1.04/1.04 YES 1.04/1.04 1.04/1.04 DP problem for innermost termination. 1.04/1.04 P = 1.04/1.04 f14#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) 1.04/1.04 f13#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, 10, 2, 1) 1.04/1.04 f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I34 + I35, I33, I34, I35) [I34 <= I35] 1.04/1.04 f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I52 - I53, I51, I52, I53) [1 + I53 <= I52] 1.04/1.04 f6#(I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I69, I55, I70, I57, I71, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) [I69 <= I71] 1.04/1.04 f6#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f8#(I72, I89, I74, I88, I76, I87, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) [1 + I89 <= I87] 1.04/1.04 f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [I90 <= I92] 1.04/1.04 f12#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f9#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 + I110 <= I108] 1.04/1.04 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f10#(I126, I127, I128, I129, I130, I131, I126, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I126 <= I130] 1.04/1.04 f11#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f10#(I144, I145, I146, I147, I148, I149, I148, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) [1 + I148 <= I144] 1.04/1.04 f10#(I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f4#(I162, I163, I164, I165, I166, I167, I168, I169, I168, I171, I172, I173, I168, I175, I176, I168 + I177, I178, I179) 1.04/1.04 f9#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f10#(I180, I181, I182, I183, I184, I185, I182, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) [I182 <= I184] 1.04/1.04 f9#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) -> f10#(I198, I199, I200, I201, I202, I203, I202, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [1 + I202 <= I200] 1.04/1.04 f8#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f7#(I216, I217, I218, I219, I220, I221, I222, I223, I224, rnd10, I226, I227, I228, I229, I230, I231, I232, I233) [rnd10 = rnd10 /\ I217 <= I219] 1.04/1.04 f8#(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f7#(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) [1 + I237 <= I235] 1.04/1.04 f7#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f3#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, rnd11, I263, I264, I265, I266, I267, I268, I269) [rnd11 = rnd11 /\ I253 <= I257] 1.04/1.04 f7#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) -> f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) [1 + I275 <= I271] 1.04/1.04 f5#(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f4#(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, rnd12, I300, I301, I302, I303, I304, I305) [rnd12 = rnd12 /\ I303 <= I304] 1.04/1.04 f5#(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f6#(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) [1 + I322 <= I321] 1.04/1.04 f3#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f4#(I324, I325, I326, I327, I328, I329, I330, I325, I332, I333, I334, I335, I336, I325, I338, I339, I340, rnd18) [rnd18 = rnd18] 1.04/1.04 R = 1.04/1.04 f14(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) 1.04/1.04 f13(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, 10, 2, 1) 1.04/1.04 f4(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I34 + I35, I33, I34, I35) [I34 <= I35] 1.04/1.04 f4(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I52 - I53, I51, I52, I53) [1 + I53 <= I52] 1.04/1.04 f6(I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I69, I55, I70, I57, I71, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) [I69 <= I71] 1.04/1.04 f6(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f8(I72, I89, I74, I88, I76, I87, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) [1 + I89 <= I87] 1.04/1.04 f12(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [I90 <= I92] 1.04/1.04 f12(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f9(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 + I110 <= I108] 1.04/1.04 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f10(I126, I127, I128, I129, I130, I131, I126, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I126 <= I130] 1.04/1.04 f11(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f10(I144, I145, I146, I147, I148, I149, I148, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) [1 + I148 <= I144] 1.04/1.04 f10(I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f4(I162, I163, I164, I165, I166, I167, I168, I169, I168, I171, I172, I173, I168, I175, I176, I168 + I177, I178, I179) 1.04/1.04 f9(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f10(I180, I181, I182, I183, I184, I185, I182, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) [I182 <= I184] 1.04/1.04 f9(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) -> f10(I198, I199, I200, I201, I202, I203, I202, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [1 + I202 <= I200] 1.04/1.04 