0.00/0.50 YES 0.00/0.50 0.00/0.50 DP problem for innermost termination. 0.00/0.50 P = 0.00/0.50 f#(x, y, z) -> f#(x, y, z + 1) [x > y && x > z] 0.00/0.50 f#(I0, I1, I2) -> f#(I0, I1 + 1, I2) [I0 > I1 && I0 > I2] 0.00/0.50 R = 0.00/0.50 f(x, y, z) -> f(x, y, z + 1) [x > y && x > z] 0.00/0.50 f(I0, I1, I2) -> f(I0, I1 + 1, I2) [I0 > I1 && I0 > I2] 0.00/0.50 0.00/0.50 We use the reverse value criterion with the projection function NU: 0.00/0.50 NU[f#(z1,z2,z3)] = z1 + -1 * z3 0.00/0.50 0.00/0.50 This gives the following inequalities: 0.00/0.50 x > y && x > z ==> x + -1 * z > x + -1 * (z + 1) with x + -1 * z >= 0 0.00/0.50 I0 > I1 && I0 > I2 ==> I0 + -1 * I2 >= I0 + -1 * I2 0.00/0.50 0.00/0.50 We remove all the strictly oriented dependency pairs. 0.00/0.50 0.00/0.50 DP problem for innermost termination. 0.00/0.50 P = 0.00/0.50 f#(I0, I1, I2) -> f#(I0, I1 + 1, I2) [I0 > I1 && I0 > I2] 0.00/0.50 R = 0.00/0.50 f(x, y, z) -> f(x, y, z + 1) [x > y && x > z] 0.00/0.50 f(I0, I1, I2) -> f(I0, I1 + 1, I2) [I0 > I1 && I0 > I2] 0.00/0.50 0.00/0.50 We use the reverse value criterion with the projection function NU: 0.00/0.50 NU[f#(z1,z2,z3)] = z1 + -1 * z2 0.00/0.50 0.00/0.50 This gives the following inequalities: 0.00/0.50 I0 > I1 && I0 > I2 ==> I0 + -1 * I1 > I0 + -1 * (I1 + 1) with I0 + -1 * I1 >= 0 0.00/0.50 0.00/0.50 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 0.00/3.48 EOF