WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalSimpleSinglestart(Ar_0, Ar_1) -> Com_1(evalSimpleSingleentryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSingleentryin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(0, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalSimpleSinglebbin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestart(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) evalSimpleSinglestart(Ar_0, Ar_1) -> Com_1(evalSimpleSingleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalSimpleSingleentryin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(0, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalSimpleSinglebbin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalSimpleSinglestart) = 2 Pol(evalSimpleSingleentryin) = 2 Pol(evalSimpleSinglebb3in) = 2 Pol(evalSimpleSinglebbin) = 2 Pol(evalSimpleSinglereturnin) = 1 Pol(evalSimpleSinglestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalSimpleSinglestart(Ar_0, Ar_1) -> Com_1(evalSimpleSingleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalSimpleSingleentryin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(0, Ar_1)) (Comp: ?, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalSimpleSinglebbin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalSimpleSinglestart) = 2*V_2 Pol(evalSimpleSingleentryin) = 2*V_2 Pol(evalSimpleSinglebb3in) = -2*V_1 + 2*V_2 Pol(evalSimpleSinglebbin) = -2*V_1 + 2*V_2 - 1 Pol(evalSimpleSinglereturnin) = -2*V_1 + 2*V_2 Pol(evalSimpleSinglestop) = -2*V_1 + 2*V_2 Pol(koat_start) = 2*V_2 orients all transitions weakly and the transition evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalSimpleSinglestart(Ar_0, Ar_1) -> Com_1(evalSimpleSingleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalSimpleSingleentryin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(0, Ar_1)) (Comp: 2*Ar_1, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalSimpleSinglebbin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalSimpleSinglestart(Ar_0, Ar_1) -> Com_1(evalSimpleSingleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalSimpleSingleentryin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(0, Ar_1)) (Comp: 2*Ar_1, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebbin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleSinglebb3in(Ar_0, Ar_1) -> Com_1(evalSimpleSinglereturnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 2*Ar_1, Cost: 1) evalSimpleSinglebbin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglebb3in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalSimpleSinglereturnin(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalSimpleSinglestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_1 + 6 Time: 0.343 sec (SMT: 0.330 sec)