/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) f13#(I0, I1, I2, I3) -> f13#(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] f11#(I8, I9, I10, I11) -> f13#(I12, I13, I14, I15) [I14 + 2 <= I8 /\ -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I8 - 1 /\ I13 + 1 <= I8 /\ I12 <= I8] f12#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] f12#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] f12#(I32, I33, I34, I35) -> f11#(I36, I37, I38, I39) [-1 <= I36 - 1 /\ -1 <= I33 - 1 /\ -1 <= I32 - 1 /\ I36 <= I33] f10#(I40, I41, I42, I43) -> f12#(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] f10#(I48, I49, I50, I51) -> f12#(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] f10#(I56, I57, I58, I59) -> f11#(I60, I61, I62, I63) [-1 <= I60 - 1 /\ 0 <= I58 - 1 /\ 0 <= I57 - 1 /\ 0 <= I56 - 1 /\ I60 + 1 <= I58 /\ I60 + 1 <= I56] f4#(I64, I65, I66, I67) -> f10#(I68, I69, I70, I71) [I67 + 2 <= I65 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ I70 <= I65 /\ I68 <= I65] f4#(I72, I73, I74, I75) -> f10#(I76, I77, I78, I79) [I76 <= I73 /\ 0 <= y1 - 1 /\ I77 + 1 <= I72 /\ I77 + 1 <= I73 /\ I78 <= I73 /\ 0 <= I72 - 1 /\ 0 <= I73 - 1 /\ 0 <= I76 - 1 /\ -1 <= I77 - 1 /\ 0 <= I78 - 1 /\ I75 + 2 <= I73] f6#(I80, I81, I82, I83) -> f10#(I84, I85, I86, I87) [I82 + 2 <= I81 /\ -1 <= I86 - 1 /\ 0 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I86 + 1 <= I81 /\ I86 + 1 <= I80 /\ I85 <= I81 /\ I84 + 1 <= I81 /\ I84 + 1 <= I80] f2#(I88, I89, I90, I91) -> f10#(I92, I93, I94, I95) [0 <= I96 - 1 /\ 0 <= I89 - 1 /\ I92 + 1 <= I88 /\ I93 + 1 <= I88 /\ I94 + 1 <= I88 /\ 0 <= I88 - 1 /\ -1 <= I92 - 1 /\ -1 <= I93 - 1 /\ -1 <= I94 - 1] f9#(I97, I98, I99, I100) -> f9#(I101, I102, I99 - 1, I100 + 1) [0 <= I99 - 1 /\ 0 <= I103 - 1 /\ -1 <= I100 - 1 /\ I101 - 2 <= I97 /\ I101 - 2 <= I98 /\ I102 - 2 <= I97 /\ I102 - 2 <= I98 /\ 1 <= I97 - 1 /\ 1 <= I98 - 1 /\ 3 <= I101 - 1 /\ 3 <= I102 - 1] f9#(I104, I105, I106, I107) -> f9#(I108, I109, I106 - 1, I107 + 1) [3 <= I109 - 1 /\ 3 <= I108 - 1 /\ 1 <= I105 - 1 /\ 1 <= I104 - 1 /\ I109 - 2 <= I105 /\ I109 - 2 <= I104 /\ I108 - 2 <= I105 /\ I108 - 2 <= I104 /\ 0 <= I106 - 1 /\ -1 <= I107 - 1] f9#(I110, I111, I112, I113) -> f9#(I114, I115, I112 - 1, I113 + 1) [0 <= I115 - 1 /\ 0 <= I114 - 1 /\ 1 <= I111 - 1 /\ 0 <= I110 - 1 /\ 0 <= I112 - 1 /\ -1 <= I113 - 1] f9#(I116, I117, I118, I119) -> f9#(I120, I121, I118 - 1, I119 + 1) [0 <= I118 - 1 /\ 0 <= I122 - 1 /\ -1 <= I119 - 1 /\ 0 <= I116 - 1 /\ 1 <= I117 - 1 /\ 0 <= I120 - 1 /\ 0 <= I121 - 1] f9#(I123, I124, I125, I126) -> f9#(I127, I128, I125 - 1, I126 + 1) [0 <= I125 - 1 /\ 0 <= I129 - 1 /\ -1 <= I126 - 1 /\ I127 <= I123 /\ I128 + 2 <= I124 /\ 0 <= I123 - 1 /\ 2 <= I124 - 1 /\ 0 <= I127 - 1 /\ 0 <= I128 - 1] f9#(I130, I131, I132, I133) -> f9#(I134, I135, I132 - 1, I133 + 1) [0 <= I135 - 1 /\ 0 <= I134 - 1 /\ 2 <= I131 - 1 /\ 0 <= I130 - 1 /\ I135 + 2 <= I131 /\ I134 <= I130 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1] f8#(I136, I137, I138, I139) -> f9#(I140, I141, I142, I143) [0 <= I142 - 1 /\ -1 <= I144 - 1 /\ 1 <= I141 - 1 /\ 1 <= I140 - 1 /\ I144 + 1 = I143] f4#(I145, I146, I147, I148) -> f8#(I149, I150, I151, I152) [0 <= I145 - 1 /\ -1 <= I153 - 1 /\ 0 <= I146 - 1 /\ I148 + 2 <= I146] f2#(I154, I155, I156, I157) -> f8#(I158, I159, I160, I161) [-1 <= I162 - 1 /\ 0 <= I155 - 1 /\ 0 <= I154 - 1] f3#(I163, I164, I165, I166) -> f8#(I167, I168, I169, I170) [-1 <= I164 - 1 /\ 0 <= I163 - 1] f7#(I171, I172, I173, I174) -> f6#(I175, I176, I173, I177) [I173 + 2 <= I172 /\ 1 <= I176 - 1 /\ 0 <= I175 - 1 /\ 1 <= I172 - 1 /\ 0 <= I171 - 1 /\ I176 <= I172 /\ I175 + 1 <= I172 /\ I175 <= I171] f2#(I178, I179, I180, I181) -> f6#(I182, I183, I184, I185) [0 <= I183 - 1 /\ 0 <= I182 - 1 /\ 0 <= I178 - 1 /\ 0 <= I179 - 1 /\ I182 <= I178] f5#(I186, I187, I188, I189) -> f4#(I190, I191, I188, I189) [I189 + 2 <= I187 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1 /\ 1 <= I187 - 1 /\ 0 <= I186 - 1 /\ I191 <= I187 /\ I190 + 1 <= I187 /\ I190 <= I186] f3#(I192, I193, I194, I195) -> f4#(I196, I197, I198, I199) [0 <= I197 - 1 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ I196 <= I192] f3#(I200, I201, I202, I203) -> f2#(I204, I205, I206, I207) [0 <= I204 - 1 /\ 0 <= I200 - 1 /\ I204 <= I200] f1#(I208, I209, I210, I211) -> f2#(I212, I209, I213, I214) [0 <= I212 - 1 /\ 0 <= I208 - 1 /\ I212 <= I208] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f13(I0, I1, I2, I3) -> f13(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] f11(I8, I9, I10, I11) -> f13(I12, I13, I14, I15) [I14 + 2 <= I8 /\ -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I8 - 1 /\ I13 + 1 <= I8 /\ I12 <= I8] f12(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] f12(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] f12(I32, I33, I34, I35) -> f11(I36, I37, I38, I39) [-1 <= I36 - 1 /\ -1 <= I33 - 1 /\ -1 <= I32 - 1 /\ I36 <= I33] f10(I40, I41, I42, I43) -> f12(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] f10(I48, I49, I50, I51) -> f12(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] f10(I56, I57, I58, I59) -> f11(I60, I61, I62, I63) [-1 <= I60 - 1 /\ 0 <= I58 - 1 /\ 0 <= I57 - 1 /\ 0 <= I56 - 1 /\ I60 + 1 <= I58 /\ I60 + 1 <= I56] f4(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [I67 + 2 <= I65 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ I70 <= I65 /\ I68 <= I65] f4(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [I76 <= I73 /\ 0 <= y1 - 1 /\ I77 + 1 <= I72 /\ I77 + 1 <= I73 /\ I78 <= I73 /\ 0 <= I72 - 1 /\ 0 <= I73 - 1 /\ 0 <= I76 - 1 /\ -1 <= I77 - 1 /\ 0 <= I78 - 1 /\ I75 + 2 <= I73] f6(I80, I81, I82, I83) -> f10(I84, I85, I86, I87) [I82 + 2 <= I81 /\ -1 <= I86 - 1 /\ 0 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I86 + 1 <= I81 /\ I86 + 1 <= I80 /\ I85 <= I81 /\ I84 + 1 <= I81 /\ I84 + 1 <= I80] f2(I88, I89, I90, I91) -> f10(I92, I93, I94, I95) [0 <= I96 - 1 /\ 0 <= I89 - 1 /\ I92 + 1 <= I88 /\ I93 + 1 <= I88 /\ I94 + 1 <= I88 /\ 0 <= I88 - 1 /\ -1 <= I92 - 1 /\ -1 <= I93 - 1 /\ -1 <= I94 - 1] f9(I97, I98, I99, I100) -> f9(I101, I102, I99 - 1, I100 + 1) [0 <= I99 - 1 /\ 0 <= I103 - 1 /\ -1 <= I100 - 1 /\ I101 - 2 <= I97 /\ I101 - 2 <= I98 /\ I102 - 2 <= I97 /\ I102 - 2 <= I98 /\ 1 <= I97 - 1 /\ 1 <= I98 - 1 /\ 3 <= I101 - 1 /\ 3 <= I102 - 1] f9(I104, I105, I106, I107) -> f9(I108, I109, I106 - 1, I107 + 1) [3 <= I109 - 1 /\ 3 <= I108 - 1 /\ 1 <= I105 - 1 /\ 1 <= I104 - 1 /\ I109 - 2 <= I105 /\ I109 - 2 <= I104 /\ I108 - 2 <= I105 /\ I108 - 2 <= I104 /\ 0 <= I106 - 1 /\ -1 <= I107 - 1] f9(I110, I111, I112, I113) -> f9(I114, I115, I112 - 1, I113 + 1) [0 <= I115 - 1 /\ 0 <= I114 - 1 /\ 1 <= I111 - 1 /\ 0 <= I110 - 1 /\ 0 <= I112 - 1 /\ -1 <= I113 - 1] f9(I116, I117, I118, I119) -> f9(I120, I121, I118 - 1, I119 + 1) [0 <= I118 - 1 /\ 0 <= I122 - 1 /\ -1 <= I119 - 1 /\ 0 <= I116 - 1 /\ 1 <= I117 - 1 /\ 0 <= I120 - 1 /\ 0 <= I121 - 1] f9(I123, I124, I125, I126) -> f9(I127, I128, I125 - 1, I126 + 1) [0 <= I125 - 1 /\ 0 <= I129 - 1 /\ -1 <= I126 - 1 /\ I127 <= I123 /\ I128 + 2 <= I124 /\ 0 <= I123 - 1 /\ 2 <= I124 - 1 /\ 0 <= I127 - 1 /\ 0 <= I128 - 1] f9(I130, I131, I132, I133) -> f9(I134, I135, I132 - 1, I133 + 1) [0 <= I135 - 1 /\ 0 <= I134 - 1 /\ 2 <= I131 - 1 /\ 0 <= I130 - 1 /\ I135 + 2 <= I131 /\ I134 <= I130 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1] f8(I136, I137, I138, I139) -> f9(I140, I141, I142, I143) [0 <= I142 - 1 /\ -1 <= I144 - 1 /\ 1 <= I141 - 1 /\ 1 <= I140 - 1 /\ I144 + 1 = I143] f4(I145, I146, I147, I148) -> f8(I149, I150, I151, I152) [0 <= I145 - 1 /\ -1 <= I153 - 1 /\ 0 <= I146 - 1 /\ I148 + 2 <= I146] f2(I154, I155, I156, I157) -> f8(I158, I159, I160, I161) [-1 <= I162 - 1 /\ 0 <= I155 - 1 /\ 0 <= I154 - 1] f3(I163, I164, I165, I166) -> f8(I167, I168, I169, I170) [-1 <= I164 - 1 /\ 0 <= I163 - 1] f7(I171, I172, I173, I174) -> f6(I175, I176, I173, I177) [I173 + 2 <= I172 /\ 1 <= I176 - 1 /\ 0 <= I175 - 1 /\ 1 <= I172 - 1 /\ 0 <= I171 - 1 /\ I176 <= I172 /\ I175 + 1 <= I172 /\ I175 <= I171] f2(I178, I179, I180, I181) -> f6(I182, I183, I184, I185) [0 <= I183 - 1 /\ 0 <= I182 - 1 /\ 0 <= I178 - 1 /\ 0 <= I179 - 1 /\ I182 <= I178] f5(I186, I187, I188, I189) -> f4(I190, I191, I188, I189) [I189 + 2 <= I187 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1 /\ 1 <= I187 - 1 /\ 0 <= I186 - 1 /\ I191 <= I187 /\ I190 + 1 <= I187 /\ I190 <= I186] f3(I192, I193, I194, I195) -> f4(I196, I197, I198, I199) [0 <= I197 - 1 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ I196 <= I192] f3(I200, I201, I202, I203) -> f2(I204, I205, I206, I207) [0 <= I204 - 1 /\ 0 <= I200 - 1 /\ I204 <= I200] f1(I208, I209, I210, I211) -> f2(I212, I209, I213, I214) [0 <= I212 - 1 /\ 0 <= I208 - 1 /\ I212 <= I208] The dependency graph for