52.01/51.21 MAYBE 52.01/51.21 52.01/51.21 DP problem for innermost termination. 52.01/51.21 P = 52.01/51.21 f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 f11#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 f11#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 f11#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 f11#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 f11#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 f11#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10#(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 f10#(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8#(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 f10#(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7#(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 f7#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 f6#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5#(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f6#(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4#(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 f5#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6#(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 f4#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1#(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 f4#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2#(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 f3#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3#(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 f1#(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2#(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 R = 52.01/51.21 f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 f11(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 f11(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f9(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 52.01/51.21 f11(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 f11(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 f11(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 f2(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f9(I140, I141, I150, I151, I152, I153, I154, I155, rnd9, rnd10, rnd11, rnd12, I156, I157) [I157 = rnd10 /\ I156 = rnd9 /\ rnd12 = I155 /\ rnd11 = I154 /\ rnd10 = rnd10 /\ rnd9 = rnd9 /\ I155 = I155 /\ I154 = I154] 52.01/51.21 f10(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 f10(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 f8(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f9(I194, I195, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [I215 = I211 /\ I214 = I210 /\ I213 = I209 /\ I212 = I208 /\ I211 = I211 /\ I210 = I210 /\ I209 = I209 /\ I208 = I208] 52.01/51.21 f7(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 f6(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f6(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 f5(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 f4(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 f4(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 f3(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 f1(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 52.01/51.21 The dependency graph for this problem is: 52.01/51.21 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9 52.01/51.21 1 -> 52.01/51.21 2 -> 10, 11 52.01/51.21 3 -> 52.01/51.21 4 -> 12 52.01/51.21 5 -> 13, 14 52.01/51.21 6 -> 15 52.01/51.21 7 -> 16, 17 52.01/51.21 8 -> 19, 20 52.01/51.21 9 -> 10, 11 52.01/51.21 10 -> 52.01/51.21 11 -> 12 52.01/51.21 12 -> 13, 14 52.01/51.21 13 -> 15 52.01/51.21 14 -> 16, 17 52.01/51.21 15 -> 13, 14 52.01/51.21 16 -> 19, 20 52.01/51.21 17 -> 52.01/51.21 18 -> 19, 20 52.01/51.21 19 -> 18 52.01/51.21 20 -> 52.01/51.21 Where: 52.01/51.21 0) f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 1) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 2) f11#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 3) f11#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8#(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 4) f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 5) f11#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 6) f11#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 7) f11#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 8) f11#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 9) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10#(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 10) f10#(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8#(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 11) f10#(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7#(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 12) f7#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 13) f6#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5#(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 14) f6#(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4#(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 15) f5#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6#(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 16) f4#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1#(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 17) f4#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2#(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 18) f3#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 19) f1#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3#(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 20) f1#(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2#(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 52.01/51.21 We have the following SCCs. 52.01/51.21 { 13, 15 } 52.01/51.21 { 18, 19 } 52.01/51.21 52.01/51.21 DP problem for innermost termination. 52.01/51.21 P = 52.01/51.21 f3#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3#(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 R = 52.01/51.21 f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 f11(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 f11(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f9(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 52.01/51.21 f11(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 f11(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 f11(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 f2(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f9(I140, I141, I150, I151, I152, I153, I154, I155, rnd9, rnd10, rnd11, rnd12, I156, I157) [I157 = rnd10 /\ I156 = rnd9 /\ rnd12 = I155 /\ rnd11 = I154 /\ rnd10 = rnd10 /\ rnd9 = rnd9 /\ I155 = I155 /\ I154 = I154] 52.01/51.21 f10(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 f10(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 f8(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f9(I194, I195, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [I215 = I211 /\ I214 = I210 /\ I213 = I209 /\ I212 = I208 /\ I211 = I211 /\ I210 = I210 /\ I209 = I209 /\ I208 = I208] 52.01/51.21 f7(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 f6(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f6(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 f5(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 f4(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 f4(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 f3(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 f1(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 52.01/51.21 We use the basic value criterion with the projection function NU: 52.01/51.21 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z14 52.01/51.21 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z14 52.01/51.21 52.01/51.21 This gives the following inequalities: 52.01/51.21 ==> I323 (>! \union =) I323 52.01/51.21 1 <= -1 + I337 ==> I337 >! -1 + I337 52.01/51.21 52.01/51.21 We remove all the strictly oriented dependency pairs. 