14.21/14.34 MAYBE 14.21/14.34 14.21/14.34 DP problem for innermost termination. 14.21/14.34 P = 14.21/14.34 f14#(x1, x2, x3) -> f13#(x1, x2, x3) 14.21/14.34 f13#(I0, I1, I2) -> f4#(rnd1, I1, I2) [y1 = y1 /\ rnd1 = rnd1] 14.21/14.34 f3#(I3, I4, I5) -> f5#(1 + I3, I4, I5) [I3 <= I4] 14.21/14.34 f3#(I6, I7, I8) -> f5#(1 + I6, I7, I8) [1 + I7 <= I6] 14.21/14.34 f2#(I9, I10, I11) -> f3#(I9, I10, I11) [1 + I11 <= 0] 14.21/14.34 f2#(I12, I13, I14) -> f3#(I12, I13, I14) [1 <= I14] 14.21/14.34 f2#(I15, I16, I17) -> f6#(I15, I16, I17) [0 <= I17 /\ I17 <= 0] 14.21/14.34 f7#(I18, I19, I20) -> f6#(-1 + I18, I19, I20) [3 <= I18] 14.21/14.34 f7#(I21, I22, I23) -> f4#(I21, I22, I23) [I21 <= 2] 14.21/14.34 f12#(I24, I25, I26) -> f11#(I24, I25, I26) 14.21/14.34 f11#(I27, I28, I29) -> f12#(I27, I28, I29) 14.21/14.34 f10#(I30, I31, I32) -> f11#(I30, I31, I32) 14.21/14.34 f6#(I36, I37, I38) -> f7#(I36, I37, I38) 14.21/14.34 f5#(I39, I40, I41) -> f1#(I39, I40, I41) 14.21/14.34 f4#(I42, I43, I44) -> f5#(I42, I43, I44) 14.21/14.34 f1#(I45, I46, I47) -> f3#(I45, I46, I47) [I45 <= I46] 14.21/14.34 f1#(I48, I49, I50) -> f2#(I48, I49, rnd3) [rnd3 = rnd3 /\ 1 + I49 <= I48] 14.21/14.34 R = 14.21/14.34 f14(x1, x2, x3) -> f13(x1, x2, x3) 14.21/14.34 f13(I0, I1, I2) -> f4(rnd1, I1, I2) [y1 = y1 /\ rnd1 = rnd1] 14.21/14.34 f3(I3, I4, I5) -> f5(1 + I3, I4, I5) [I3 <= I4] 14.21/14.34 f3(I6, I7, I8) -> f5(1 + I6, I7, I8) [1 + I7 <= I6] 14.21/14.34 f2(I9, I10, I11) -> f3(I9, I10, I11) [1 + I11 <= 0] 14.21/14.34 f2(I12, I13, I14) -> f3(I12, I13, I14) [1 <= I14] 14.21/14.34 f2(I15, I16, I17) -> f6(I15, I16, I17) [0 <= I17 /\ I17 <= 0] 14.21/14.34 f7(I18, I19, I20) -> f6(-1 + I18, I19, I20) [3 <= I18] 14.21/14.34 f7(I21, I22, I23) -> f4(I21, I22, I23) [I21 <= 2] 14.21/14.34 f12(I24, I25, I26) -> f11(I24, I25, I26) 14.21/14.34 f11(I27, I28, I29) -> f12(I27, I28, I29) 14.21/14.34 f10(I30, I31, I32) -> f11(I30, I31, I32) 14.21/14.34 f8(I33, I34, I35) -> f9(I33, I34, I35) 14.21/14.34 f6(I36, I37, I38) -> f7(I36, I37, I38) 14.21/14.34 f5(I39, I40, I41) -> f1(I39, I40, I41) 14.21/14.34 f4(I42, I43, I44) -> f5(I42, I43, I44) 14.21/14.34 f1(I45, I46, I47) -> f3(I45, I46, I47) [I45 <= I46] 14.21/14.34 f1(I48, I49, I50) -> f2(I48, I49, rnd3) [rnd3 = rnd3 /\ 1 + I49 <= I48] 14.21/14.34 14.21/14.34 The dependency graph for this problem is: 14.21/14.34 0 -> 1 14.21/14.34 1 -> 14 14.21/14.34 2 -> 13 14.21/14.34 3 -> 13 14.21/14.34 4 -> 2, 3 14.21/14.34 5 -> 2, 3 14.21/14.34 6 -> 12 14.21/14.34 7 -> 12 14.21/14.34 8 -> 14 14.21/14.34 9 -> 10 14.21/14.34 10 -> 9 14.21/14.34 11 -> 10 14.21/14.34 12 -> 7, 8 14.21/14.34 13 -> 15, 16 14.21/14.34 14 -> 13 14.21/14.34 15 -> 2 14.21/14.34 16 -> 4, 5, 6 14.21/14.34 Where: 14.21/14.34 0) f14#(x1, x2, x3) -> f13#(x1, x2, x3) 14.21/14.34 1) f13#(I0, I1, I2) -> f4#(rnd1, I1, I2) [y1 = y1 /\ rnd1 = rnd1] 14.21/14.34 2) f3#(I3, I4, I5) -> f5#(1 + I3, I4, I5) [I3 <= I4] 14.21/14.34 3) f3#(I6, I7, I8) -> f5#(1 + I6, I7, I8) [1 + I7 <= I6] 14.21/14.34 