WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaleasy1start(Ar_0, Ar_1) -> Com_1(evaleasy1entryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evaleasy1entryin(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(0, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] (Comp: ?, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb1in(Ar_0, Ar_1)) [ Ar_1 = 0 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evaleasy1bb1in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb2in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 2, Ar_1)) (Comp: ?, Cost: 1) evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evaleasy1start(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) evaleasy1start(Ar_0, Ar_1) -> Com_1(evaleasy1entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evaleasy1entryin(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(0, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] (Comp: ?, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb1in(Ar_0, Ar_1)) [ Ar_1 = 0 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evaleasy1bb1in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb2in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 2, Ar_1)) (Comp: ?, Cost: 1) evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evaleasy1start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaleasy1start) = 2 Pol(evaleasy1entryin) = 2 Pol(evaleasy1bb3in) = 2 Pol(evaleasy1bbin) = 2 Pol(evaleasy1returnin) = 1 Pol(evaleasy1bb1in) = 2 Pol(evaleasy1bb2in) = 2 Pol(evaleasy1stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evaleasy1start(Ar_0, Ar_1) -> Com_1(evaleasy1entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evaleasy1entryin(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(0, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] (Comp: 2, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb1in(Ar_0, Ar_1)) [ Ar_1 = 0 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evaleasy1bb1in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb2in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 2, Ar_1)) (Comp: 2, Cost: 1) evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evaleasy1start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaleasy1start) = 118 Pol(evaleasy1entryin) = 118 Pol(evaleasy1bb3in) = -3*V_1 + 118 Pol(evaleasy1bbin) = -3*V_1 + 117 Pol(evaleasy1returnin) = -3*V_1 + 118 Pol(evaleasy1bb1in) = -3*V_1 + 116 Pol(evaleasy1bb2in) = -3*V_1 + 116 Pol(evaleasy1stop) = -3*V_1 + 118 Pol(koat_start) = 118 orients all transitions weakly and the transition evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evaleasy1start(Ar_0, Ar_1) -> Com_1(evaleasy1entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evaleasy1entryin(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(0, Ar_1)) (Comp: 118, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] (Comp: 2, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb1in(Ar_0, Ar_1)) [ Ar_1 = 0 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evaleasy1bb1in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evaleasy1bb2in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 2, Ar_1)) (Comp: 2, Cost: 1) evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evaleasy1start(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) evaleasy1start(Ar_0, Ar_1) -> Com_1(evaleasy1entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evaleasy1entryin(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(0, Ar_1)) (Comp: 118, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1bbin(Ar_0, Ar_1)) [ 39 >= Ar_0 ] (Comp: 2, Cost: 1) evaleasy1bb3in(Ar_0, Ar_1) -> Com_1(evaleasy1returnin(Ar_0, Ar_1)) [ Ar_0 >= 40 ] (Comp: 118, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb1in(Ar_0, Ar_1)) [ Ar_1 = 0 ] (Comp: 118, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ] (Comp: 118, Cost: 1) evaleasy1bbin(Ar_0, Ar_1) -> Com_1(evaleasy1bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ] (Comp: 118, Cost: 1) evaleasy1bb1in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 1, Ar_1)) (Comp: 236, Cost: 1) evaleasy1bb2in(Ar_0, Ar_1) -> Com_1(evaleasy1bb3in(Ar_0 + 2, Ar_1)) (Comp: 2, Cost: 1) evaleasy1returnin(Ar_0, Ar_1) -> Com_1(evaleasy1stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evaleasy1start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 832 Time: 0.671 sec (SMT: 0.652 sec)