4.78/4.73 MAYBE 4.78/4.73 4.78/4.73 DP problem for innermost termination. 4.78/4.73 P = 4.78/4.73 f9#(x1, x2, x3, x4, x5, x6) -> f8#(x1, x2, x3, x4, x5, x6) 4.78/4.73 f8#(I0, I1, I2, I3, I4, I5) -> f1#(I0, rnd2, rnd3, rnd4, 0, 4) [rnd4 = 4 /\ 1 <= rnd3 /\ rnd3 = rnd2 /\ rnd2 = rnd2] 4.78/4.73 f2#(I6, I7, I8, I9, I10, I11) -> f5#(I6, I7, I8, I9, I10, I11) [I9 <= 0] 4.78/4.73 f2#(I12, I13, I14, I15, I16, I17) -> f7#(rnd1, I13, I14, I15, I16, I17) [rnd1 = rnd1 /\ 1 <= I15] 4.78/4.73 f7#(I18, I19, I20, I21, I22, I23) -> f1#(I18, I19, -1 + I20, -2 + I21, 1 + I22, I23) [1 <= I18] 4.78/4.73 f7#(I24, I25, I26, I27, I28, I29) -> f1#(I24, I25, I26, -2 + I27, I28, I29) [1 + I26 <= I27 /\ I24 <= 0] 4.78/4.73 f6#(I30, I31, I32, I33, I34, I35) -> f5#(I30, I31, I32, I33, I34, I35) 4.78/4.73 f5#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 4.78/4.73 f1#(I48, I49, I50, I51, I52, I53) -> f2#(I48, I49, I50, I51, I52, I53) 4.78/4.73 R = 4.78/4.73 f9(x1, x2, x3, x4, x5, x6) -> f8(x1, x2, x3, x4, x5, x6) 4.78/4.73 f8(I0, I1, I2, I3, I4, I5) -> f1(I0, rnd2, rnd3, rnd4, 0, 4) [rnd4 = 4 /\ 1 <= rnd3 /\ rnd3 = rnd2 /\ rnd2 = rnd2] 4.78/4.73 f2(I6, I7, I8, I9, I10, I11) -> f5(I6, I7, I8, I9, I10, I11) [I9 <= 0] 4.78/4.73 f2(I12, I13, I14, I15, I16, I17) -> f7(rnd1, I13, I14, I15, I16, I17) [rnd1 = rnd1 /\ 1 <= I15] 4.78/4.73 f7(I18, I19, I20, I21, I22, I23) -> f1(I18, I19, -1 + I20, -2 + I21, 1 + I22, I23) [1 <= I18] 4.78/4.73 f7(I24, I25, I26, I27, I28, I29) -> f1(I24, I25, I26, -2 + I27, I28, I29) [1 + I26 <= I27 /\ I24 <= 0] 4.78/4.73 f6(I30, I31, I32, I33, I34, I35) -> f5(I30, I31, I32, I33, I34, I35) 4.78/4.73 f5(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 4.78/4.73 f3(I42, I43, I44, I45, I46, I47) -> f4(I42, I43, I44, I45, I46, I47) 4.78/4.73 f1(I48, I49, I50, I51, I52, I53) -> f2(I48, I49, I50, I51, I52, I53) 4.78/4.73 4.78/4.73 The dependency graph for this problem is: 4.78/4.73 0 -> 1 4.78/4.73 1 -> 8 4.78/4.73 2 -> 7 4.78/4.73 3 -> 4, 5 4.78/4.73 4 -> 8 4.78/4.73 5 -> 8 4.78/4.73 6 -> 7 4.78/4.73 7 -> 6 4.78/4.73 8 -> 2, 3 4.78/4.73 Where: 4.78/4.73 0) f9#(x1, x2, x3, x4, x5, x6) -> f8#(x1, x2, x3, x4, x5, x6) 4.78/4.73 1) f8#(I0, I1, I2, I3, I4, I5) -> f1#(I0, rnd2, rnd3, rnd4, 0, 4) [rnd4 = 4 /\ 1 <= rnd3 /\ rnd3 = rnd2 /\ rnd2 = rnd2] 4.78/4.73 2) f2#(I6, I7, I8, I9, I10, I11) -> f5#(I6, I7, I8, I9, I10, I11) [I9 <= 0] 4.78/4.73 3) f2#(I12, I13, I14, I15, I16, I17) -> f7#(rnd1, I13, I14, I15, I16, I17) [rnd1 = rnd1 /\ 1 <= I15] 4.78/4.73 4) f7#(I18, I19, I20, I21, I22, I23) -> f1#(I18, I19, -1 + I20, -2 + I21, 1 + I22, I23) [1 <= I18] 4.78/4.73 5) f7#(I24, I25, I26, I27, I28, I29) -> f1#(I24, I25, I26, -2 + I27, I28, I29) [1 + I26 <= I27 /\ I24 <= 0] 4.78/4.73 6) f6#(I30, I31, I32, I33, I34, I35) -> f5#(I30, I31, I32, I33, I34, I35) 4.78/4.73 7) f5#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 4.78/4.73 8) f1#(I48, I49, I50, I51, I52, I53) -> f2#(I48, I49, I50, I51, I52, I53) 4.78/4.73 4.78/4.73 We have the following SCCs. 4.78/4.73 { 3, 4, 5, 8 } 4.78/4.73 { 6, 7 } 4.78/4.73 4.78/4.73 DP problem for innermost termination. 4.78/4.73 P = 4.78/4.73 f6#(I30, I31, I32, I33, I34, I35) -> f5#(I30, I31, I32, I33, I34, I35) 4.78/4.73 f5#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 4.78/4.73 R = 4.78/4.73 f9(x1, x2, x3, x4, x5, x6) -> f8(x1, x2, x3, x4, x5, x6) 4.78/4.73 f8(I0, I1, I2, I3, I4, I5) -> f1(I0, rnd2, rnd3, rnd4, 0, 4) [rnd4 = 4 /\ 1 <= rnd3 /\ rnd3 = rnd2 /\ rnd2 = rnd2] 4.78/4.73 f2(I6, I7, I8, I9, I10, I11) -> f5(I6, I7, I8, I9, I10, I11) [I9 <= 0] 4.78/4.73 f2(I12, I13, I14, I15, I16, I17) -> f7(rnd1, I13, I14, I15, I16, I17) [rnd1 = rnd1 /\ 1 <= I15] 4.78/4.73 f7(I18, I19, I20, I21, I22, I23) -> f1(I18, I19, -1 + I20, -2 + I21, 1 + I22, I23) [1 <= I18] 4.78/4.73 f7(I24, I25, I26, I27, I28, I29) -> f1(I24, I25, I26, -2 + I27, I28, I29) [1 + I26 <= I27 /\ I24 <= 0] 4.78/4.73 f6(I30, I31, I32, I33, I34, I35) -> f5(I30, I31, I32, I33, I34, I35) 4.78/4.73 f5(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 4.78/4.73 f3(I42, I43, I44, I45, I46, I47) -> f4(I42, I43, I44, I45, I46, I47) 4.78/4.73 f1(I48, I49, I50, I51, I52, I53) -> f2(I48, I49, I50, I51, I52, I53) 4.78/4.73 4.78/7.71 EOF