/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = f23#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f20#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f21#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) f21#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f19#(rnd1, I11, I12, I13, I14, I15, I16, I17, I18, I19) [rnd1 <= 1 /\ 0 <= rnd1 /\ rnd1 = rnd1 /\ 1 <= I12] f20#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2#(I30, I31, rnd3, rnd4, rnd5, rnd6, 0, 1, 0, rnd10) [0 <= rnd3 /\ rnd3 <= rnd4 /\ rnd3 = rnd3 /\ rnd4 <= rnd5 /\ 0 <= rnd4 /\ rnd4 = rnd4 /\ 0 <= rnd5 /\ rnd5 = rnd5 /\ 0 <= rnd10 /\ rnd10 = rnd10 /\ rnd6 = 1] f19#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f18#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [I49 <= 0] f19#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f13#(I50, I51, I52, I53, I54, I55, I56, I57, I58, -1 + I59) [1 <= I59] f18#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f13#(I60, I61, I62, I63, I64, I65, 1 + I66, I67, I68, I69) [I60 <= 0 /\ I66 <= 0] f18#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f17#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) [1 <= I76] f13#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11#(I80, rnd2, I82, I83, I84, I85, I86, I87, I88, I89) [rnd2 <= 1 /\ 0 <= rnd2 /\ rnd2 = rnd2 /\ 1 <= I80] f13#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) [1 + I90 <= 1] f17#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f16#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [I106 <= 1] f17#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f13#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) [2 <= I116] f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f13#(I120, I121, I122, I123, I124, I125, I126, I127, 1 + I128, I129) [1 <= I120 /\ I128 <= 0] f16#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f15#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) [1 <= I138] f15#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f14#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) [I148 <= 1] f15#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f12#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) [2 <= I158] f14#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f13#(I160, I161, I162, I163, I164, -1 + I165, I166, I167, 0, I169) [I160 <= 0 /\ 1 <= I165] f14#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f12#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) [I175 <= 0] f12#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f13#(I180, I181, I182, I183, I184, I190, 0, 1 + I187, 0, I191) [0 <= I191 /\ I191 = I191 /\ I190 = 1 + I187] f11#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) -> f10#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) [I201 <= 0] f11#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I202, I203, I204, I205, I206, I207, I208, I209, I210, -1 + I211) [1 <= I211] f10#(I212, I213, I214, I215, I216, I217, I218, I219, I220, I221) -> f5#(I212, I213, I214, I215, I216, I217, 1 + I218, I219, I220, I221) [I213 <= 0 /\ I218 <= 0] f10#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f9#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) [1 <= I228] f5#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f3#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) [1 <= I233] f5#(I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f1#(I242, I243, -1 + I244, I245, I246, I247, I248, I249, I250, I251) [1 + I243 <= 1] f9#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f8#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) [I258 <= 1] f9#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f5#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [2 <= I268] f8#(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f5#(I272, I273, I274, I275, I276, I277, I278, I279, 1 + I280, I281) [1 <= I273 /\ I280 <= 0] f8#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f7#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) [1 <= I290] f7#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) -> f6#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [I300 <= 1] f7#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) -> f4#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) [2 <= I310] f6#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f5#(I312, I313, I314, I315, I316, -1 + I317, I318, I319, 0, I321) [I313 <= 0 /\ 1 <= I317] f6#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f4#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) [I327 <= 0] f4#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f5#(I332, I333, I334, I335, I336, I342, 0, 1 + I339, 0, I343) [0 <= I343 /\ I343 = I343 /\ I342 = 1 + I339] f3#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353) -> f1#(I344, I345, 1 + I346, I347, I348, I349, I350, I351, I352, I353) [1 + I346 <= I347] f3#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f1#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I357 <= I356] f1#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) -> f2#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) [I371 <= 1 + I368] R = f23(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f21(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) f21(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f19(rnd1, I11, I12, I13, I14, I15, I16, I17, I18, I19) [rnd1 <= 1 /\ 0 <= rnd1 /\ rnd1 = rnd1 /\ 1 <= I12] f21(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f22(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I22 <= 0] f20(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(I30, I31, rnd3, rnd4, rnd5, rnd6, 0, 1, 0, rnd10) [0 <= rnd3 /\ rnd3 <= rnd4 /\ rnd3 = rnd3 /\ rnd4 <= rnd5 /\ 0 <= rnd4 /\ rnd4 = rnd4 /\ 0 <= rnd5 /\ rnd5 = rnd5 /\ 0 <= rnd10 /\ rnd10 = rnd10 /\ rnd6 = 1] f19(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f18(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [I49 <= 0] f19(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f13(I50, I51, I52, I53, I54, I55, I56, I57, I58, -1 + I59) [1 <= I59] f18(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f13(I60, I61, I62, I63, I64, I65, 1 + I66, I67, I68, I69) [I60 <= 0 /\ I66 <= 0] f18(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f17(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) [1 <= I76] f13(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, rnd2, I82, I83, I84, I85, I86, I87, I88, I89) [rnd2 <= 1 /\ 0 <= rnd2 /\ rnd2 = rnd2 /\ 1 <= I80] f13(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) [1 + I90 <= 1] f17(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f16(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [I106 <= 1] f17(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f13(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) [2 <= I116] f16(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f13(I120, I121, I122, I123, I124, I125, I126, I127, 1 + I128, I129) [1 <= I120 /\ I128 <= 0] f16(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f15(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) [1 <= I138] f15(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f14(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) [I148 <= 1] f15(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f12(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) [2 <= I158] f14(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f13(I160, I161, I162, I163, I164, -1 + I165, I166, I167, 0, I169) [I160 <= 0 /\ 1 <= I165] f14(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f12(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) [I175 <= 0] f12(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f13(I180, I181, I182, I183, I184, I190, 0, 1 + I187, 0, I191) [0 <= I191 /\ I191 = I191 /\ I190 = 1 + I187] f11(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) -> f10(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) [I201 <= 0] f11(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I202, I203, I204, I205, I206, I207, I208, I209, I210, -1 + I211) [1 <= I211] f10(I212, I213, I214, I215, I216, I217, I218, I219, I220, I221) -> f5(I212, I213, I214, I215, I216, I217, 1 + I218, I219, I220, I221) [I213 <= 0 /\ I218 <= 0] f10(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f9(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) [1 <= I228] f5(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f3(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) [1 <= I233] f5(I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f1(I242, I243, -1 + I244, I245, I246, I247, I248, I249, I250, I251) [1 + I243 <= 1] f9(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f8(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) [I258 <= 1] f9(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f5(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [2 <= I268] f8(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f5(I272, I273, I274, I275, I276, I277, I278, I279, 1 + I280, I281) [1 <= I273 /\ I280 <= 0] f8(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f7(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) [1 <= I290] f7(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) -> f6(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [I300 <= 1] f7(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) -> f4(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) [2 <= I310] f6(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f5(I312, I313, I314, I315, I316, -1 + I317, I318, I319, 0, I321) [I313 <= 0 /\ 1 <= I317] f6(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f4(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) [I327 <= 0] f4(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f5(I332, I333, I334, I335, I336, I342, 0, 1 + I339, 0, I343) [0 <= I343 /\ I343 = I343 /\ I342 = 1 + I339] f3(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353) -> f1(I344, I345, 1 + I346, I347, I348, I349, I350, I351, I352, I353) [1 + I346 <= I347] f3(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f1(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I357 <= I356] f1(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) -> f2(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) [I371 <= 1 + I368] The dependency graph for this problem is: 0 -> 3 1 -> 2 2 -> 4, 5 3 -> 1 4 -> 6, 7 5 -> 8, 9 6 -> 9 7 -> 10, 11 8 -> 19, 20 9 -> 36 10 -> 12, 13 11 -> 8, 9 12 -> 8 13 -> 14, 15 14 -> 16, 17 15 -> 18 16 -> 9 17 -> 18 18 -> 8, 9 19 -> 21, 22 20 -> 23, 24 21 -> 24 22 -> 25, 26 23 -> 34, 35 24 -> 36 25 -> 27, 28 26 -> 23, 24 27 -> 23 28 -> 29, 30 29 -> 31, 32 30 -> 33 31 -> 24 32 -> 33 33 -> 23, 24 34 -> 36 35 -> 36 36 -> 1 Where: 0) f23#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f20#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 1) f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f21#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) 2) f21#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f19#(rnd1, I11, I12, I13, I14, I15, I16, I17, I18, I19) [rnd1 <= 1 /\ 0 <= rnd1 /\ rnd1 = rnd1 /\ 1 <= I12] 3) f20#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2#(I30, I31, rnd3, rnd4, rnd5, rnd6, 0, 1, 0, rnd10) [0 <= rnd3 /\ rnd3 <= rnd4 /\ rnd3 = rnd3 /\ rnd4 <= rnd5 /\ 0 <= rnd4 /\ rnd4 = rnd4 /\ 0 <= rnd5 /\ rnd5 = rnd5 /\ 0 <= rnd10 /\ rnd10 = rnd10 /\ rnd6 = 1] 4) f19#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f18#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [I49 <= 0] 5) f19#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f13#(I50, I51, I52, I53, I54, I55, I56, I57, I58, -1 + I59) [1 <= I59] 6) f18#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f13#(I60, I61, I62, I63, I64, I65, 1 + I66, I67, I68, I69) [I60 <= 0 /\ I66 <= 0] 7) f18#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f17#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) [1 <= I76] 8) f13#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11#(I80, rnd2, I82, I83, I84, I85, I86, I87, I88, I89) [rnd2 <= 1 /\ 0 <= rnd2 /\ rnd2 = rnd2 /\ 1 <= I80] 9) f13#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) [1 + I90 <= 1] 10) f17#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f16#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [I106 <= 1] 11) f17#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f13#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) [2 <= I116] 12) f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f13#(I120, I121, I122, I123, I124, I125, I126, I127, 1 + I128, I129) [1 <= I120 /\ I128 <= 0] 13) f16#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f15#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) [1 <= I138] 14) f15#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f14#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) [I148 <= 1] 15) f15#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f12#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) [2 <= I158] 16) f14#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f13#(I160, I161, I162, I163, I164, -1 + I165, I166, I167, 0, I169) [I160 <= 0 /\ 1 <= I165] 17) f14#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f12#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) [I175 <= 0] 18) f12#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f13#(I180, I181, I182, I183, I184, I190, 0, 1 + I187, 0, I191) [0 <= I191 /\ I191 = I191 /\ I190 = 1 + I187] 19) f11#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) -> f10#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) [I201 <= 0] 20) f11#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I202, I203, I204, I205, I206, I207, I208, I209, I210, -1 + I211) [1 <= I211] 21) f10#(I212, I213, I214, I215, I216, I217, I218, I219, I220, I221) -> f5#(I212, I213, I214, I215, I216, I217, 1 + I218, I219, I220, I221) [I213 <= 0 /\ I218 <= 0] 22) f10#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f9#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) [1 <= I228] 23) f5#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f3#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) [1 <= I233] 24) f5#(I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f1#(I242, I243, -1 + I244, I245, I246, I247, I248, I249, I250, I251) [1 + I243 <= 1] 25) f9#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f8#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) [I258 <= 1] 26) f9#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f5#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [2 <= I268] 27) f8#(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f5#(I272, I273, I274, I275, I276, I277, I278, I279, 1 + I280, I281) [1 <= I273 /\ I280 <= 0] 28) f8#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f7#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) [1 <= I290] 29) f7#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) -> f6#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [I300 <= 1] 30) f7#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) -> f4#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) [2 <= I310] 31) f6#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f5#(I312, I313, I314, I315, I316, -1 + I317, I318, I319, 0, I321) [I313 <= 0 /\ 1 <= I317] 32) f6#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f4#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) [I327 <= 0] 33) f4#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f5#(I332, I333, I334, I335, I336, I342, 0, 1 + I339, 0, I343) [0 <= I343 /\ I343 = I343 /\ I342 = 1 + I339] 34) f3#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353) -> f1#(I344, I345, 