3.22/3.23	YES
3.22/3.23	
3.22/3.23	DP problem for innermost termination.
3.22/3.23	P =
3.22/3.23	  init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23) 
3.22/3.23	  f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22) -> f7#(I23, I1 - 1, 0, 1, 1, I24, I25, I7, I26, I9, I27, I11, 0, 2, I28, I29, I30, I31, I32, I19 + 1, I33, I21 + 1, I22 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I22 - 1 /\ -1 <= I21 - 1 /\ 11 <= I0 - 1 /\ 13 <= I23 - 1 /\ I20 + 9 <= I0 /\ I22 + 3 <= I0 /\ I21 + 5 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15]
3.22/3.23	  f7#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7#(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	  f2#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f7#(I95, I72, I84, I82, I78, I83, I77, I96, I74, I85, I76, 0, I75, I79, I80, I81, I86, I87, I88, I90, I97, I91, I92) [I91 + 5 <= I73 /\ I92 + 3 <= I73 /\ 11 <= I95 - 1 /\ 11 <= I73 - 1]
3.22/3.23	  f3#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1#(I121, I122, I123, I124, 1, 0, 0, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) [7 <= I122 - 1 /\ 0 <= I98 - 1 /\ I122 - 7 <= I98 /\ 0 <= I99 - 1 /\ -1 <= I121 - 1]
3.22/3.23	  f6#(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6#(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	  f4#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f6#(1, I208, I185, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228) [0 <= I185 - 1]
3.22/3.23	  f4#(I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f6#(0, 0, I229, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [0 <= I230 - 1 /\ 0 <= I229 - 1]
3.22/3.23	  f5#(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294) -> f4#(I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317) [-1 <= I273 - 1 /\ I296 <= I273 - 1 /\ -1 <= I272 - 1 /\ I295 <= I272 - 1]
3.22/3.23	  f3#(I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340) -> f4#(I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [-1 <= I364 - 1 /\ 0 <= I319 - 1 /\ -1 <= I365 - 1 /\ I341 <= I365 - 1 /\ -1 <= y3 - 1 /\ I342 <= y3 - 1 /\ 0 <= I318 - 1]
3.22/3.23	  f1#(I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f2#(I366, I389, 0, 0, I369, I390, I391, 0, 0, 0, I392, I393, I394, I395, I368, I368, I369, I396, I370, I371, I372, I397, I398) [I390 = I391 /\ I371 + 5 <= I367 /\ I372 + 3 <= I367 /\ 9 <= I389 - 1 /\ 9 <= I367 - 1 /\ I389 <= I367]
3.22/3.23	R = 
3.22/3.23	  init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23) 
3.22/3.23	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22) -> f7(I23, I1 - 1, 0, 1, 1, I24, I25, I7, I26, I9, I27, I11, 0, 2, I28, I29, I30, I31, I32, I19 + 1, I33, I21 + 1, I22 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I22 - 1 /\ -1 <= I21 - 1 /\ 11 <= I0 - 1 /\ 13 <= I23 - 1 /\ I20 + 9 <= I0 /\ I22 + 3 <= I0 /\ I21 + 5 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15]
3.22/3.23	  f7(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	  f2(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f7(I95, I72, I84, I82, I78, I83, I77, I96, I74, I85, I76, 0, I75, I79, I80, I81, I86, I87, I88, I90, I97, I91, I92) [I91 + 5 <= I73 /\ I92 + 3 <= I73 /\ 11 <= I95 - 1 /\ 11 <= I73 - 1]
3.22/3.23	  f3(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I121, I122, I123, I124, 1, 0, 0, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) [7 <= I122 - 1 /\ 0 <= I98 - 1 /\ I122 - 7 <= I98 /\ 0 <= I99 - 1 /\ -1 <= I121 - 1]
3.22/3.23	  f6(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	  f4(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f6(1, I208, I185, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228) [0 <= I185 - 1]
3.22/3.23	  f4(I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f6(0, 0, I229, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [0 <= I230 - 1 /\ 0 <= I229 - 1]
3.22/3.23	  f5(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294) -> f4(I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317) [-1 <= I273 - 1 /\ I296 <= I273 - 1 /\ -1 <= I272 - 1 /\ I295 <= I272 - 1]
3.22/3.23	  f3(I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340) -> f4(I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [-1 <= I364 - 1 /\ 0 <= I319 - 1 /\ -1 <= I365 - 1 /\ I341 <= I365 - 1 /\ -1 <= y3 - 1 /\ I342 <= y3 - 1 /\ 0 <= I318 - 1]
3.22/3.23	  f1(I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f2(I366, I389, 0, 0, I369, I390, I391, 0, 0, 0, I392, I393, I394, I395, I368, I368, I369, I396, I370, I371, I372, I397, I398) [I390 = I391 /\ I371 + 5 <= I367 /\ I372 + 3 <= I367 /\ 9 <= I389 - 1 /\ 9 <= I367 - 1 /\ I389 <= I367]
3.22/3.23	
3.22/3.23	The dependency graph for this problem is:
3.22/3.23	  0 -> 4, 9
3.22/3.23	  1 -> 
3.22/3.23	  2 -> 1, 2
3.22/3.23	  3 -> 
3.22/3.23	  4 -> 10
3.22/3.23	  5 -> 5
3.22/3.23	  6 -> 5
3.22/3.23	  7 -> 
3.22/3.23	  8 -> 6, 7
3.22/3.23	  9 -> 6, 7
3.22/3.23	  10 -> 3
3.22/3.23	Where:
3.22/3.23	  0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23) 
