WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f20(Ar_0, 1, Ar_0, 1, Ar_0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f20(Ar_0, 1, Ar_0, 1, Ar_0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 1) f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f20(Ar_0, 1, Ar_0, 1, Ar_0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 1 Time: 0.134 sec (SMT: 0.132 sec)