13.22/13.44 MAYBE 13.22/13.44 13.22/13.44 DP problem for innermost termination. 13.22/13.44 P = 13.22/13.44 f14#(x1, x2, x3) -> f13#(x1, x2, x3) 13.22/13.44 f13#(I0, I1, I2) -> f1#(rnd1, rnd2, I2) [y1 = y1 /\ rnd2 = rnd2 /\ rnd1 = rnd2] 13.22/13.44 f3#(I3, I4, I5) -> f12#(I3, I4, I5) [I3 <= 5] 13.22/13.44 f3#(I6, I7, I8) -> f11#(I6, I7, I8) [6 <= I6] 13.22/13.44 f12#(I9, I10, I11) -> f4#(I9, I10, I11) [1 <= I11] 13.22/13.44 f12#(I12, I13, I14) -> f11#(I12, I13, I14) [I14 <= 0] 13.22/13.44 f11#(I15, I16, I17) -> f2#(1 + I15, I16, I17) [I15 <= 5] 13.22/13.44 f11#(I18, I19, I20) -> f2#(1 + I18, I19, I20) [6 <= I18] 13.22/13.44 f10#(I21, I22, I23) -> f9#(I21, I22, I23) 13.22/13.44 f9#(I24, I25, I26) -> f10#(I24, I25, I26) 13.22/13.44 f5#(I27, I28, I29) -> f1#(I27, I28, I29) [I27 <= 2] 13.22/13.44 f5#(I30, I31, I32) -> f4#(-1 + I30, I31, I32) [3 <= I30] 13.22/13.44 f8#(I33, I34, I35) -> f9#(I33, I34, I35) 13.22/13.44 f4#(I39, I40, I41) -> f5#(I39, I40, I41) 13.22/13.44 f2#(I42, I43, I44) -> f3#(I42, I43, rnd3) [rnd3 = rnd3] 13.22/13.44 f1#(I45, I46, I47) -> f2#(I45, I46, I47) 13.22/13.44 R = 13.22/13.44 f14(x1, x2, x3) -> f13(x1, x2, x3) 13.22/13.44 f13(I0, I1, I2) -> f1(rnd1, rnd2, I2) [y1 = y1 /\ rnd2 = rnd2 /\ rnd1 = rnd2] 13.22/13.44 f3(I3, I4, I5) -> f12(I3, I4, I5) [I3 <= 5] 13.22/13.44 f3(I6, I7, I8) -> f11(I6, I7, I8) [6 <= I6] 13.22/13.44 f12(I9, I10, I11) -> f4(I9, I10, I11) [1 <= I11] 13.22/13.44 f12(I12, I13, I14) -> f11(I12, I13, I14) [I14 <= 0] 13.22/13.44 f11(I15, I16, I17) -> f2(1 + I15, I16, I17) [I15 <= 5] 13.22/13.44 f11(I18, I19, I20) -> f2(1 + I18, I19, I20) [6 <= I18] 13.22/13.44 f10(I21, I22, I23) -> f9(I21, I22, I23) 13.22/13.44 f9(I24, I25, I26) -> f10(I24, I25, I26) 13.22/13.44 f5(I27, I28, I29) -> f1(I27, I28, I29) [I27 <= 2] 13.22/13.44 f5(I30, I31, I32) -> f4(-1 + I30, I31, I32) [3 <= I30] 13.22/13.44 f8(I33, I34, I35) -> f9(I33, I34, I35) 13.22/13.44 f6(I36, I37, I38) -> f7(I36, I37, I38) 13.22/13.44 f4(I39, I40, I41) -> f5(I39, I40, I41) 13.22/13.44 f2(I42, I43, I44) -> f3(I42, I43, rnd3) [rnd3 = rnd3] 13.22/13.44 f1(I45, I46, I47) -> f2(I45, I46, I47) 13.22/13.44 13.22/13.44 The dependency graph for this problem is: 13.22/13.44 0 -> 1 13.22/13.44 1 -> 15 13.22/13.44 2 -> 4, 5 13.22/13.44 3 -> 7 13.22/13.44 4 -> 13 13.22/13.44 5 -> 6, 7 13.22/13.44 6 -> 14 13.22/13.44 7 -> 14 13.22/13.44 8 -> 9 13.22/13.44 9 -> 8 13.22/13.44 10 -> 15 13.22/13.44 11 -> 13 13.22/13.44 12 -> 9 13.22/13.44 13 -> 10, 11 13.22/13.44 14 -> 2, 3 13.22/13.44 15 -> 14 13.22/13.44 Where: 13.22/13.44 0) f14#(x1, x2, x3) -> f13#(x1, x2, x3) 13.22/13.44 1) f13#(I0, I1, I2) -> f1#(rnd1, rnd2, I2) [y1 = y1 /\ rnd2 = rnd2 /\ rnd1 = rnd2] 13.22/13.44 2) f3#(I3, I4, I5) -> f12#(I3, I4, I5) [I3 <= 5] 13.22/13.44 