21.17/21.15	MAYBE
21.17/21.15	
21.17/21.15	DP problem for innermost termination.
21.17/21.15	P =
21.17/21.15	  f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 
21.17/21.15	  f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f1#(rnd1, I1, I2, I3, I4, I5, I6, I7, I1, I9, I10, 1) [y1 = 1 /\ rnd1 = rnd1]
21.17/21.15	  f3#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) [I22 <= 0]
21.17/21.15	  f3#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) [1 <= I34]
21.17/21.15	  f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f10#(I36, I37, I38, I39, rnd5, I41, I42, I43, I44, rnd10, I46, 0) [rnd10 = rnd5 /\ rnd5 = rnd5 /\ 1 <= I47]
21.17/21.15	  f2#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [I59 <= 0]
21.17/21.15	  f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
21.17/21.15	  f7#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 
21.17/21.15	  f10#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I84, I85, I86, I87, I88, rnd6, I90, rnd8, I92, I93, I94, I95) [rnd8 = rnd6 /\ rnd6 = rnd6 /\ I95 <= 0]
21.17/21.15	  f10#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f8#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 <= I107]
21.17/21.15	  f9#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f8#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, 1) [1000 <= I115 - I117]
21.17/21.15	  f9#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f8#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) [1 + I127 - I129 <= 1000]
21.17/21.15	  f8#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6#(I132, I133, rnd3, I135, I136, I137, I138, I139, I140, I141, I142, I143) [rnd3 = rnd3]
21.17/21.15	  f6#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f7#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 
21.17/21.15	  f1#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3#(I168, I169, I170, rnd4, I172, I173, 1, I175, 0, I177, rnd11, I179) [rnd11 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I176]
21.17/21.15	  f1#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f2#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) [I188 <= 0]
21.17/21.15	R = 
21.17/21.15	  f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 
21.17/21.15	  f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f1(rnd1, I1, I2, I3, I4, I5, I6, I7, I1, I9, I10, 1) [y1 = 1 /\ rnd1 = rnd1]
21.17/21.15	  f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) [I22 <= 0]
21.17/21.15	  f3(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) [1 <= I34]
21.17/21.15	  f2(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f10(I36, I37, I38, I39, rnd5, I41, I42, I43, I44, rnd10, I46, 0) [rnd10 = rnd5 /\ rnd5 = rnd5 /\ 1 <= I47]
21.17/21.15	  f2(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f10(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [I59 <= 0]
21.17/21.15	  f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
21.17/21.15	  f7(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 
21.17/21.15	  f10(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I84, I85, I86, I87, I88, rnd6, I90, rnd8, I92, I93, I94, I95) [rnd8 = rnd6 /\ rnd6 = rnd6 /\ I95 <= 0]
21.17/21.15	  f10(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f8(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 <= I107]
21.17/21.15	  f9(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f8(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, 1) [1000 <= I115 - I117]
21.17/21.15	  f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f8(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) [1 + I127 - I129 <= 1000]
21.17/21.15	  f8(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, rnd3, I135, I136, I137, I138, I139, I140, I141, I142, I143) [rnd3 = rnd3]
21.17/21.15	  f6(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f7(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 
21.17/21.15	  f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f5(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 
21.17/21.15	  f1(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(I168, I169, I170, rnd4, I172, I173, 1, I175, 0, I177, rnd11, I179) [rnd11 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I176]
21.17/21.15	  f1(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f2(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) [I188 <= 0]
21.17/21.15	
21.17/21.15	The dependency graph for this problem is:
21.17/21.15	  0 -> 1
21.17/21.15	  1 -> 14, 15
21.17/21.15	  2 -> 13
21.17/21.15	  3 -> 4, 5
21.17/21.15	  4 -> 8
21.17/21.15	  5 -> 8
21.17/21.15	  6 -> 7
21.17/21.15	  7 -> 6
21.17/21.15	  8 -> 10, 11
21.17/21.15	  9 -> 12
21.17/21.15	  10 -> 12
21.17/21.15	  11 -> 12
21.17/21.15	  12 -> 13
