71 /\ -1 <= I72 - 1 /\ -1 <= I73 - 1 /\ -1 <= I78 - 1] 13.80/14.01 f8(I80, I81, I82, I83, I84, I85) -> f9(I86, I87, I88, I89, I90, I91) [-1 <= I92 - 1 /\ -1 <= I88 - 1 /\ I87 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I87 - 1 /\ I81 + 1 <= I80 /\ I88 - 1 = I86 /\ I92 + 1 = I89] 13.80/14.01 f6(I93, I94, I95, I96, I97, I98) -> f8(I99, I98, I100, I101, I102, I103) [I99 <= I96 /\ 0 <= I104 - 1 /\ 0 <= I93 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ 0 <= I99 - 1 /\ I98 + 1 <= I96] 13.80/14.01 f5(I105, I106, I107, I108, I109, I110) -> f8(I111, I112, I113, I114, I115, I116) [0 <= I117 - 1 /\ 0 <= I108 - 1 /\ I111 <= I106 /\ 0 <= I105 - 1 /\ 0 <= I106 - 1 /\ 0 <= I111 - 1 /\ I112 + 1 <= I106] 13.80/14.01 f7(I118, I119, I120, I121, I122, I123) -> f7(I118, I119 - 1, I120, I124, I125, I126) [1 <= I121 - 1 /\ I118 - 1 <= I118 - 1 /\ 0 <= I119 - 1 /\ 0 <= I118 - 1] 13.80/14.01 f7(I127, I128, I129, I130, I131, I132) -> f7(1, I128 - 1, I129, I130, I133, I134) [1 = I127 /\ 1 <= I130 - 1 /\ 0 <= I128 - 1] 13.80/14.01 f7(I135, I136, I137, I138, I139, I140) -> f2(I135 - 1, I137, I138, I141, I142, I143) [1 <= I138 - 1 /\ I135 - 1 <= I135 - 1 /\ 0 <= I136 - 1 /\ 0 <= I135 - 1] 13.80/14.01 f2(I144, I145, I146, I147, I148, I149) -> f7(I144, I150, I145, I146 + 1, I151, I152) [-1 <= I150 - 1 /\ 0 <= I144 - 1 /\ 0 <= I146 - 1 /\ -1 <= I145 - 1] 13.80/14.01 f6(I153, I154, I155, I156, I157, I158) -> f5(I159, I160, I154 - 1, I154, I161, I162) [I159 <= I153 /\ 0 <= I163 - 1 /\ I159 <= I155 /\ I159 <= I156 /\ 0 <= I153 - 1 /\ 0 <= I155 - 1 /\ 0 <= I156 - 1 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ I158 + 1 <= I156] 13.80/14.01 f5(I164, I165, I166, I167, I168, I169) -> f6(I170, I166, I171, I172, I173, I174) [0 <= I175 - 1 /\ 0 <= I167 - 1 /\ I170 <= I164 /\ I170 <= I165 /\ I172 <= I165 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 0 <= I170 - 1 /\ 1 <= I171 - 1 /\ 0 <= I172 - 1 /\ I174 + 1 <= I165] 13.80/14.01 f5(I176, I177, I178, I179, I180, I181) -> f6(I182, I178, I183, I184, I185, I186) [0 <= I187 - 1 /\ 0 <= I179 - 1 /\ I182 <= I176 /\ I182 <= I177 /\ I184 <= I177 /\ 0 <= I176 - 1 /\ 0 <= I177 - 1 /\ 0 <= I182 - 1 /\ -1 <= I183 - 1 /\ 0 <= I184 - 1 /\ I186 + 1 <= I177] 13.80/14.01 f3(I188, I189, I190, I191, I192, I193) -> f5(I194, I195, I196, I197, I198, I199) [0 <= I200 - 1 /\ -1 <= I197 - 1 /\ I194 + 1 <= I188 /\ I195 <= I188 /\ 1 <= I188 - 1 /\ 0 <= I194 - 1 /\ 1 <= I195 - 1 /\ I191 + 2 <= I188 /\ 0 = I190 /\ I197 - 1 = I196 /\ I200 + 1 = I198] 13.80/14.01 f1(I201, I202, I203, I204, I205, I206) -> f5(I207, I208, I209, I210, 2, I211) [I210 - 1 = I209 /\ -1 <= I208 - 1 /\ 0 <= I207 - 1 /\ 0 <= I201 - 1 /\ I208 + 1 <= I201 /\ I207 <= I201 /\ -1 <= I210 - 1 /\ 0 <= I202 - 1] 13.80/14.01 f4(I212, I213, I214, I215, I216, I217) -> f3(I218, I219, 0, I216, I220, I221) [0 = I215 /\ I216 + 2 <= I213 /\ 1 <= I218 - 1 /\ 1 <= I213 - 1 /\ 0 <= I212 - 1 /\ I218 <= I213] 13.80/14.01 f1(I222, I223, I224, I225, I226, I227) -> f3(I228, I223, 0, I229, I230, I231) [0 <= I223 - 1 /\ -1 <= I232 - 1 /\ 0 <= I222 - 1 /\ 1 <= I228 - 1] 13.80/14.01 f1(I233, I234, I235, I236, I237, I238) -> f2(I239, I234, 1, I240, I241, I242) [0 <= I233 - 1 /\ -1 <= I239 - 1 /\ 0 <= I234 - 1] 13.80/14.01 13.80/16.99 EOF