YES(?, 6567) Initial complexity problem: 1: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (?, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (?, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (?, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (?, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f21(a, b, c) -> f39(a, b, c) [ a >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (?, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (?, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (?, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (?, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (?, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (?, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 5 Pol(f10) = 5 Pol(f13) = 5 Pol(f21) = -6 Pol(f24) = -6 Pol(f27) = -6 orients all transitions weakly and the transition f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] strictly and produces the following problem: 3: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (?, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (?, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (?, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (?, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 9 Pol(f10) = 9 Pol(f13) = 9 Pol(f21) = -2*V_1 + 11 Pol(f24) = -2*V_1 + 10 Pol(f27) = -2*V_1 + 10 orients all transitions weakly and the transition f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] strictly and produces the following problem: 4: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (?, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (9, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (?, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (?, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f27) = 5 Pol(f24) = 5 Pol(f21) = 4 Pol(f13) = -6 Pol(f10) = -6 and size complexities S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-0) = 1 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-1) = 6 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-2) = c S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-0) = ? S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-1) = 6 S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-2) = c S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-0) = ? S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-1) = ? S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-0) = ? S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-1) = ? S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-0) = ? S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-1) = ? S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-2) = 6 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-0) = ? S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-1) = ? S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-2) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-0) = ? S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-2) = c + 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-0) = ? S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-1) = 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-2) = c S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-0) = ? S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-2) = c S("f0(a, b, c) -> f10(1, b, c)", 0-0) = 1 S("f0(a, b, c) -> f10(1, b, c)", 0-1) = b S("f0(a, b, c) -> f10(1, b, c)", 0-2) = c orients the transitions f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] weakly and the transition f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] strictly and produces the following problem: 5: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (?, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (9, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (?, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (51, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f27) = -2*V_2 + 10 Pol(f24) = -2*V_2 + 11 Pol(f13) = -2*V_1 + 10 Pol(f10) = -2*V_1 + 11 and size complexities S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-0) = 1 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-1) = 6 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-2) = c S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-0) = ? S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-1) = 6 S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-2) = c S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-0) = 52 S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-1) = ? S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-0) = 52 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-1) = ? S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-0) = 52 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-1) = ? S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-2) = 6 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-0) = 52 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-1) = ? S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-2) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-0) = 52 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-2) = c + 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-0) = ? S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-1) = 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-2) = c S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-0) = ? S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-2) = c S("f0(a, b, c) -> f10(1, b, c)", 0-0) = 1 S("f0(a, b, c) -> f10(1, b, c)", 0-1) = b S("f0(a, b, c) -> f10(1, b, c)", 0-2) = c orients the transitions f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] weakly and the transitions f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] strictly and produces the following problem: 6: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (130, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (9, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (130, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (?, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (51, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (?, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f27) = 5 Pol(f24) = 4 Pol(f13) = 5 Pol(f10) = 4 and size complexities S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-0) = 1 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-1) = 6 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-2) = c S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-0) = ? S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-1) = 6 S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-2) = c S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-0) = 52 S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-1) = ? S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-0) = 52 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-1) = ? S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-0) = 52 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-1) = ? S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-2) = 6 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-0) = 52 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-1) = ? S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-2) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-0) = 52 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-2) = c + 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-0) = ? S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-1) = 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-2) = c S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-0) = ? S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-2) = c S("f0(a, b, c) -> f10(1, b, c)", 0-0) = 1 S("f0(a, b, c) -> f10(1, b, c)", 0-1) = b S("f0(a, b, c) -> f10(1, b, c)", 0-2) = c orients the transitions f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] weakly and the transitions f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] strictly and produces the following problem: 7: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (130, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (?, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (9, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (130, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (?, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (1300, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (51, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (1300, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f27) = -V_3 + 6 Pol(f13) = -V_2 + 6 and size complexities S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-0) = 1 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-1) = 6 S("f10(a, b, c) -> f21(1, b, c) [ a >= 6 ]", 0-2) = c S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-0) = 1301 S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-1) = 6 S("f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ]", 0-2) = c S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-0) = 52 S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-1) = 1301 S("f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-0) = 52 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-1) = 1301 S("f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ]", 0-2) = 6 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-0) = 52 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-1) = 1301 S("f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ]", 0-2) = 6 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-0) = 52 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-1) = 1301 S("f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ]", 0-2) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-0) = 52 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ]", 0-2) = c + 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-0) = 1301 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-1) = 6 S("f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ]", 0-2) = c S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-0) = 1301 S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-1) = 1 S("f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ]", 0-2) = c S("f0(a, b, c) -> f10(1, b, c)", 0-0) = 1 S("f0(a, b, c) -> f10(1, b, c)", 0-1) = b S("f0(a, b, c) -> f10(1, b, c)", 0-2) = c orients the transitions f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] weakly and the transitions f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] strictly and produces the following problem: 8: T: (1, 1) f0(a, b, c) -> f10(1, b, c) (130, 1) f10(a, b, c) -> f13(a, 1, c) [ 5 >= a ] (1820, 1) f13(a, b, c) -> f13(a, b + 1, c) [ 5 >= b ] (9, 1) f21(a, b, c) -> f24(a, 1, c) [ 5 >= a ] (130, 1) f24(a, b, c) -> f27(a, b, 1) [ 5 >= b ] (1820, 1) f27(a, b, c) -> f27(a, b, c + 1) [ 5 >= c ] (1300, 1) f27(a, b, c) -> f24(a, b + 1, c) [ c >= 6 ] (51, 1) f24(a, b, c) -> f21(a + 1, b, c) [ b >= 6 ] (1300, 1) f13(a, b, c) -> f10(a + 1, b, c) [ b >= 6 ] (5, 1) f10(a, b, c) -> f21(1, b, c) [ a >= 6 ] start location: f0 leaf cost: 1 Complexity upper bound 6567 Time: 0.373 sec (SMT: 0.349 sec)