WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f3(1, Ar_1)) (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f3(Ar_0 + 1, -Ar_0 + 10)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1)) [ Ar_0 >= 11 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 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, Ar_1) -> Com_1(f3(1, Ar_1)) (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f3(Ar_0 + 1, -Ar_0 + 10)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1)) [ Ar_0 >= 11 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 1 Pol(f3) = 1 Pol(f10) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f3(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1)) [ Ar_0 >= 11 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f3(1, Ar_1)) (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f3(Ar_0 + 1, -Ar_0 + 10)) [ 10 >= Ar_0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1)) [ Ar_0 >= 11 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 10 Pol(f3) = -V_1 + 11 Pol(f10) = -V_1 + 11 Pol(koat_start) = 10 orients all transitions weakly and the transition f3(Ar_0, Ar_1) -> Com_1(f3(Ar_0 + 1, -Ar_0 + 10)) [ 10 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f3(1, Ar_1)) (Comp: 10, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f3(Ar_0 + 1, -Ar_0 + 10)) [ 10 >= Ar_0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1)) [ Ar_0 >= 11 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 12 Time: 0.491 sec (SMT: 0.478 sec)