52.01/51.21 52.01/51.21 DP problem for innermost termination. 52.01/51.21 P = 52.01/51.21 f3#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 R = 52.01/51.21 f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 f11(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 f11(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f9(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 52.01/51.21 f11(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 f11(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 f11(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 f2(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f9(I140, I141, I150, I151, I152, I153, I154, I155, rnd9, rnd10, rnd11, rnd12, I156, I157) [I157 = rnd10 /\ I156 = rnd9 /\ rnd12 = I155 /\ rnd11 = I154 /\ rnd10 = rnd10 /\ rnd9 = rnd9 /\ I155 = I155 /\ I154 = I154] 52.01/51.21 f10(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 f10(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 f8(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f9(I194, I195, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [I215 = I211 /\ I214 = I210 /\ I213 = I209 /\ I212 = I208 /\ I211 = I211 /\ I210 = I210 /\ I209 = I209 /\ I208 = I208] 52.01/51.21 f7(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 f6(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f6(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 f5(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 f4(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 f4(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 f3(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 f1(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 52.01/51.21 The dependency graph for this problem is: 52.01/51.21 18 -> 52.01/51.21 Where: 52.01/51.21 18) f3#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 52.01/51.21 We have the following SCCs. 52.01/51.21 52.01/51.21 52.01/51.21 DP problem for innermost termination. 52.01/51.21 P = 52.01/51.21 f6#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5#(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f5#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6#(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 R = 52.01/51.21 f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 52.01/51.21 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) 52.01/51.21 f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f10(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) 52.01/51.21 f11(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) -> f8(I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41) 52.01/51.21 f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f7(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55) 52.01/51.21 f11(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f9(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 52.01/51.21 f11(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 52.01/51.21 f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) -> f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97) 52.01/51.21 f11(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f4(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) 52.01/51.21 f11(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f1(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125) 52.01/51.21 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f10(I126, I127, I136, I137, I138, I139, rnd7, rnd8, I134, I135, I136, I137, rnd13, rnd14) [rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd8 = rnd8 /\ rnd7 = rnd7] 52.01/51.21 f2(I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f9(I140, I141, I150, I151, I152, I153, I154, I155, rnd9, rnd10, rnd11, rnd12, I156, I157) [I157 = rnd10 /\ I156 = rnd9 /\ rnd12 = I155 /\ rnd11 = I154 /\ rnd10 = rnd10 /\ rnd9 = rnd9 /\ I155 = I155 /\ I154 = I154] 52.01/51.21 f10(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171) -> f8(I158, I159, I168, I169, I170, I171, I172, I173, I166, I167, I168, I169, I174, I175) [I175 = I173 /\ I174 = I172 /\ I173 = I173 /\ I172 = I172] 52.01/51.21 f10(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f7(I176, I177, I186, I187, I188, I189, I190, I191, I184, I185, I186, I187, I192, I193) [I193 = I191 /\ I192 = I190 /\ I191 = I191 /\ I190 = I190] 52.01/51.21 f8(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f9(I194, I195, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215) [I215 = I211 /\ I214 = I210 /\ I213 = I209 /\ I212 = I208 /\ I211 = I211 /\ I210 = I210 /\ I209 = I209 /\ I208 = I208] 52.01/51.21 f7(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I216, I217, I226, I227, I228, I229, I230, I223, I224, I225, I226, I227, I227, I231) [I231 = I230 /\ I230 = I230] 52.01/51.21 f6(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245) -> f5(I232, I233, I242, I243, I244, I245, I246, I239, I240, I241, I242, I243, I244, I247) [I247 = I246 /\ 1 + I232 <= I244 /\ I246 = I246] 52.01/51.21 f6(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261) -> f4(I248, I249, I258, I259, I260, I261, I262, I255, I256, I257, I258, I259, I260, I263) [I263 = I262 /\ I260 <= I248 /\ I262 = I262] 52.01/51.21 f5(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I264, I265, I274, I275, I276, I277, I278, I271, I272, I273, I274, I275, -1 * I265 + I276, I279) [I279 = I278 /\ I278 = I278] 52.01/51.21 f4(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f1(I280, I281, I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, I292) [1 <= I292] 52.01/51.21 f4(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307) -> f2(I294, I295, I304, I305, I306, I307, I308, I301, I302, I303, I304, I305, I306, I309) [I309 = I308 /\ I306 <= 0 /\ I308 = I308] 52.01/51.21 f3(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f1(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) 52.01/51.21 f1(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337) -> f3(I324, I325, I334, I335, I336, I337, I330, I331, I332, I333, I334, I335, I336, -1 + I337) [1 <= -1 + I337] 52.01/51.21 f1(I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f2(I338, I339, I348, I349, I350, I351, I344, I345, I346, I347, I348, I349, I350, I351) [-1 + I351 <= 0] 52.01/51.21 52.01/54.18 EOF