f8(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f7(I216, I217, I218, I219, I220, I221, I222, I223, I224, rnd10, I226, I227, I228, I229, I230, I231, I232, I233) [rnd10 = rnd10 /\ I217 <= I219] 1.04/1.04 f8(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f7(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) [1 + I237 <= I235] 1.04/1.04 f7(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f3(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, rnd11, I263, I264, I265, I266, I267, I268, I269) [rnd11 = rnd11 /\ I253 <= I257] 1.04/1.04 f7(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) -> f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) [1 + I275 <= I271] 1.04/1.04 f5(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f4(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, rnd12, I300, I301, I302, I303, I304, I305) [rnd12 = rnd12 /\ I303 <= I304] 1.04/1.04 f5(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f6(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) [1 + I322 <= I321] 1.04/1.04 f3(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f4(I324, I325, I326, I327, I328, I329, I330, I325, I332, I333, I334, I335, I336, I325, I338, I339, I340, rnd18) [rnd18 = rnd18] 1.04/1.04 f1(I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f2(I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) 1.04/1.04 1.04/1.04 The dependency graph for this problem is: 1.04/1.04 0 -> 1 1.04/1.04 1 -> 18 1.04/1.04 2 -> 1.04/1.04 3 -> 1.04/1.04 4 -> 6, 7 1.04/1.04 5 -> 13, 14 1.04/1.04 6 -> 8, 9 1.04/1.04 7 -> 11, 12 1.04/1.04 8 -> 10 1.04/1.04 9 -> 10 1.04/1.04 10 -> 2, 3 1.04/1.04 11 -> 10 1.04/1.04 12 -> 10 1.04/1.04 13 -> 15, 16 1.04/1.04 14 -> 15, 16 1.04/1.04 15 -> 19 1.04/1.04 16 -> 19 1.04/1.04 17 -> 2, 3 1.04/1.04 18 -> 4, 5 1.04/1.04 19 -> 2, 3 1.04/1.04 Where: 1.04/1.04 0) f14#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) 1.04/1.04 1) f13#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, 10, 2, 1) 1.04/1.04 2) f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I34 + I35, I33, I34, I35) [I34 <= I35] 1.04/1.04 3) f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I52 - I53, I51, I52, I53) [1 + I53 <= I52] 1.04/1.04 4) f6#(I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I69, I55, I70, I57, I71, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) [I69 <= I71] 1.04/1.04 5) f6#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f8#(I72, I89, I74, I88, I76, I87, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) [1 + I89 <= I87] 1.04/1.04 6) f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [I90 <= I92] 1.04/1.04 7) f12#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f9#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 + I110 <= I108] 1.04/1.04 8) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f10#(I126, I127, I128, I129, I130, I131, I126, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I126 <= I130] 1.04/1.04 9) f11#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f10#(I144, I145, I146, I147, I148, I149, I148, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161) [1 + I148 <= I144] 1.04/1.04 10) f10#(I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f4#(I162, I163, I164, I165, I166, I167, I168, I169, I168, I171, I172, I173, I168, I175, I176, I168 + I177, I178, I179) 1.04/1.04 11) f9#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f10#(I180, I181, I182, I183, I184, I185, I182, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) [I182 <= I184] 1.04/1.04 12) f9#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) -> f10#(I198, I199, I200, I201, I202, I203, I202, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [1 + I202 <= I200] 1.04/1.04 13) f8#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f7#(I216, I217, I218, I219, I220, I221, I222, I223, I224, rnd10, I226, I227, I228, I229, I230, I231, I232, I233) [rnd10 = rnd10 /\ I217 <= I219] 1.04/1.04 14) f8#(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f7#(I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) [1 + I237 <= I235] 1.04/1.04 15) f7#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f3#(I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, rnd11, I263, I264, I265, I266, I267, I268, I269) [rnd11 = rnd11 /\ I253 <= I257] 1.04/1.04 16) f7#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) -> f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287) [1 + I275 <= I271] 1.04/1.04 17) f5#(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f4#(I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, rnd12, I300, I301, I302, I303, I304, I305) [rnd12 = rnd12 /\ I303 <= I304] 1.04/1.04 18) f5#(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f6#(I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) [1 + I322 <= I321] 1.04/1.04 19) f3#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341) -> f4#(I324, I325, I326, I327, I328, I329, I330, I325, I332, I333, I334, I335, I336, I325, I338, I339, I340, rnd18) [rnd18 = rnd18] 1.04/1.04 1.04/1.04 We have the following SCCs. 1.04/1.04 1.04/4.01 EOF