this problem is: 0 -> 22, 26, 27 1 -> 1 2 -> 1 3 -> 6, 7, 8 4 -> 6, 7, 8 5 -> 2 6 -> 3, 4, 5 7 -> 3, 4, 5 8 -> 2 9 -> 6, 7, 8 10 -> 6, 7, 8 11 -> 6, 7, 8 12 -> 6, 7, 8 13 -> 13, 14, 15, 16, 17, 18 14 -> 13, 14, 15, 16, 17, 18 15 -> 13, 14, 15, 16, 17, 18 16 -> 13, 14, 15, 16, 17, 18 17 -> 13, 14, 15, 16, 17, 18 18 -> 13, 14, 15, 16, 17, 18 19 -> 13, 14, 15, 16, 17, 18 20 -> 19 21 -> 19 22 -> 19 23 -> 11 24 -> 11 25 -> 9, 10, 20 26 -> 9, 10, 20 27 -> 12, 21, 24 28 -> 12, 21, 24 Where: 0) init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 1) f13#(I0, I1, I2, I3) -> f13#(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 2) f11#(I8, I9, I10, I11) -> f13#(I12, I13, I14, I15) [I14 + 2 <= I8 /\ -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I8 - 1 /\ I13 + 1 <= I8 /\ I12 <= I8] 3) f12#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] 4) f12#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] 5) f12#(I32, I33, I34, I35) -> f11#(I36, I37, I38, I39) [-1 <= I36 - 1 /\ -1 <= I33 - 1 /\ -1 <= I32 - 1 /\ I36 <= I33] 6) f10#(I40, I41, I42, I43) -> f12#(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] 7) f10#(I48, I49, I50, I51) -> f12#(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] 8) f10#(I56, I57, I58, I59) -> f11#(I60, I61, I62, I63) [-1 <= I60 - 1 /\ 0 <= I58 - 1 /\ 0 <= I57 - 1 /\ 0 <= I56 - 1 /\ I60 + 1 <= I58 /\ I60 + 1 <= I56] 9) f4#(I64, I65, I66, I67) -> f10#(I68, I69, I70, I71) [I67 + 2 <= I65 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ I70 <= I65 /\ I68 <= I65] 10) f4#(I72, I73, I74, I75) -> f10#(I76, I77, I78, I79) [I76 <= I73 /\ 0 <= y1 - 1 /\ I77 + 1 <= I72 /\ I77 + 1 <= I73 /\ I78 <= I73 /\ 0 <= I72 - 1 /\ 0 <= I73 - 1 /\ 0 <= I76 - 1 /\ -1 <= I77 - 1 /\ 0 <= I78 - 1 /\ I75 + 2 <= I73] 11) f6#(I80, I81, I82, I83) -> f10#(I84, I85, I86, I87) [I82 + 2 <= I81 /\ -1 <= I86 - 1 /\ 0 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I86 + 1 <= I81 /\ I86 + 1 <= I80 /\ I85 <= I81 /\ I84 + 1 <= I81 /\ I84 + 1 <= I80] 12) f2#(I88, I89, I90, I91) -> f10#(I92, I93, I94, I95) [0 <= I96 - 1 /\ 0 <= I89 - 1 /\ I92 + 1 <= I88 /\ I93 + 1 <= I88 /\ I94 + 1 <= I88 /\ 0 <= I88 - 1 /\ -1 <= I92 - 1 /\ -1 <= I93 - 1 /\ -1 <= I94 - 1] 13) f9#(I97, I98, I99, I100) -> f9#(I101, I102, I99 - 1, I100 + 1) [0 <= I99 - 1 /\ 0 <= I103 - 1 /\ -1 <= I100 - 1 /\ I101 - 2 <= I97 /\ I101 - 2 <= I98 /\ I102 - 2 <= I97 /\ I102 - 2 <= I98 /\ 1 <= I97 - 1 /\ 1 <= I98 - 1 /\ 3 <= I101 - 1 /\ 3 <= I102 - 1] 14) f9#(I104, I105, I106, I107) -> f9#(I108, I109, I106 - 1, I107 + 1) [3 <= I109 - 1 /\ 3 <= I108 - 1 /\ 1 <= I105 - 1 /\ 1 <= I104 - 1 /\ I109 - 2 <= I105 /\ I109 - 2 <= I104 /\ I108 - 2 <= I105 /\ I108 - 2 <= I104 /\ 0 <= I106 - 1 /\ -1 <= I107 - 1] 15) f9#(I110, I111, I112, I113) -> f9#(I114, I115, I112 - 1, I113 + 1) [0 <= I115 - 1 /\ 0 <= I114 - 1 /\ 1 <= I111 - 1 /\ 0 <= I110 - 1 /\ 0 <= I112 - 1 /\ -1 <= I113 - 1] 