2.37/2.36 YES 2.37/2.36 2.37/2.36 DP problem for innermost termination. 2.37/2.36 P = 2.37/2.36 b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.36 b14#(I0, I1, I2) -> Cond_b14#(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.36 Cond_b14#(true, I3, I4, I5) -> b15#(I3, I4, I5) 2.37/2.36 b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.36 R = 2.37/2.36 b15(sv14_14, sv23_37, sv24_38) -> b10(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.36 b14(I0, I1, I2) -> Cond_b14(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.36 Cond_b14(true, I3, I4, I5) -> b15(I3, I4, I5) 2.37/2.36 b10(I6, I7, I8) -> b14(I6, I7, I8) 2.37/2.36 2.37/2.36 This problem is converted using chaining, where edges between chained DPs are removed. 2.37/2.36 2.37/2.36 DP problem for innermost termination. 2.37/2.36 P = 2.37/2.36 b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.36 b14#(I0, I1, I2) -> Cond_b14#(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.36 Cond_b14#(true, I3, I4, I5) -> b15#(I3, I4, I5) 2.37/2.36 b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.36 b14#(I0, I1, I2) -> b15#(I0, I1, I2) [I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1] 2.37/2.37 R = 2.37/2.37 b15(sv14_14, sv23_37, sv24_38) -> b10(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 b14(I0, I1, I2) -> Cond_b14(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.37 Cond_b14(true, I3, I4, I5) -> b15(I3, I4, I5) 2.37/2.37 b10(I6, I7, I8) -> b14(I6, I7, I8) 2.37/2.37 2.37/2.37 The dependency graph for this problem is: 2.37/2.37 0 -> 3 2.37/2.37 1 -> 2.37/2.37 2 -> 0 2.37/2.37 3 -> 4, 1 2.37/2.37 4 -> 0 2.37/2.37 Where: 2.37/2.37 0) b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 1) b14#(I0, I1, I2) -> Cond_b14#(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.37 2) Cond_b14#(true, I3, I4, I5) -> b15#(I3, I4, I5) 2.37/2.37 3) b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.37 4) b14#(I0, I1, I2) -> b15#(I0, I1, I2) [I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1] 2.37/2.37 2.37/2.37 We have the following SCCs. 2.37/2.37 { 0, 3, 4 } 2.37/2.37 2.37/2.37 DP problem for innermost termination. 2.37/2.37 P = 2.37/2.37 b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.37 b14#(I0, I1, I2) -> b15#(I0, I1, I2) [I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1] 2.37/2.37 R = 2.37/2.37 b15(sv14_14, sv23_37, sv24_38) -> b10(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 b14(I0, I1, I2) -> Cond_b14(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.37 Cond_b14(true, I3, I4, I5) -> b15(I3, I4, I5) 2.37/2.37 b10(I6, I7, I8) -> b14(I6, I7, I8) 2.37/2.37 2.37/2.37 We use the extended value criterion with the projection function NU: 2.37/2.37 NU[b14#(x0,x1,x2)] = x1 - 2 2.37/2.37 NU[b10#(x0,x1,x2)] = x1 - 2 2.37/2.37 NU[b15#(x0,x1,x2)] = -x0 + x1 - 2 2.37/2.37 2.37/2.37 This gives the following inequalities: 2.37/2.37 ==> -sv14_14 + sv23_37 - 2 >= (sv23_37 - sv14_14) - 2 2.37/2.37 ==> I7 - 2 >= I7 - 2 2.37/2.37 I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1 ==> I1 - 2 > -I0 + I1 - 2 with I1 - 2 >= 0 2.37/2.37 2.37/2.37 We remove all the strictly oriented dependency pairs. 2.37/2.37 2.37/2.37 DP problem for innermost termination. 2.37/2.37 P = 2.37/2.37 b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.37 R = 2.37/2.37 b15(sv14_14, sv23_37, sv24_38) -> b10(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 b14(I0, I1, I2) -> Cond_b14(I1 >= I0 && 1 < I0 && 0 < I2 && 1 < I1, I0, I1, I2) 2.37/2.37 Cond_b14(true, I3, I4, I5) -> b15(I3, I4, I5) 2.37/2.37 b10(I6, I7, I8) -> b14(I6, I7, I8) 2.37/2.37 2.37/2.37 The dependency graph for this problem is: 2.37/2.37 0 -> 3 2.37/2.37 3 -> 2.37/2.37 Where: 2.37/2.37 0) b15#(sv14_14, sv23_37, sv24_38) -> b10#(sv14_14, sv23_37 - sv14_14, sv24_38 + 1) 2.37/2.37 3) b10#(I6, I7, I8) -> b14#(I6, I7, I8) 2.37/2.37 2.37/2.37 We have the following SCCs. 2.37/2.37 2.37/5.34 EOF