48.78/48.01 YES 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f15#(x1, x2, x3, x4, x5, x6, x7) -> f14#(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14#(I0, I1, I2, I3, I4, I5, I6) -> f1#(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5#(I22, I23, I24, I25, I26, I27, I28) -> f3#(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7#(I29, I30, I31, I32, I33, I34, I35) -> f6#(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7#(I36, I37, I38, I39, I40, I41, I42) -> f10#(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9#(I43, I44, I45, I46, I47, I48, I49) -> f8#(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11#(I57, I58, I59, I60, I61, I62, I63) -> f13#(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13#(I65, I66, I67, I68, I69, I70, I71) -> f12#(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12#(I72, I73, I74, I75, I76, I77, I78) -> f13#(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12#(I79, I80, I81, I82, I83, I84, I85) -> f9#(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10#(I87, I88, I89, I90, I91, I92, I93) -> f11#(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8#(I94, I95, I96, I97, I98, I99, I100) -> f9#(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8#(I101, I102, I103, I104, I105, I106, I107) -> f5#(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6#(I108, I109, I110, I111, I112, I113, I114) -> f7#(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3#(I115, I116, I117, I118, I119, I120, I121) -> f5#(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f1#(I129, I130, I131, I132, I133, I134, I135) -> f2#(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 0 -> 1 48.78/48.01 1 -> 18 48.78/48.01 2 -> 18 48.78/48.01 3 -> 16 48.78/48.01 4 -> 17 48.78/48.01 5 -> 16 48.78/48.01 6 -> 13 48.78/48.01 7 -> 14, 15 48.78/48.01 8 -> 13 48.78/48.01 9 -> 10 48.78/48.01 10 -> 11, 12 48.78/48.01 11 -> 10 48.78/48.01 12 -> 7 48.78/48.01 13 -> 8, 9 48.78/48.01 14 -> 7 48.78/48.01 15 -> 4 48.78/48.01 16 -> 5, 6 48.78/48.01 17 -> 4 48.78/48.01 18 -> 2, 3 48.78/48.01 Where: 48.78/48.01 0) f15#(x1, x2, x3, x4, x5, x6, x7) -> f14#(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 1) f14#(I0, I1, I2, I3, I4, I5, I6) -> f1#(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 2) f2#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 3) f2#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 4) f5#(I22, I23, I24, I25, I26, I27, I28) -> f3#(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 5) f7#(I29, I30, I31, I32, I33, I34, I35) -> f6#(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 6) f7#(I36, I37, I38, I39, I40, I41, I42) -> f10#(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 7) f9#(I43, I44, I45, I46, I47, I48, I49) -> f8#(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 8) f11#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 9) f11#(I57, I58, I59, I60, I61, I62, I63) -> f13#(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 10) f13#(I65, I66, I67, I68, I69, I70, I71) -> f12#(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 11) f12#(I72, I73, I74, I75, I76, I77, I78) -> f13#(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 12) f12#(I79, I80, I81, I82, I83, I84, I85) -> f9#(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 13) f10#(I87, I88, I89, I90, I91, I92, I93) -> f11#(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 14) f8#(I94, I95, I96, I97, I98, I99, I100) -> f9#(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 15) f8#(I101, I102, I103, I104, I105, I106, I107) -> f5#(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 16) f6#(I108, I109, I110, I111, I112, I113, I114) -> f7#(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 17) f3#(I115, I116, I117, I118, I119, I120, I121) -> f5#(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 