4) f2#(I9, I10, I11) -> f3#(I9, I10, I11) [1 + I11 <= 0] 14.21/14.34 5) f2#(I12, I13, I14) -> f3#(I12, I13, I14) [1 <= I14] 14.21/14.34 6) f2#(I15, I16, I17) -> f6#(I15, I16, I17) [0 <= I17 /\ I17 <= 0] 14.21/14.34 7) f7#(I18, I19, I20) -> f6#(-1 + I18, I19, I20) [3 <= I18] 14.21/14.34 8) f7#(I21, I22, I23) -> f4#(I21, I22, I23) [I21 <= 2] 14.21/14.34 9) f12#(I24, I25, I26) -> f11#(I24, I25, I26) 14.21/14.34 10) f11#(I27, I28, I29) -> f12#(I27, I28, I29) 14.21/14.34 11) f10#(I30, I31, I32) -> f11#(I30, I31, I32) 14.21/14.34 12) f6#(I36, I37, I38) -> f7#(I36, I37, I38) 14.21/14.34 13) f5#(I39, I40, I41) -> f1#(I39, I40, I41) 14.21/14.34 14) f4#(I42, I43, I44) -> f5#(I42, I43, I44) 14.21/14.34 15) f1#(I45, I46, I47) -> f3#(I45, I46, I47) [I45 <= I46] 14.21/14.34 16) f1#(I48, I49, I50) -> f2#(I48, I49, rnd3) [rnd3 = rnd3 /\ 1 + I49 <= I48] 14.21/14.34 14.21/14.34 We have the following SCCs. 14.21/14.34 { 9, 10 } 14.21/14.34 { 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16 } 14.21/14.34 14.21/14.34 DP problem for innermost termination. 14.21/14.34 P = 14.21/14.34 f3#(I3, I4, I5) -> f5#(1 + I3, I4, I5) [I3 <= I4] 14.21/14.34 f3#(I6, I7, I8) -> f5#(1 + I6, I7, I8) [1 + I7 <= I6] 14.21/14.34 f2#(I9, I10, I11) -> f3#(I9, I10, I11) [1 + I11 <= 0] 14.21/14.34 f2#(I12, I13, I14) -> f3#(I12, I13, I14) [1 <= I14] 14.21/14.34 f2#(I15, I16, I17) -> f6#(I15, I16, I17) [0 <= I17 /\ I17 <= 0] 14.21/14.34 f7#(I18, I19, I20) -> f6#(-1 + I18, I19, I20) [3 <= I18] 14.21/14.34 f7#(I21, I22, I23) -> f4#(I21, I22, I23) [I21 <= 2] 14.21/14.34 f6#(I36, I37, I38) -> f7#(I36, I37, I38) 14.21/14.34 f5#(I39, I40, I41) -> f1#(I39, I40, I41) 14.21/14.34 f4#(I42, I43, I44) -> f5#(I42, I43, I44) 14.21/14.34 f1#(I45, I46, I47) -> f3#(I45, I46, I47) [I45 <= I46] 14.21/14.34 f1#(I48, I49, I50) -> f2#(I48, I49, rnd3) [rnd3 = rnd3 /\ 1 + I49 <= I48] 14.21/14.34 R = 14.21/14.34 f14(x1, x2, x3) -> f13(x1, x2, x3) 14.21/14.34 f13(I0, I1, I2) -> f4(rnd1, I1, I2) [y1 = y1 /\ rnd1 = rnd1] 14.21/14.34 f3(I3, I4, I5) -> f5(1 + I3, I4, I5) [I3 <= I4] 14.21/14.34 f3(I6, I7, I8) -> f5(1 + I6, I7, I8) [1 + I7 <= I6] 14.21/14.34 f2(I9, I10, I11) -> f3(I9, I10, I11) [1 + I11 <= 0] 14.21/14.34 f2(I12, I13, I14) -> f3(I12, I13, I14) [1 <= I14] 14.21/14.34 f2(I15, I16, I17) -> f6(I15, I16, I17) [0 <= I17 /\ I17 <= 0] 14.21/14.34 f7(I18, I19, I20) -> f6(-1 + I18, I19, I20) [3 <= I18] 14.21/14.34 f7(I21, I22, I23) -> f4(I21, I22, I23) [I21 <= 2] 14.21/14.34 f12(I24, I25, I26) -> f11(I24, I25, I26) 14.21/14.34 f11(I27, I28, I29) -> f12(I27, I28, I29) 14.21/14.34 f10(I30, I31, I32) -> f11(I30, I31, I32) 14.21/14.34 f8(I33, I34, I35) -> f9(I33, I34, I35) 14.21/14.34 f6(I36, I37, I38) -> f7(I36, I37, I38) 14.21/14.34 f5(I39, I40, I41) -> f1(I39, I40, I41) 14.21/14.34 f4(I42, I43, I44) -> f5(I42, I43, I44) 14.21/14.34 f1(I45, I46, I47) -> f3(I45, I46, I47) [I45 <= I46] 14.21/14.34 f1(I48, I49, I50) -> f2(I48, I49, rnd3) [rnd3 = rnd3 /\ 1 + I49 <= I48] 14.21/14.34 14.21/17.31 EOF