1.30/1.32 YES 1.30/1.32 1.30/1.32 DP problem for innermost termination. 1.30/1.32 P = 1.30/1.32 f20#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 1.30/1.32 f19#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f1#(I0, I1, I2, I3, I4, I5, I6, 100, I8, I9, rnd11, I11, I12, I13) [rnd11 = rnd11] 1.30/1.32 f2#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f18#(I14, I15, I16, rnd4, I18, I19, I20, I21, I22, I23, I24, I15, I26, I27) [rnd4 = I15] 1.30/1.32 f18#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f17#(I28, I29, I30, I31, 100, I33, I34, I35, rnd9, I37, I38, I39, I40, I41) [rnd9 = rnd9 /\ 1 <= I31 /\ I31 <= 1] 1.30/1.32 f18#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) [1 + I45 <= 1] 1.30/1.32 f18#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [2 <= I59] 1.30/1.32 f17#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f15#(I70, I71, 1, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 1.30/1.32 f17#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f15#(I84, I85, 0, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 1.30/1.32 f16#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) [1 + I101 <= 1] 1.30/1.32 f16#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f14#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [2 <= I115] 1.30/1.32 f16#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, rnd14) [rnd14 = rnd14 /\ 1 <= I129 /\ I129 <= 1] 1.30/1.32 f15#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f16#(I140, I141, I142, I142, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 1.30/1.32 f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f13#(I154, I155, I156, I157, I158, 100, I160, I161, I162, I163, I164, I165, I166, I167) 1.30/1.32 f13#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f12#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) 1.30/1.32 f13#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f11#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) 1.30/1.32 f13#(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f12#(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 1.30/1.32 f12#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) -> f11#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) 1.30/1.32 f10#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f9#(I238, I239, I240, I241, I242, I243, 100, I245, I246, I247, I248, I249, I250, I251) 1.30/1.32 f9#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) -> f8#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) 1.30/1.32 f9#(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) -> f7#(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) 1.30/1.32 f9#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f8#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) 1.30/1.32 f8#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f7#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) 1.30/1.32 f6#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f5#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) [1 + I335 <= -1] 1.30/1.32 f6#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) -> f5#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) [0 <= I349] 1.30/1.32 f6#(I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f3#(100, I351, I352, I353, I354, I355, I356, I357, I358, rnd10, I360, I361, I362, I363) [rnd10 = rnd10 /\ -1 <= I363 /\ I363 <= -1] 1.30/1.32 f5#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377) -> f3#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, rnd13, I377) [rnd13 = rnd13] 1.30/1.32 f1#(I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) -> f2#(I392, 1, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) 1.30/1.32 f1#(I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f2#(I406, 0, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) 1.30/1.32 R = 1.30/1.32 f20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 1.30/1.32 f19(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f1(I0, I1, I2, I3, I4, I5, I6, 100, I8, I9, rnd11, I11, I12, I13) [rnd11 = rnd11] 1.30/1.32 f2(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f18(I14, I15, I16, rnd4, I18, I19, I20, I21, I22, I23, I24, I15, I26, I27) [rnd4 = I15] 1.30/1.32 f18(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f17(I28, I29, I30, I31, 100, I33, I34, I35, rnd9, I37, I38, I39, I40, I41) [rnd9 = rnd9 /\ 1 <= I31 /\ I31 <= 1] 1.30/1.32 f18(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) [1 + I45 <= 1] 1.30/1.32 f18(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [2 <= I59] 1.30/1.32 f17(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f15(I70, I71, 1, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 1.30/1.32 f17(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f15(I84, I85, 0, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 1.30/1.32 f16(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) [1 + I101 <= 1] 1.30/1.32 f16(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f14(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [2 <= I115] 1.30/1.32 f16(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, rnd14) [rnd14 = rnd14 /\ 1 <= I129 /\ I129 <= 1] 1.30/1.32 f15(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f16(I140, I141, I142, I142, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 1.30/1.32 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f13(I154, I155, I156, I157, I158, 100, I160, I161, I162, I163, I164, I165, I166, I167) 1.30/1.32 f13(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f12(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) 1.30/1.32 f13(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f11(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) 1.30/1.32 f13(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f12(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 1.30/1.32 f12(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) -> f11(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) 1.30/1.32 f11(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f4(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) 1.30/1.32 f10(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f9(I238, I239, I240, I241, I242, I243, 100, I245, I246, I247, I248, I249, I250, I251) 