WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminientryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalexminientryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalexminibbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_0 - 1, Ar_2, Ar_1 + 1)) (Comp: ?, Cost: 1) evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2)) [ 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) evalexministart(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminientryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalexminientryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalexminibbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_0 - 1, Ar_2, Ar_1 + 1)) (Comp: ?, Cost: 1) evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalexministart) = 2 Pol(evalexminientryin) = 2 Pol(evalexminibb1in) = 2 Pol(evalexminibbin) = 2 Pol(evalexminireturnin) = 1 Pol(evalexministop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminientryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalexminientryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalexminibbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_0 - 1, Ar_2, Ar_1 + 1)) (Comp: 2, Cost: 1) evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalexministart) = -V_1 + V_2 - V_3 + 101 Pol(evalexminientryin) = -V_1 + V_2 - V_3 + 101 Pol(evalexminibb1in) = V_1 - V_2 - V_3 + 101 Pol(evalexminibbin) = V_1 - V_2 - V_3 + 100 Pol(evalexminireturnin) = V_1 - V_2 - V_3 + 101 Pol(evalexministop) = V_1 - V_2 - V_3 + 101 Pol(koat_start) = -V_1 + V_2 - V_3 + 101 orients all transitions weakly and the transition evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminientryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalexminientryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_1, Ar_0, Ar_2)) (Comp: Ar_0 + Ar_1 + Ar_2 + 101, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalexminibbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_0 - 1, Ar_2, Ar_1 + 1)) (Comp: 2, Cost: 1) evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2)) [ 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) evalexministart(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminientryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalexminientryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_1, Ar_0, Ar_2)) (Comp: Ar_0 + Ar_1 + Ar_2 + 101, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibbin(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_1 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminireturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_1 + Ar_2 + 101, Cost: 1) evalexminibbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexminibb1in(Ar_0 - 1, Ar_2, Ar_1 + 1)) (Comp: 2, Cost: 1) evalexminireturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*Ar_0 + 2*Ar_1 + 2*Ar_2 + 210 Time: 0.555 sec (SMT: 0.520 sec)