3) f3#(I6, I7, I8) -> f11#(I6, I7, I8) [6 <= I6] 13.22/13.44 4) f12#(I9, I10, I11) -> f4#(I9, I10, I11) [1 <= I11] 13.22/13.44 5) f12#(I12, I13, I14) -> f11#(I12, I13, I14) [I14 <= 0] 13.22/13.44 6) f11#(I15, I16, I17) -> f2#(1 + I15, I16, I17) [I15 <= 5] 13.22/13.44 7) f11#(I18, I19, I20) -> f2#(1 + I18, I19, I20) [6 <= I18] 13.22/13.44 8) f10#(I21, I22, I23) -> f9#(I21, I22, I23) 13.22/13.44 9) f9#(I24, I25, I26) -> f10#(I24, I25, I26) 13.22/13.44 10) f5#(I27, I28, I29) -> f1#(I27, I28, I29) [I27 <= 2] 13.22/13.44 11) f5#(I30, I31, I32) -> f4#(-1 + I30, I31, I32) [3 <= I30] 13.22/13.44 12) f8#(I33, I34, I35) -> f9#(I33, I34, I35) 13.22/13.44 13) f4#(I39, I40, I41) -> f5#(I39, I40, I41) 13.22/13.44 14) f2#(I42, I43, I44) -> f3#(I42, I43, rnd3) [rnd3 = rnd3] 13.22/13.44 15) f1#(I45, I46, I47) -> f2#(I45, I46, I47) 13.22/13.44 13.22/13.44 We have the following SCCs. 13.22/13.44 { 8, 9 } 13.22/13.44 { 2, 3, 4, 5, 6, 7, 10, 11, 13, 14, 15 } 13.22/13.44 13.22/13.44 DP problem for innermost termination. 13.22/13.44 P = 13.22/13.44 f3#(I3, I4, I5) -> f12#(I3, I4, I5) [I3 <= 5] 13.22/13.44 f3#(I6, I7, I8) -> f11#(I6, I7, I8) [6 <= I6] 13.22/13.44 f12#(I9, I10, I11) -> f4#(I9, I10, I11) [1 <= I11] 13.22/13.44 f12#(I12, I13, I14) -> f11#(I12, I13, I14) [I14 <= 0] 13.22/13.44 f11#(I15, I16, I17) -> f2#(1 + I15, I16, I17) [I15 <= 5] 13.22/13.44 f11#(I18, I19, I20) -> f2#(1 + I18, I19, I20) [6 <= I18] 13.22/13.44 f5#(I27, I28, I29) -> f1#(I27, I28, I29) [I27 <= 2] 13.22/13.44 f5#(I30, I31, I32) -> f4#(-1 + I30, I31, I32) [3 <= I30] 13.22/13.44 f4#(I39, I40, I41) -> f5#(I39, I40, I41) 13.22/13.44 f2#(I42, I43, I44) -> f3#(I42, I43, rnd3) [rnd3 = rnd3] 13.22/13.44 f1#(I45, I46, I47) -> f2#(I45, I46, I47) 13.22/13.44 R = 13.22/13.44 f14(x1, x2, x3) -> f13(x1, x2, x3) 13.22/13.44 f13(I0, I1, I2) -> f1(rnd1, rnd2, I2) [y1 = y1 /\ rnd2 = rnd2 /\ rnd1 = rnd2] 13.22/13.44 f3(I3, I4, I5) -> f12(I3, I4, I5) [I3 <= 5] 13.22/13.44 f3(I6, I7, I8) -> f11(I6, I7, I8) [6 <= I6] 13.22/13.44 f12(I9, I10, I11) -> f4(I9, I10, I11) [1 <= I11] 13.22/13.44 f12(I12, I13, I14) -> f11(I12, I13, I14) [I14 <= 0] 13.22/13.44 f11(I15, I16, I17) -> f2(1 + I15, I16, I17) [I15 <= 5] 13.22/13.44 f11(I18, I19, I20) -> f2(1 + I18, I19, I20) [6 <= I18] 13.22/13.44 f10(I21, I22, I23) -> f9(I21, I22, I23) 13.22/13.44 f9(I24, I25, I26) -> f10(I24, I25, I26) 13.22/13.44 f5(I27, I28, I29) -> f1(I27, I28, I29) [I27 <= 2] 13.22/13.44 f5(I30, I31, I32) -> f4(-1 + I30, I31, I32) [3 <= I30] 13.22/13.44 f8(I33, I34, I35) -> f9(I33, I34, I35) 13.22/13.44 f6(I36, I37, I38) -> f7(I36, I37, I38) 13.22/13.44 f4(I39, I40, I41) -> f5(I39, I40, I41) 13.22/13.44 f2(I42, I43, I44) -> f3(I42, I43, rnd3) [rnd3 = rnd3] 13.22/13.44 f1(I45, I46, I47) -> f2(I45, I46, I47) 13.22/13.44 13.22/16.41 EOF