1.30/1.32 f9(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) -> f8(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) 1.30/1.32 f9(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) -> f7(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) 1.30/1.32 f9(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f8(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) 1.30/1.32 f8(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f7(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) 1.30/1.32 f7(I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f4(I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) 1.30/1.32 f6(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f5(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) [1 + I335 <= -1] 1.30/1.32 f6(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) -> f5(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) [0 <= I349] 1.30/1.32 f6(I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f3(100, I351, I352, I353, I354, I355, I356, I357, I358, rnd10, I360, I361, I362, I363) [rnd10 = rnd10 /\ -1 <= I363 /\ I363 <= -1] 1.30/1.32 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377) -> f3(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, rnd13, I377) [rnd13 = rnd13] 1.30/1.32 f3(I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391) -> f4(I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391) 1.30/1.32 f1(I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) -> f2(I392, 1, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) 1.30/1.32 f1(I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f2(I406, 0, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) 1.30/1.32 1.30/1.32 The dependency graph for this problem is: 1.30/1.32 0 -> 1 1.30/1.32 1 -> 26, 27 1.30/1.32 2 -> 3, 4, 5 1.30/1.32 3 -> 6, 7 1.30/1.32 4 -> 17 1.30/1.32 5 -> 17 1.30/1.32 6 -> 11 1.30/1.32 7 -> 11 1.30/1.32 8 -> 12 1.30/1.32 9 -> 12 1.30/1.32 10 -> 22, 23, 24 1.30/1.32 11 -> 8, 9, 10 1.30/1.32 12 -> 13, 14, 15 1.30/1.32 13 -> 16 1.30/1.32 14 -> 1.30/1.32 15 -> 16 1.30/1.32 16 -> 1.30/1.32 17 -> 18, 19, 20 1.30/1.32 18 -> 21 1.30/1.32 19 -> 1.30/1.32 20 -> 21 1.30/1.32 21 -> 1.30/1.32 22 -> 25 1.30/1.32 23 -> 25 1.30/1.32 24 -> 1.30/1.32 25 -> 1.30/1.32 26 -> 2 1.30/1.32 27 -> 2 1.30/1.32 Where: 1.30/1.32 0) f20#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 1.30/1.32 1) f19#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f1#(I0, I1, I2, I3, I4, I5, I6, 100, I8, I9, rnd11, I11, I12, I13) [rnd11 = rnd11] 1.30/1.32 2) f2#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f18#(I14, I15, I16, rnd4, I18, I19, I20, I21, I22, I23, I24, I15, I26, I27) [rnd4 = I15] 1.30/1.32 3) f18#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f17#(I28, I29, I30, I31, 100, I33, I34, I35, rnd9, I37, I38, I39, I40, I41) [rnd9 = rnd9 /\ 1 <= I31 /\ I31 <= 1] 1.30/1.32 4) f18#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) [1 + I45 <= 1] 1.30/1.32 5) f18#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [2 <= I59] 1.30/1.32 6) f17#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f15#(I70, I71, 1, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 1.30/1.32 7) f17#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f15#(I84, I85, 0, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 1.30/1.32 8) f16#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) [1 + I101 <= 1] 1.30/1.32 9) f16#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f14#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [2 <= I115] 1.30/1.32 10) f16#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, rnd14) [rnd14 = rnd14 /\ 1 <= I129 /\ I129 <= 1] 1.30/1.32 11) f15#(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f16#(I140, I141, I142, I142, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 1.30/1.32 12) f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f13#(I154, I155, I156, I157, I158, 100, I160, I161, I162, I163, I164, I165, I166, I167) 1.30/1.32 13) f13#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f12#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) 1.30/1.32 14) f13#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f11#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) 1.30/1.32 15) f13#(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f12#(I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 1.30/1.32 16) f12#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) -> f11#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223) 1.30/1.32 17) f10#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f9#(I238, I239, I240, I241, I242, I243, 100, I245, I246, I247, I248, I249, I250, I251) 1.30/1.32 18) f9#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) -> f8#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265) 1.30/1.32 19) f9#(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) -> f7#(I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278, I279) 1.30/1.32 20) f9#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f8#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) 1.30/1.32 21) f8#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f7#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) 1.30/1.32 22) f6#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f5#(I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) [1 + I335 <= -1] 1.30/1.32 23) f6#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) -> f5#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349) [0 <= I349] 1.30/1.32 24) f6#(I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f3#(100, I351, I352, I353, I354, I355, I356, I357, I358, rnd10, I360, I361, I362, I363) [rnd10 = rnd10 /\ -1 <= I363 /\ I363 <= -1] 1.30/1.32 25) f5#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377) -> f3#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, rnd13, I377) [rnd13 = rnd13] 1.30/1.32 26) f1#(I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) -> f2#(I392, 1, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405) 1.30/1.32 27) f1#(I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f2#(I406, 0, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) 1.30/1.32 1.30/1.32 We have the following SCCs. 1.30/1.32 1.30/4.29 EOF