18) f1#(I129, I130, I131, I132, I133, I134, I135) -> f2#(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 { 2, 18 } 48.78/48.01 { 5, 16 } 48.78/48.01 { 8, 13 } 48.78/48.01 { 10, 11 } 48.78/48.01 { 7, 14 } 48.78/48.01 { 4, 17 } 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f5#(I22, I23, I24, I25, I26, I27, I28) -> f3#(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f3#(I115, I116, I117, I118, I119, I120, I121) -> f5#(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z5) 48.78/48.01 NU[f5#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z5) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 ==> 50 + -1 * (1 + I26) >= 50 + -1 * (1 + I26) 48.78/48.01 1 + I119 <= 50 ==> 50 + -1 * (1 + I119) > 50 + -1 * (1 + (1 + I119)) with 50 + -1 * (1 + I119) >= 0 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f5#(I22, I23, I24, I25, I26, I27, I28) -> f3#(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 4 -> 48.78/48.01 Where: 48.78/48.01 4) f5#(I22, I23, I24, I25, I26, I27, I28) -> f3#(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f9#(I43, I44, I45, I46, I47, I48, I49) -> f8#(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f8#(I94, I95, I96, I97, I98, I99, I100) -> f9#(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f8#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z2) 48.78/48.01 NU[f9#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z2) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 ==> 50 + -1 * (1 + I44) >= 50 + -1 * (1 + I44) 48.78/48.01 1 + I95 <= 50 ==> 50 + -1 * (1 + I95) > 50 + -1 * (1 + (1 + I95)) with 50 + -1 * (1 + I95) >= 0 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f9#(I43, I44, I45, I46, I47, I48, I49) -> f8#(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 7 -> 48.78/48.01 Where: 48.78/48.01 7) f9#(I43, I44, I45, I46, I47, I48, I49) -> f8#(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f13#(I65, I66, I67, I68, I69, I70, I71) -> f12#(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12#(I72, I73, I74, I75, I76, I77, I78) -> f13#(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f12#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z1) 48.78/48.01 NU[f13#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z1) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 ==> 50 + -1 * (1 + I65) >= 50 + -1 * (1 + I65) 48.78/48.01 1 + I72 <= 50 ==> 50 + -1 * (1 + I72) > 50 + -1 * (1 + (1 + I72)) with 50 + -1 * (1 + I72) >= 0 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f13#(I65, I66, I67, I68, I69, I70, I71) -> f12#(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 10 -> 48.78/48.01 Where: 48.78/48.01 10) f13#(I65, I66, I67, I68, I69, I70, I71) -> f12#(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f11#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f10#(I87, I88, I89, I90, I91, I92, I93) -> f11#(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f10#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z5) 48.78/48.01 NU[f11#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z5) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 1 + I54 <= 50 ==> 50 + -1 * (1 + I54) > 50 + -1 * (1 + (1 + I54)) with 50 + -1 * (1 + I54) >= 0 48.78/48.01 ==> 50 + -1 * (1 + I91) >= 50 + -1 * (1 + I91) 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f10#(I87, I88, I89, I90, I91, I92, I93) -> f11#(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 13 -> 48.78/48.01 Where: 48.78/48.01 13) f10#(I87, I88, I89, I90, I91, I92, I93) -> f11#(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f7#(I29, I30, I31, I32, I33, I34, I35) -> f6#(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f6#(I108, I109, I110, I111, I112, I113, I114) -> f7#(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f6#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z4) 48.78/48.01 