WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f11(100, Fresh_8, 1, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f11(100, Fresh_7, 0, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f23(Ar_0, Ar_1, 1, 1, 1, 100, Fresh_6, 1, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f23(Ar_0, Ar_1, 1, 1, 1, 100, Fresh_5, 0, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_7, Ar_5, Ar_6, Ar_7, 100, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_7, Ar_5, Ar_6, Ar_7, 100, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_2, Ar_2, Ar_5, Ar_6, Ar_7, Ar_8, 100, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_2, Ar_2, Ar_5, Ar_6, Ar_7, Ar_8, 100, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, Ar_6, 1, Ar_8, Ar_9, Fresh_3, Fresh_4, Ar_12, Ar_13)) [ 0 >= Fresh_3 + 2 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, Ar_6, 1, Ar_8, Ar_9, Fresh_1, Fresh_2, Ar_12, Ar_13)) [ Fresh_1 >= 0 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, Ar_6, 1, Ar_8, Ar_9, -1, Ar_11, 100, Fresh_0)) [ Ar_7 = 1 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) (Comp: ?, Cost: 1) f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f32(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_2, Ar_7]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_7) -> Com_1(f0(Ar_2, Ar_7)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: ?, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: ?, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Fresh_1 >= 0 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ 0 >= Fresh_3 + 2 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f36(Ar_2, Ar_7)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f36(Ar_2, Ar_7)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f26(Ar_2, Ar_7)) [ Ar_7 >= 2 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f26(Ar_2, Ar_7)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 0)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 1)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(0, Ar_7)) (Comp: ?, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(1, Ar_7)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f11(Ar_2, Ar_7) -> Com_1(f36(Ar_2, Ar_7)) [ Ar_2 >= 2 ] f23(Ar_2, Ar_7) -> Com_1(f26(Ar_2, Ar_7)) [ Ar_7 >= 2 ] We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ 0 >= Fresh_3 + 2 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Fresh_1 >= 0 /\ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Ar_7 = 1 ] (Comp: ?, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f26(Ar_2, Ar_7)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: ?, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 1)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 0)) [ Ar_2 = 1 ] (Comp: ?, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f36(Ar_2, Ar_7)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(1, Ar_7)) (Comp: ?, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(0, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_7) -> Com_1(f0(Ar_2, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: 1, Cost: 1) f26(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: 1, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ 0 >= Fresh_3 + 2 /\ Ar_7 = 1 ] (Comp: 1, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Fresh_1 >= 0 /\ Ar_7 = 1 ] (Comp: 1, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f32(Ar_2, 1)) [ Ar_7 = 1 ] (Comp: 1, Cost: 1) f23(Ar_2, Ar_7) -> Com_1(f26(Ar_2, Ar_7)) [ 0 >= Ar_7 ] (Comp: 1, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) [ 0 >= O + 1 ] (Comp: 1, Cost: 1) f36(Ar_2, Ar_7) -> Com_1(f32(Ar_2, Ar_7)) (Comp: 1, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 1)) [ Ar_2 = 1 ] (Comp: 1, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f23(1, 0)) [ Ar_2 = 1 ] (Comp: 1, Cost: 1) f11(Ar_2, Ar_7) -> Com_1(f36(Ar_2, Ar_7)) [ 0 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(1, Ar_7)) (Comp: 1, Cost: 1) f0(Ar_2, Ar_7) -> Com_1(f11(0, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_7) -> Com_1(f0(Ar_2, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 13 Time: 0.645 sec (SMT: 0.628 sec)