21.17/21.15	  13 -> 7
21.17/21.15	  14 -> 2, 3
21.17/21.15	  15 -> 4, 5
21.17/21.15	Where:
21.17/21.15	  0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 
21.17/21.15	  1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f1#(rnd1, I1, I2, I3, I4, I5, I6, I7, I1, I9, I10, 1) [y1 = 1 /\ rnd1 = rnd1]
21.17/21.15	  2) f3#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) [I22 <= 0]
21.17/21.15	  3) f3#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) [1 <= I34]
21.17/21.15	  4) f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f10#(I36, I37, I38, I39, rnd5, I41, I42, I43, I44, rnd10, I46, 0) [rnd10 = rnd5 /\ rnd5 = rnd5 /\ 1 <= I47]
21.17/21.15	  5) f2#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [I59 <= 0]
21.17/21.15	  6) f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
21.17/21.15	  7) f7#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 
21.17/21.15	  8) f10#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I84, I85, I86, I87, I88, rnd6, I90, rnd8, I92, I93, I94, I95) [rnd8 = rnd6 /\ rnd6 = rnd6 /\ I95 <= 0]
21.17/21.15	  9) f10#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f8#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 <= I107]
21.17/21.15	  10) f9#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f8#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, 1) [1000 <= I115 - I117]
21.17/21.15	  11) f9#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f8#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) [1 + I127 - I129 <= 1000]
21.17/21.15	  12) f8#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6#(I132, I133, rnd3, I135, I136, I137, I138, I139, I140, I141, I142, I143) [rnd3 = rnd3]
21.17/21.15	  13) f6#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f7#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 
21.17/21.15	  14) f1#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3#(I168, I169, I170, rnd4, I172, I173, 1, I175, 0, I177, rnd11, I179) [rnd11 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I176]
21.17/21.15	  15) f1#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f2#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) [I188 <= 0]
21.17/21.15	
21.17/21.15	We have the following SCCs.
21.17/21.15	  { 6, 7 }
21.17/21.15	
21.17/21.15	DP problem for innermost termination.
21.17/21.15	P =
21.17/21.15	  f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
21.17/21.15	  f7#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 
21.17/21.15	R = 
21.17/21.15	  f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 
21.17/21.15	  f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f1(rnd1, I1, I2, I3, I4, I5, I6, I7, I1, I9, I10, 1) [y1 = 1 /\ rnd1 = rnd1]
21.17/21.15	  f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) [I22 <= 0]
21.17/21.15	  f3(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) [1 <= I34]
21.17/21.15	  f2(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f10(I36, I37, I38, I39, rnd5, I41, I42, I43, I44, rnd10, I46, 0) [rnd10 = rnd5 /\ rnd5 = rnd5 /\ 1 <= I47]
21.17/21.15	  f2(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f10(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [I59 <= 0]
21.17/21.15	  f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
21.17/21.15	  f7(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 
21.17/21.15	  f10(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I84, I85, I86, I87, I88, rnd6, I90, rnd8, I92, I93, I94, I95) [rnd8 = rnd6 /\ rnd6 = rnd6 /\ I95 <= 0]
21.17/21.15	  f10(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f8(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 <= I107]
21.17/21.15	  f9(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f8(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, 1) [1000 <= I115 - I117]
21.17/21.15	  f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f8(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) [1 + I127 - I129 <= 1000]
21.17/21.15	  f8(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, rnd3, I135, I136, I137, I138, I139, I140, I141, I142, I143) [rnd3 = rnd3]
21.17/21.15	  f6(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f7(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 
21.17/21.15	  f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f5(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 
21.17/21.15	  f1(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(I168, I169, I170, rnd4, I172, I173, 1, I175, 0, I177, rnd11, I179) [rnd11 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I176]
21.17/21.15	  f1(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f2(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) [I188 <= 0]
21.17/21.15	
21.17/24.13	EOF