3.22/3.23	  1) f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22) -> f7#(I23, I1 - 1, 0, 1, 1, I24, I25, I7, I26, I9, I27, I11, 0, 2, I28, I29, I30, I31, I32, I19 + 1, I33, I21 + 1, I22 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I22 - 1 /\ -1 <= I21 - 1 /\ 11 <= I0 - 1 /\ 13 <= I23 - 1 /\ I20 + 9 <= I0 /\ I22 + 3 <= I0 /\ I21 + 5 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15]
3.22/3.23	  2) f7#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7#(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	  3) f2#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f7#(I95, I72, I84, I82, I78, I83, I77, I96, I74, I85, I76, 0, I75, I79, I80, I81, I86, I87, I88, I90, I97, I91, I92) [I91 + 5 <= I73 /\ I92 + 3 <= I73 /\ 11 <= I95 - 1 /\ 11 <= I73 - 1]
3.22/3.23	  4) f3#(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1#(I121, I122, I123, I124, 1, 0, 0, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) [7 <= I122 - 1 /\ 0 <= I98 - 1 /\ I122 - 7 <= I98 /\ 0 <= I99 - 1 /\ -1 <= I121 - 1]
3.22/3.23	  5) f6#(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6#(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	  6) f4#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f6#(1, I208, I185, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228) [0 <= I185 - 1]
3.22/3.23	  7) f4#(I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f6#(0, 0, I229, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [0 <= I230 - 1 /\ 0 <= I229 - 1]
3.22/3.23	  8) f5#(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294) -> f4#(I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317) [-1 <= I273 - 1 /\ I296 <= I273 - 1 /\ -1 <= I272 - 1 /\ I295 <= I272 - 1]
3.22/3.23	  9) f3#(I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340) -> f4#(I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [-1 <= I364 - 1 /\ 0 <= I319 - 1 /\ -1 <= I365 - 1 /\ I341 <= I365 - 1 /\ -1 <= y3 - 1 /\ I342 <= y3 - 1 /\ 0 <= I318 - 1]
3.22/3.23	  10) f1#(I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f2#(I366, I389, 0, 0, I369, I390, I391, 0, 0, 0, I392, I393, I394, I395, I368, I368, I369, I396, I370, I371, I372, I397, I398) [I390 = I391 /\ I371 + 5 <= I367 /\ I372 + 3 <= I367 /\ 9 <= I389 - 1 /\ 9 <= I367 - 1 /\ I389 <= I367]
3.22/3.23	
3.22/3.23	We have the following SCCs.
3.22/3.23	  { 2 }
3.22/3.23	  { 5 }
3.22/3.23	
3.22/3.23	DP problem for innermost termination.
3.22/3.23	P =
3.22/3.23	  f6#(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6#(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	R = 
3.22/3.23	  init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23) 
3.22/3.23	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22) -> f7(I23, I1 - 1, 0, 1, 1, I24, I25, I7, I26, I9, I27, I11, 0, 2, I28, I29, I30, I31, I32, I19 + 1, I33, I21 + 1, I22 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I22 - 1 /\ -1 <= I21 - 1 /\ 11 <= I0 - 1 /\ 13 <= I23 - 1 /\ I20 + 9 <= I0 /\ I22 + 3 <= I0 /\ I21 + 5 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15]
3.22/3.23	  f7(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	  f2(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f7(I95, I72, I84, I82, I78, I83, I77, I96, I74, I85, I76, 0, I75, I79, I80, I81, I86, I87, I88, I90, I97, I91, I92) [I91 + 5 <= I73 /\ I92 + 3 <= I73 /\ 11 <= I95 - 1 /\ 11 <= I73 - 1]
3.22/3.23	  f3(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I121, I122, I123, I124, 1, 0, 0, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) [7 <= I122 - 1 /\ 0 <= I98 - 1 /\ I122 - 7 <= I98 /\ 0 <= I99 - 1 /\ -1 <= I121 - 1]
3.22/3.23	  f6(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	  f4(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f6(1, I208, I185, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228) [0 <= I185 - 1]
3.22/3.23	  f4(I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f6(0, 0, I229, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [0 <= I230 - 1 /\ 0 <= I229 - 1]
3.22/3.23	  f5(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294) -> f4(I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317) [-1 <= I273 - 1 /\ I296 <= I273 - 1 /\ -1 <= I272 - 1 /\ I295 <= I272 - 1]
3.22/3.23	  f3(I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340) -> f4(I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [-1 <= I364 - 1 /\ 0 <= I319 - 1 /\ -1 <= I365 - 1 /\ I341 <= I365 - 1 /\ -1 <= y3 - 1 /\ I342 <= y3 - 1 /\ 0 <= I318 - 1]
3.22/3.23	  f1(I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f2(I366, I389, 0, 0, I369, I390, I391, 0, 0, 0, I392, I393, I394, I395, I368, I368, I369, I396, I370, I371, I372, I397, I398) [I390 = I391 /\ I371 + 5 <= I367 /\ I372 + 3 <= I367 /\ 9 <= I389 - 1 /\ 9 <= I367 - 1 /\ I389 <= I367]
3.22/3.23	
3.22/3.23	We use the basic value criterion with the projection function NU:
3.22/3.23	  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23)] = z3
3.22/3.23	
3.22/3.23	This gives the following inequalities:
3.22/3.23	  I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1  ==>  I143 >! I164
3.22/3.23	
3.22/3.23	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
3.22/3.23	
3.22/3.23	DP problem for innermost termination.
