YES(?, 5) Initial complexity problem: 1: T: (?, 1) f11(a, b, c, d, e, f, g, h, i, j, k) -> f54(a, b, b + a, d, e, f, g, h, i, j, k) [ a >= b ] (?, 1) f11(a, b, c, d, e, f, g, h, i, j, k) -> f54(a, b, b - a, d, e, f, g, h, i, j, k) [ b >= a + 1 ] (?, 1) f38(a, b, c, d, e, f, g, h, i, j, k) -> f11(l, b, c, d, e, d, d, h, i, j, k) [ d >= e + 1 ] (?, 1) f38(a, b, c, d, e, f, g, h, i, j, k) -> f11(l, b, c, d, e, d, d, m, i, j, k) [ e >= d ] (1, 1) f0(a, b, c, d, e, f, g, h, i, j, k) -> f38(1, 2, c, 1, 10, f, g, h, 10, 2, l) start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, d, e]. We thus obtain the following problem: 2: T: (1, 1) f0(a, b, d, e) -> f38(1, 2, 1, 10) (?, 1) f38(a, b, d, e) -> f11(l, b, d, e) [ e >= d ] (?, 1) f38(a, b, d, e) -> f11(l, b, d, e) [ d >= e + 1 ] (?, 1) f11(a, b, d, e) -> f54(a, b, d, e) [ b >= a + 1 ] (?, 1) f11(a, b, d, e) -> f54(a, b, d, e) [ a >= b ] start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (none) start location: f0 leaf cost: 5 Complexity upper bound 5 Time: 0.032 sec (SMT: 0.030 sec)