YES(?, 276) Initial complexity problem: 1: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (?, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (?, 1) f28(a, b, c) -> f23(a + 1, b, c) (?, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f23(a, b, c) -> f38(a, b, c) [ a >= 10 ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] 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) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (?, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (?, 1) f28(a, b, c) -> f23(a + 1, b, c) (?, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 8 Pol(f8) = 8 Pol(f14) = 8 Pol(f23) = 0 Pol(f28) = 0 orients all transitions weakly and the transition f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] strictly and produces the following problem: 3: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (?, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (?, 1) f28(a, b, c) -> f23(a + 1, b, c) (?, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 19 Pol(f8) = 19 Pol(f14) = 19 Pol(f23) = -2*V_1 + 19 Pol(f28) = -2*V_1 + 18 orients all transitions weakly and the transitions f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] strictly and produces the following problem: 4: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (?, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (19, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (?, 1) f28(a, b, c) -> f23(a + 1, b, c) (?, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 19 Pol(f8) = 19 Pol(f14) = 19 Pol(f23) = -2*V_1 + 19 Pol(f28) = -2*V_1 + 18 orients all transitions weakly and the transition f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] strictly and produces the following problem: 5: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (19, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (?, 1) f28(a, b, c) -> f23(a + 1, b, c) (?, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (?, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (19, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (38, 1) f28(a, b, c) -> f23(a + 1, b, c) (38, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (?, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f8) = -2*V_1 + 19 Pol(f14) = -2*V_1 + 18 and size complexities S("f8(a, b, c) -> f23(0, b, c) [ a >= 10 ]", 0-0) = 0 S("f8(a, b, c) -> f23(0, b, c) [ a >= 10 ]", 0-1) = ? S("f8(a, b, c) -> f23(0, b, c) [ a >= 10 ]", 0-2) = c S("f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ]", 0-0) = ? S("f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ]", 0-1) = ? S("f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ]", 0-2) = c S("f14(a, b, c) -> f8(a + 1, b, c)", 0-0) = ? S("f14(a, b, c) -> f8(a + 1, b, c)", 0-1) = ? S("f14(a, b, c) -> f8(a + 1, b, c)", 0-2) = c S("f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ]", 0-0) = ? S("f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ]", 0-1) = ? S("f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ]", 0-2) = c S("f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ]", 0-0) = 86 S("f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ]", 0-1) = ? S("f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ]", 0-2) = ? S("f28(a, b, c) -> f23(a + 1, b, c)", 0-0) = 86 S("f28(a, b, c) -> f23(a + 1, b, c)", 0-1) = ? S("f28(a, b, c) -> f23(a + 1, b, c)", 0-2) = ? S("f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ]", 0-0) = 86 S("f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ]", 0-1) = ? S("f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ]", 0-2) = ? S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a ]", 0-0) = 86 S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a ]", 0-1) = ? S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a ]", 0-2) = ? S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\\ 0 >= e + 1 ]", 0-0) = 86 S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\\ 0 >= e + 1 ]", 0-1) = ? S("f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\\ 0 >= e + 1 ]", 0-2) = ? S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a ]", 0-0) = ? S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a ]", 0-1) = ? S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a ]", 0-2) = c S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\\ 9 >= d ]", 0-0) = ? S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\\ 9 >= d ]", 0-1) = ? S("f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\\ 9 >= d ]", 0-2) = c S("f0(a, b, c) -> f8(0, b, c)", 0-0) = 0 S("f0(a, b, c) -> f8(0, b, c)", 0-1) = b S("f0(a, b, c) -> f8(0, b, c)", 0-2) = c orients the transitions f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] f14(a, b, c) -> f8(a + 1, b, c) weakly and the transitions f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] strictly and produces the following problem: 7: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (19, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (19, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (19, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (38, 1) f28(a, b, c) -> f23(a + 1, b, c) (38, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (19, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (?, 1) f14(a, b, c) -> f8(a + 1, b, c) (?, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (1, 1) f0(a, b, c) -> f8(0, b, c) (19, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a /\ 9 >= d ] (19, 1) f8(a, b, c) -> f14(a, a, c) [ 9 >= a ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a /\ 0 >= e + 1 ] (19, 1) f23(a, b, c) -> f28(a, b, d) [ 9 >= a ] (19, 1) f23(a, b, c) -> f23(a + 1, b, c) [ 9 >= a ] (38, 1) f28(a, b, c) -> f23(a + 1, b, c) (38, 1) f28(a, b, c) -> f23(a + 1, b, c) [ 8 >= d ] (19, 1) f8(a, b, c) -> f8(a + 1, a, c) [ 9 >= a ] (38, 1) f14(a, b, c) -> f8(a + 1, b, c) (38, 1) f14(a, b, c) -> f8(a + 1, b, c) [ 8 >= d ] (8, 1) f8(a, b, c) -> f23(0, b, c) [ a >= 10 ] start location: f0 leaf cost: 1 Complexity upper bound 276 Time: 0.440 sec (SMT: 0.414 sec)