3.22/3.23	P =
3.22/3.23	  f7#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7#(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	R = 
3.22/3.23	  init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23) 
3.22/3.23	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22) -> f7(I23, I1 - 1, 0, 1, 1, I24, I25, I7, I26, I9, I27, I11, 0, 2, I28, I29, I30, I31, I32, I19 + 1, I33, I21 + 1, I22 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I22 - 1 /\ -1 <= I21 - 1 /\ 11 <= I0 - 1 /\ 13 <= I23 - 1 /\ I20 + 9 <= I0 /\ I22 + 3 <= I0 /\ I21 + 5 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15]
3.22/3.23	  f7(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f7(I57, I35 - 1, I36, I58, I59, I39, I40, I41, I60, I43, I61, I45, I62, I63, I64, I65, I66, I67, I68, I53 + 1, I69, I55 + 1, I56 + 1) [0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34]
3.22/3.23	  f2(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f7(I95, I72, I84, I82, I78, I83, I77, I96, I74, I85, I76, 0, I75, I79, I80, I81, I86, I87, I88, I90, I97, I91, I92) [I91 + 5 <= I73 /\ I92 + 3 <= I73 /\ 11 <= I95 - 1 /\ 11 <= I73 - 1]
3.22/3.23	  f3(I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I121, I122, I123, I124, 1, 0, 0, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) [7 <= I122 - 1 /\ 0 <= I98 - 1 /\ I122 - 7 <= I98 /\ 0 <= I99 - 1 /\ -1 <= I121 - 1]
3.22/3.23	  f6(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f6(I141, I142, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184) [I164 <= I143 - 1 /\ 0 <= I141 - 1 /\ 0 <= I143 - 1 /\ 0 <= I142 - 1]
3.22/3.23	  f4(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207) -> f6(1, I208, I185, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228) [0 <= I185 - 1]
3.22/3.23	  f4(I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251) -> f6(0, 0, I229, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) [0 <= I230 - 1 /\ 0 <= I229 - 1]
3.22/3.23	  f5(I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294) -> f4(I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317) [-1 <= I273 - 1 /\ I296 <= I273 - 1 /\ -1 <= I272 - 1 /\ I295 <= I272 - 1]
3.22/3.23	  f3(I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340) -> f4(I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [-1 <= I364 - 1 /\ 0 <= I319 - 1 /\ -1 <= I365 - 1 /\ I341 <= I365 - 1 /\ -1 <= y3 - 1 /\ I342 <= y3 - 1 /\ 0 <= I318 - 1]
3.22/3.23	  f1(I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f2(I366, I389, 0, 0, I369, I390, I391, 0, 0, 0, I392, I393, I394, I395, I368, I368, I369, I396, I370, I371, I372, I397, I398) [I390 = I391 /\ I371 + 5 <= I367 /\ I372 + 3 <= I367 /\ 9 <= I389 - 1 /\ 9 <= I367 - 1 /\ I389 <= I367]
3.22/3.23	
3.22/3.23	We use the basic value criterion with the projection function NU:
3.22/3.23	  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23)] = z2
3.22/3.23	
3.22/3.23	This gives the following inequalities:
3.22/3.23	  0 <= I35 - 1 /\ -1 <= I70 - 1 /\ 0 <= I39 - 1 /\ 0 <= I36 - 1 /\ -1 <= I53 - 1 /\ I53 <= I70 - 1 /\ 0 <= I43 - 1 /\ 0 <= I37 - 1 /\ 0 <= I46 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ -1 <= I71 - 1 /\ 0 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I51 - 1 /\ 0 <= I47 - 1 /\ 0 <= I52 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 9 <= I34 - 1 /\ 9 <= I57 - 1 /\ I54 + 9 <= I34 /\ I56 + 3 <= I34 /\ I55 + 5 <= I34  ==>  I35 >! I35 - 1
3.22/3.23	
3.22/3.23	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
3.22/6.21	EOF