1 + I346, I347, I348, I349, I350, I351, I352, I353) [1 + I346 <= I347] 35) f3#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f1#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I357 <= I356] 36) f1#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) -> f2#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) [I371 <= 1 + I368] We have the following SCCs. { 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 } DP problem for innermost termination. P = f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f21#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) f21#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f19#(rnd1, I11, I12, I13, I14, I15, I16, I17, I18, I19) [rnd1 <= 1 /\ 0 <= rnd1 /\ rnd1 = rnd1 /\ 1 <= I12] f19#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f18#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [I49 <= 0] f19#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f13#(I50, I51, I52, I53, I54, I55, I56, I57, I58, -1 + I59) [1 <= I59] f18#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f13#(I60, I61, I62, I63, I64, I65, 1 + I66, I67, I68, I69) [I60 <= 0 /\ I66 <= 0] f18#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f17#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) [1 <= I76] f13#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11#(I80, rnd2, I82, I83, I84, I85, I86, I87, I88, I89) [rnd2 <= 1 /\ 0 <= rnd2 /\ rnd2 = rnd2 /\ 1 <= I80] f13#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) [1 + I90 <= 1] f17#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f16#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [I106 <= 1] f17#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f13#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) [2 <= I116] f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f13#(I120, I121, I122, I123, I124, I125, I126, I127, 1 + I128, I129) [1 <= I120 /\ I128 <= 0] f16#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f15#(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) [1 <= I138] f15#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f14#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) [I148 <= 1] f15#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f12#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) [2 <= I158] f14#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f13#(I160, I161, I162, I163, I164, -1 + I165, I166, I167, 0, I169) [I160 <= 0 /\ 1 <= I165] f14#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f12#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) [I175 <= 0] f12#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f13#(I180, I181, I182, I183, I184, I190, 0, 1 + I187, 0, I191) [0 <= I191 /\ I191 = I191 /\ I190 = 1 + I187] f11#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) -> f10#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) [I201 <= 0] f11#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I202, I203, I204, I205, I206, I207, I208, I209, I210, -1 + I211) [1 <= I211] f10#(I212, I213, I214, I215, I216, I217, I218, I219, I220, I221) -> f5#(I212, I213, I214, I215, I216, I217, 1 + I218, I219, I220, I221) [I213 <= 0 /\ I218 <= 0] f10#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f9#(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) [1 <= I228] f5#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f3#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) [1 <= I233] f5#(I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f1#(I242, I243, -1 + I244, I245, I246, I247, I248, I249, I250, I251) [1 + I243 <= 1] f9#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f8#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) [I258 <= 1] f9#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f5#(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [2 <= I268] f8#(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f5#(I272, I273, I274, I275, I276, I277, I278, I279, 1 + I280, I281) [1 <= I273 /\ I280 <= 0] f8#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f7#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) [1 <= I290] f7#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) -> f6#(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [I300 <= 1] f7#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) -> f4#(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) [2 <= I310] f6#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f5#(I312, I313, I314, I315, I316, -1 + I317, I318, I319, 0, I321) [I313 <= 0 /\ 1 <= I317] f6#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f4#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) [I327 <= 0] f4#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f5#(I332, I333, I334, I335, I336, I342, 0, 1 + I339, 0, I343) [0 <= I343 /\ I343 = I343 /\ I342 = 1 + I339] f3#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353) -> f1#(I344, I345, 1 + I346, I347, I348, I349, I350, I351, I352, I353) [1 + I346 <= I347] f3#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f1#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I357 <= I356] f1#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) -> f2#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) [I371 <= 1 + I368] R = f23(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f21(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) f21(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f19(rnd1, I11, I12, I13, I14, I15, I16, I17, I18, I19) [rnd1 <= 1 /\ 0 <= rnd1 /\ rnd1 = rnd1 /\ 1 <= I12] f21(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f22(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I22 <= 0] f20(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(I30, I31, rnd3, rnd4, rnd5, rnd6, 0, 1, 0, rnd10) [0 <= rnd3 /\ rnd3 <= rnd4 /\ rnd3 = rnd3 /\ rnd4 <= rnd5 /\ 0 <= rnd4 /\ rnd4 = rnd4 /\ 0 <= rnd5 /\ rnd5 = rnd5 /\ 0 <= rnd10 /\ rnd10 = rnd10 /\ rnd6 = 1] f19(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f18(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [I49 <= 0] f19(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f13(I50, I51, I52, I53, I54, I55, I56, I57, I58, -1 + I59) [1 <= I59] f18(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f13(I60, I61, I62, I63, I64, I65, 1 + I66, I67, I68, I69) [I60 <= 0 /\ I66 <= 0] f18(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f17(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) [1 <= I76] f13(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, rnd2, I82, I83, I84, I85, I86, I87, I88, I89) [rnd2 <= 1 /\ 0 <= rnd2 /\ rnd2 = rnd2 /\ 1 <= I80] f13(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) [1 + I90 <= 1] f17(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f16(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [I106 <= 1] f17(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f13(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) [2 <= I116] f16(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f13(I120, I121, I122, I123, I124, I125, I126, I127, 1 + I128, I129) [1 <= I120 /\ I128 <= 0] f16(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f15(I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) [1 <= I138] f15(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f14(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) [I148 <= 1] f15(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f12(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) [2 <= I158] f14(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f13(I160, I161, I162, I163, I164, -1 + I165, I166, I167, 0, I169) [I160 <= 0 /\ 1 <= I165] f14(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f12(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) [I175 <= 0] f12(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f13(I180, I181, I182, I183, I184, I190, 0, 1 + I187, 0, I191) [0 <= I191 /\ I191 = I191 /\ I190 = 1 + I187] f11(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) -> f10(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201) [I201 <= 0] f11(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I202, I203, I204, I205, I206, I207, I208, I209, I210, -1 + I211) [1 <= I211] f10(I212, I213, I214, I215, I216, I217, I218, I219, I220, I221) -> f5(I212, I213, I214, I215, I216, I217, 1 + I218, I219, I220, I221) [I213 <= 0 /\ I218 <= 0] f10(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f9(I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) [1 <= I228] f5(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f3(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) [1 <= I233] f5(I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f1(I242, I243, -1 + I244, I245, I246, I247, I248, I249, I250, I251) [1 + I243 <= 1] f9(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f8(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) [I258 <= 1] f9(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f5(I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [2 <= I268] f8(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f5(I272, I273, I274, I275, I276, I277, I278, I279, 1 + I280, I281) [1 <= I273 /\ I280 <= 0] f8(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f7(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) [1 <= I290] f7(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) -> f6(I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [I300 <= 1] f7(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) -> f4(I302, I303, I304, I305, I306, I307, I308, I309, I310, I311) [2 <= I310] f6(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f5(I312, I313, I314, I315, I316, -1 + I317, I318, I319, 0, I321) [I313 <= 0 /\ 1 <= I317] f6(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f4(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331) [I327 <= 0] f4(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f5(I332, I333, I334, I335, I336, I342, 0, 1 + I339, 0, I343) [0 <= I343 /\ I343 = I343 /\ I342 = 1 + I339] f3(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353) -> f1(I344, I345, 1 + I346, I347, I348, I349, I350, I351, I352, I353) [1 + I346 <= I347] f3(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f1(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I357 <= I356] f1(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) -> f2(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373) [I371 <= 1 + I368]