NU[f7#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z4) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 1 + I32 <= 50 ==> 50 + -1 * (1 + I32) > 50 + -1 * (1 + (1 + I32)) with 50 + -1 * (1 + I32) >= 0 48.78/48.01 ==> 50 + -1 * (1 + I111) >= 50 + -1 * (1 + I111) 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f6#(I108, I109, I110, I111, I112, I113, I114) -> f7#(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 16 -> 48.78/48.01 Where: 48.78/48.01 16) f6#(I108, I109, I110, I111, I112, I113, I114) -> f7#(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f2#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f1#(I129, I130, I131, I132, I133, I134, I135) -> f2#(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We use the reverse value criterion with the projection function NU: 48.78/48.01 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z3) 48.78/48.01 NU[f2#(z1,z2,z3,z4,z5,z6,z7)] = 50 + -1 * (1 + z3) 48.78/48.01 48.78/48.01 This gives the following inequalities: 48.78/48.01 1 + I9 <= 50 ==> 50 + -1 * (1 + I9) > 50 + -1 * (1 + (1 + I9)) with 50 + -1 * (1 + I9) >= 0 48.78/48.01 ==> 50 + -1 * (1 + I131) >= 50 + -1 * (1 + I131) 48.78/48.01 48.78/48.01 We remove all the strictly oriented dependency pairs. 48.78/48.01 48.78/48.01 DP problem for innermost termination. 48.78/48.01 P = 48.78/48.01 f1#(I129, I130, I131, I132, I133, I134, I135) -> f2#(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 R = 48.78/48.01 f15(x1, x2, x3, x4, x5, x6, x7) -> f14(x1, x2, x3, x4, x5, x6, x7) 48.78/48.01 f14(I0, I1, I2, I3, I4, I5, I6) -> f1(I0, I1, 0, I3, 0, rnd6, rnd7) [rnd6 = rnd6 /\ rnd7 = rnd7 /\ y1 = 0] 48.78/48.01 f2(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, 1 + I9, I10, I11, I12, I13) [1 + I9 <= 50] 48.78/48.01 f2(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, 0, I18, I19, I20) [50 <= I16 /\ I21 = 0] 48.78/48.01 f5(I22, I23, I24, I25, I26, I27, I28) -> f3(I22, I23, I24, I25, I26, I27, I28) 48.78/48.01 f7(I29, I30, I31, I32, I33, I34, I35) -> f6(I29, I30, I31, 1 + I32, I33, I34, I35) [1 + I32 <= 50] 48.78/48.01 f7(I36, I37, I38, I39, I40, I41, I42) -> f10(I36, I37, I38, I39, 0, I41, I42) [50 <= I39] 48.78/48.01 f9(I43, I44, I45, I46, I47, I48, I49) -> f8(I43, I44, I45, I46, I47, I48, I49) 48.78/48.01 f11(I50, I51, I52, I53, I54, I55, I56) -> f10(I50, I51, I52, I53, 1 + I54, I55, I56) [1 + I54 <= 50] 48.78/48.01 f11(I57, I58, I59, I60, I61, I62, I63) -> f13(0, I58, I59, I60, I61, I62, I63) [50 <= I61 /\ I64 = 0] 48.78/48.01 f13(I65, I66, I67, I68, I69, I70, I71) -> f12(I65, I66, I67, I68, I69, I70, I71) 48.78/48.01 f12(I72, I73, I74, I75, I76, I77, I78) -> f13(1 + I72, I73, I74, I75, I76, I77, I78) [1 + I72 <= 50] 48.78/48.01 f12(I79, I80, I81, I82, I83, I84, I85) -> f9(I79, 0, I81, I82, I83, I84, I85) [50 <= I79 /\ I86 = 0] 48.78/48.01 f10(I87, I88, I89, I90, I91, I92, I93) -> f11(I87, I88, I89, I90, I91, I92, I93) 48.78/48.01 f8(I94, I95, I96, I97, I98, I99, I100) -> f9(I94, 1 + I95, I96, I97, I98, I99, I100) [1 + I95 <= 50] 48.78/48.01 f8(I101, I102, I103, I104, I105, I106, I107) -> f5(I101, I102, I103, I104, 0, I106, I107) [50 <= I102] 48.78/48.01 f6(I108, I109, I110, I111, I112, I113, I114) -> f7(I108, I109, I110, I111, I112, I113, I114) 48.78/48.01 f3(I115, I116, I117, I118, I119, I120, I121) -> f5(I115, I116, I117, I118, 1 + I119, I120, I121) [1 + I119 <= 50] 48.78/48.01 f3(I122, I123, I124, I125, I126, I127, I128) -> f4(I122, I123, I124, I125, I126, I127, I128) [50 <= I126] 48.78/48.01 f1(I129, I130, I131, I132, I133, I134, I135) -> f2(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 The dependency graph for this problem is: 48.78/48.01 18 -> 48.78/48.01 Where: 48.78/48.01 18) f1#(I129, I130, I131, I132, I133, I134, I135) -> f2#(I129, I130, I131, I132, I133, I134, I135) 48.78/48.01 48.78/48.01 We have the following SCCs. 48.78/48.01 48.78/50.98 EOF