16) f9#(I116, I117, I118, I119) -> f9#(I120, I121, I118 - 1, I119 + 1) [0 <= I118 - 1 /\ 0 <= I122 - 1 /\ -1 <= I119 - 1 /\ 0 <= I116 - 1 /\ 1 <= I117 - 1 /\ 0 <= I120 - 1 /\ 0 <= I121 - 1] 17) f9#(I123, I124, I125, I126) -> f9#(I127, I128, I125 - 1, I126 + 1) [0 <= I125 - 1 /\ 0 <= I129 - 1 /\ -1 <= I126 - 1 /\ I127 <= I123 /\ I128 + 2 <= I124 /\ 0 <= I123 - 1 /\ 2 <= I124 - 1 /\ 0 <= I127 - 1 /\ 0 <= I128 - 1] 18) f9#(I130, I131, I132, I133) -> f9#(I134, I135, I132 - 1, I133 + 1) [0 <= I135 - 1 /\ 0 <= I134 - 1 /\ 2 <= I131 - 1 /\ 0 <= I130 - 1 /\ I135 + 2 <= I131 /\ I134 <= I130 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1] 19) f8#(I136, I137, I138, I139) -> f9#(I140, I141, I142, I143) [0 <= I142 - 1 /\ -1 <= I144 - 1 /\ 1 <= I141 - 1 /\ 1 <= I140 - 1 /\ I144 + 1 = I143] 20) f4#(I145, I146, I147, I148) -> f8#(I149, I150, I151, I152) [0 <= I145 - 1 /\ -1 <= I153 - 1 /\ 0 <= I146 - 1 /\ I148 + 2 <= I146] 21) f2#(I154, I155, I156, I157) -> f8#(I158, I159, I160, I161) [-1 <= I162 - 1 /\ 0 <= I155 - 1 /\ 0 <= I154 - 1] 22) f3#(I163, I164, I165, I166) -> f8#(I167, I168, I169, I170) [-1 <= I164 - 1 /\ 0 <= I163 - 1] 23) f7#(I171, I172, I173, I174) -> f6#(I175, I176, I173, I177) [I173 + 2 <= I172 /\ 1 <= I176 - 1 /\ 0 <= I175 - 1 /\ 1 <= I172 - 1 /\ 0 <= I171 - 1 /\ I176 <= I172 /\ I175 + 1 <= I172 /\ I175 <= I171] 24) f2#(I178, I179, I180, I181) -> f6#(I182, I183, I184, I185) [0 <= I183 - 1 /\ 0 <= I182 - 1 /\ 0 <= I178 - 1 /\ 0 <= I179 - 1 /\ I182 <= I178] 25) f5#(I186, I187, I188, I189) -> f4#(I190, I191, I188, I189) [I189 + 2 <= I187 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1 /\ 1 <= I187 - 1 /\ 0 <= I186 - 1 /\ I191 <= I187 /\ I190 + 1 <= I187 /\ I190 <= I186] 26) f3#(I192, I193, I194, I195) -> f4#(I196, I197, I198, I199) [0 <= I197 - 1 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ I196 <= I192] 27) f3#(I200, I201, I202, I203) -> f2#(I204, I205, I206, I207) [0 <= I204 - 1 /\ 0 <= I200 - 1 /\ I204 <= I200] 28) f1#(I208, I209, I210, I211) -> f2#(I212, I209, I213, I214) [0 <= I212 - 1 /\ 0 <= I208 - 1 /\ I212 <= I208] We have the following SCCs. { 13, 14, 15, 16, 17, 18 } { 3, 4, 6, 7 } { 1 } DP problem for innermost termination. P = f13#(I0, I1, I2, I3) -> f13#(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f13(I0, I1, I2, I3) -> f13(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] f11(I8, I9, I10, I11) -> f13(I12, I13, I14, I15) [I14 + 2 <= I8 /\ -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I8 - 1 /\ I13 + 1 <= I8 /\ I12 <= I8] f12(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] f12(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] f12(I32, I33, I34, I35) -> f11(I36, I37, I38, I39) [-1 <= I36 - 1 /\ -1 <= I33 - 1 /\ -1 <= I32 - 1 /\ I36 <= I33] f10(I40, I41, I42, I43) -> f12(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] f10(I48, I49, I50, I51) -> f12(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] f10(I56, I57, I58, I59) -> f11(I60, I61, I62, I63) [-1 <= I60 - 1 /\ 0 <= I58 - 1 /\ 0 <= I57 - 1 /\ 0 <= I56 - 1 /\ I60 + 1 <= I58 /\ I60 + 1 <= I56] f4(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [I67 + 2 <= I65 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ I70 <= I65 /\ I68 <= I65] f4(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [I76 <= I73 /\ 0 <= y1 - 1 /\ I77 + 1 <= I72 /\ I77 + 1 <= I73 /\ I78 <= I73 /\ 0 <= I72 - 1 /\ 0 <= I73 - 1 /\ 0 <= I76 - 1 /\ -1 <= I77 - 1 /\ 0 <= I78 - 1 /\ I75 + 2 <= I73] f6(I80, I81, I82, I83) -> f10(I84, I85, I86, I87) [I82 + 2 <= I81 /\ -1 <= I86 - 1 /\ 0 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I86 + 1 <= I81 /\ I86 + 1 <= I80 /\ I85 <= I81 /\ I84 + 1 <= I81 /\ I84 + 1 <= I80] f2(I88, I89, I90, I91) -> f10(I92, I93, I94, I95) [0 <= I96 - 1 /\ 0 <= I89 - 1 /\ I92 + 1 <= I88 /\ I93 + 1 <= I88 /\ I94 + 1 <= I88 /\ 0 <= I88 - 1 /\ -1 <= I92 - 1 /\ -1 <= I93 - 1 /\ -1 <= I94 - 1] f9(I97, I98, I99, I100) -> f9(I101, I102, I99 - 1, I100 + 1) [0 <= I99 - 1 /\ 0 <= I103 - 1 /\ -1 <= I100 - 1 /\ I101 - 2 <= I97 /\ I101 - 2 <= I98 /\ I102 - 2 <= I97 /\ I102 - 2 <= I98 /\ 1 <= I97 - 1 /\ 1 <= I98 - 1 /\ 3 <= I101 - 1 /\ 3 <= I102 - 1] f9(I104, I105, I106, I107) -> f9(I108, I109, I106 - 1, I107 + 1) [3 <= I109 - 1 /\ 3 <= I108 - 1 /\ 1 <= I105 - 1 /\ 1 <= I104 - 1 /\ I109 - 2 <= I105 /\ I109 - 2 <= I104 /\ I108 - 2 <= I105 /\ I108 - 2 <= I104 /\ 0 <= I106 - 1 /\ -1 <= I107 - 1] f9(I110, I111, I112, I113) -> f9(I114, I115, I112 - 1, I113 + 1) [0 <= I115 - 1 /\ 0 <= I114 - 1 /\ 1 <= I111 - 1 /\ 0 <= I110 - 1 /\ 0 <= I112 - 1 /\ -1 <= I113 - 1] f9(I116, I117, I118, I119) -> f9(I120, I121, I118 - 1, I119 + 1) [0 <= I118 - 1 /\ 0 <= I122 - 1 /\ -1 <= I119 - 1 /\ 0 <= I116 - 1 /\ 1 <= I117 - 1 /\ 0 <= I120 - 1 /\ 0 <= I121 - 1] f9(I123, I124, I125, I126) -> f9(I127, I128, I125 - 1, I126 + 1) [0 <= I125 - 1 /\ 0 <= I129 - 1 /\ -1 <= I126 - 1 /\ I127 <= I123 /\ I128 + 2 <= I124 /\ 0 <= I123 - 1 /\ 2 <= I124 - 1 /\ 0 <= I127 - 1 /\ 0 <= I128 - 1] f9(I130, I131, I132, I133) -> f9(I134, I135, I132 - 1, I133 + 1) [0 <= I135 - 1 /\ 0 <= I134 - 1 /\ 2 <= I131 - 1 /\ 0 <= I130 - 1 /\ I135 + 2 <= I131 /\ I134 <= I130 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1] f8(I136, I137, I138, I139) -> f9(I140, I141, I142, I143) [0 <= I142 - 1 /\ -1 <= I144 - 1 /\ 1 <= I141 - 1 /\ 1 <= I140 - 1 /\ I144 + 1 = I143] f4(I145, I146, I147, I148) -> f8(I149, I150, I151, I152) [0 <= I145 - 1 /\ -1 <= I153 - 1 /\ 0 <= I146 - 1 /\ I148 + 2 <= I146] f2(I154, I155, I156, I157) -> f8(I158, I159, I160, I161) [-1 <= I162 - 1 /\ 0 <= I155 - 1 /\ 0 <= I154 - 1] f3(I163, I164, I165, I166) -> f8(I167, I168, I169, I170) [-1 <= I164 - 1 /\ 0 <= I163 - 1] f7(I171, I172, I173, I174) -> f6(I175, I176, I173, I177) [I173 + 2 <= I172 /\ 1 <= I176 - 1 /\ 0 <= I175 - 1 /\ 1 <= I172 - 1 /\ 0 <= I171 - 1 /\ I176 <= I172 /\ I175 + 1 <= I172 /\ I175 <= I171] f2(I178, I179, I180, I181) -> f6(I182, I183, I184, I185) [0 <= I183 - 1 /\ 0 <= I182 - 1 /\ 0 <= I178 - 1 /\ 0 <= I179 - 1 /\ I182 <= I178] f5(I186, I187, I188, I189) -> f4(I190, I191, I188, I189) [I189 + 2 <= I187 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1 /\ 1 <= I187 - 1 /\ 0 <= I186 - 1 /\ I191 <= I187 /\ I190 + 1 <= I187 /\ I190 <= I186] f3(I192, I193, I194, I195) -> f4(I196, I197, I198, I199) [0 <= I197 - 1 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ I196 <= I192] f3(I200, I201, I202, I203) -> f2(I204, I205, I206, I207) [0 <= I204 - 1 /\ 0 <= I200 - 1 /\ I204 <= I200] f1(I208, I209, I210, I211) -> f2(I212, I209, I213, I214) [0 <= I212 - 1 /\ 0 <= I208 - 1 /\ I212 <= I208] We use the basic value criterion with the projection function NU: NU[f13#(z1,z2,z3,z4)] = z2 This gives the following inequalities: I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0 ==> I1 >! I5 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f12#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] f12#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] f10#(I40, I41, I42, I43) -> f12#(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] f10#(I48, I49, I50, I51) -> f12#(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f13(I0, I1, I2, I3) -> f13(I4, I5, I6, I7) [I6 + 2 <= I1 /\ I2 + 2 <= I0 /\ I6 + 4 <= I0 /\ -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] f11(I8, I9, I10, I11) -> f13(I12, I13, I14, I15) [I14 + 2 <= I8 /\ -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I8 - 1 /\ I13 + 1 <= I8 /\ I12 <= I8] f12(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ -1 <= I20 - 1 /\ -1 <= I17 - 1 /\ -1 <= I16 - 1 /\ I22 <= I16 /\ I20 <= I16] f12(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ -1 <= I25 - 1 /\ -1 <= I24 - 1 /\ I30 <= I24 /\ I28 <= I24] f12(I32, I33, I34, I35) -> f11(I36, I37, I38, I39) [-1 <= I36 - 1 /\ -1 <= I33 - 1 /\ -1 <= I32 - 1 /\ I36 <= I33] f10(I40, I41, I42, I43) -> f12(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I42 - 1 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ I45 + 1 <= I41] f10(I48, I49, I50, I51) -> f12(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I49] f10(I56, I57, I58, I59) -> f11(I60, I61, I62, I63) [-1 <= I60 - 1 /\ 0 <= I58 - 1 /\ 0 <= I57 - 1 /\ 0 <= I56 - 1 /\ I60 + 1 <= I58 /\ I60 + 1 <= I56] f4(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [I67 + 2 <= I65 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ I70 <= I65 /\ I68 <= I65] f4(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [I76 <= I73 /\ 0 <= y1 - 1 /\ I77 + 1 <= I72 /\ I77 + 1 <= I73 /\ I78 <= I73 /\ 0 <= I72 - 1 /\ 0 <= I73 - 1 /\ 0 <= I76 - 1 /\ -1 <= I77 - 1 /\ 0 <= I78 - 1 /\ I75 + 2 <= I73] f6(I80, I81, I82, I83) -> f10(I84, I85, I86, I87) [I82 + 2 <= I81 /\ -1 <= I86 - 1 /\ 0 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I86 + 1 <= I81 /\ I86 + 1 <= I80 /\ I85 <= I81 /\ I84 + 1 <= I81 /\ I84 + 1 <= I80] f2(I88, I89, I90, I91) -> f10(I92, I93, I94, I95) [0 <= I96 - 1 /\ 0 <= I89 - 1 /\ I92 + 1 <= I88 /\ I93 + 1 <= I88 /\ I94 + 1 <= I88 /\ 0 <= I88 - 1 /\ -1 <= I92 - 1 /\ -1 <= I93 - 1 /\ -1 <= I94 - 1] f9(I97, I98, I99, I100) -> f9(I101, I102, I99 - 1, I100 + 1) [0 <= I99 - 1 /\ 0 <= I103 - 1 /\ -1 <= I100 - 1 /\ I101 - 2 <= I97 /\ I101 - 2 <= I98 /\ I102 - 2 <= I97 /\ I102 - 2 <= I98 /\ 1 <= I97 - 1 /\ 1 <= I98 - 1 /\ 3 <= I101 - 1 /\ 3 <= I102 - 1] f9(I104, I105, I106, I107) -> f9(I108, I109, I106 - 1, I107 + 1) [3 <= I109 - 1 /\ 3 <= I108 - 1 /\ 1 <= I105 - 1 /\ 1 <= I104 - 1 /\ I109 - 2 <= I105 /\ I109 - 2 <= I104 /\ I108 - 2 <= I105 /\ I108 - 2 <= I104 /\ 0 <= I106 - 1 /\ -1 <= I107 - 1] f9(I110, I111, I112, I113) -> f9(I114, I115, I112 - 1, I113 + 1) [0 <= I115 - 1 /\ 0 <= I114 - 1 /\ 1 <= I111 - 1 /\ 0 <= I110 - 1 /\ 0 <= I112 - 1 /\ -1 <= I113 - 1] f9(I116, I117, I118, I119) -> f9(I120, I121, I118 - 1, I119 + 1) [0 <= I118 - 1 /\ 0 <= I122 - 1 /\ -1 <= I119 - 1 /\ 0 <= I116 - 1 /\ 1 <= I117 - 1 /\ 0 <= I120 - 1 /\ 0 <= I121 - 1] f9(I123, I124, I125, I126) -> f9(I127, I128, I125 - 1, I126 + 1) [0 <= I125 - 1 /\ 0 <= I129 - 1 /\ -1 <= I126 - 1 /\ I127 <= I123 /\ I128 + 2 <= I124 /\ 0 <= I123 - 1 /\ 2 <= I124 - 1 /\ 0 <= I127 - 1 /\ 0 <= I128 - 1] f9(I130, I131, I132, I133) -> f9(I134, I135, I132 - 1, I133 + 1) [0 <= I135 - 1 /\ 0 <= I134 - 1 /\ 2 <= I131 - 1 /\ 0 <= I130 - 1 /\ I135 + 2 <= I131 /\ I134 <= I130 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1] f8(I136, I137, I138, I139) -> f9(I140, I141, I142, I143) [0 <= I142 - 1 /\ -1 <= I144 - 1 /\ 1 <= I141 - 1 /\ 1 <= I140 - 1 /\ I144 + 1 = I143] f4(I145, I146, I147, I148) -> f8(I149, I150, I151, I152) [0 <= I145 - 1 /\ -1 <= I153 - 1 /\ 0 <= I146 - 1 /\ I148 + 2 <= I146] f2(I154, I155, I156, I157) -> f8(I158, I159, I160, I161) [-1 <= I162 - 1 /\ 0 <= I155 - 1 /\ 0 <= I154 - 1] f3(I163, I164, I165, I166) -> f8(I167, I168, I169, I170) [-1 <= I164 - 1 /\ 0 <= I163 - 1] f7(I171, I172, I173, I174) -> f6(I175, I176, I173, I177) [I173 + 2 <= I172 /\ 1 <= I176 - 1 /\ 0 <= I175 - 1 /\ 1 <= I172 - 1 /\ 0 <= I171 - 1 /\ I176 <= I172 /\ I175 + 1 <= I172 /\ I175 <= I171] f2(I178, I179, I180, I181) -> f6(I182, I183, I184, I185) [0 <= I183 - 1 /\ 0 <= I182 - 1 /\ 0 <= I178 - 1 /\ 0 <= I179 - 1 /\ I182 <= I178] f5(I186, I187, I188, I189) -> f4(I190, I191, I188, I189) [I189 + 2 <= I187 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1 /\ 1 <= I187 - 1 /\ 0 <= I186 - 1 /\ I191 <= I187 /\ I190 + 1 <= I187 /\ I190 <= I186] f3(I192, I193, I194, I195) -> f4(I196, I197, I198, I199) [0 <= I197 - 1 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ I196 <= I192] f3(I200, I201, I202, I203) -> f2(I204, I205, I206, I207) [0 <= I204 - 1 /\ 0 <= I200 - 1 /\ I204 <= I200] f1(I208, I209, I210, I211) -> f2(I212, I209, I213, I214) [0 <= I212 - 1 /\ 0 <= I208 - 1 /\ I212 <= I208]