WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0) -> Com_1(f3(0)) (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 /\ 0 >= B + 1 ] (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f13(Ar_0)) [ Ar_0 >= 42 ] (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f3(0)) (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 /\ 0 >= B + 1 ] (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f13(Ar_0)) [ Ar_0 >= 42 ] (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 1 Pol(f3) = 1 Pol(f13) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f3(Ar_0) -> Com_1(f13(Ar_0)) [ Ar_0 >= 42 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f3(0)) (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 /\ 0 >= B + 1 ] (Comp: 1, Cost: 1) f3(Ar_0) -> Com_1(f13(Ar_0)) [ Ar_0 >= 42 ] (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 42 Pol(f3) = -V_1 + 42 Pol(f13) = -V_1 + 42 Pol(koat_start) = 42 orients all transitions weakly and the transitions f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 /\ 0 >= B + 1 ] f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f3(0)) (Comp: 42, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 ] (Comp: 42, Cost: 1) f3(Ar_0) -> Com_1(f3(Ar_0 + 1)) [ 41 >= Ar_0 /\ 0 >= B + 1 ] (Comp: 1, Cost: 1) f3(Ar_0) -> Com_1(f13(Ar_0)) [ Ar_0 >= 42 ] (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 86 Time: 0.568 sec (SMT: 0.555 sec)