WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1) -> Com_1(evalfentryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_1, Ar_0)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfstart(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) evalfstart(Ar_0, Ar_1) -> Com_1(evalfentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_1, Ar_0)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb1in) = 2 Pol(evalfbbin) = 2 Pol(evalfreturnin) = 1 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1) -> Com_1(evalfentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_1, Ar_0)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 2, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_0, Ar_1 + 1)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = -2*V_1 + 2*V_2 + 2 Pol(evalfentryin) = -2*V_1 + 2*V_2 + 2 Pol(evalfbb1in) = 2*V_1 - 2*V_2 + 2 Pol(evalfbbin) = 2*V_1 - 2*V_2 + 1 Pol(evalfreturnin) = 2*V_1 - 2*V_2 + 2 Pol(evalfstop) = 2*V_1 - 2*V_2 + 2 Pol(koat_start) = -2*V_1 + 2*V_2 + 2 orients all transitions weakly and the transition evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1) -> Com_1(evalfentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_1, Ar_0)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 2, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_0, Ar_1 + 1)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfstart(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) evalfstart(Ar_0, Ar_1) -> Com_1(evalfentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_1, Ar_0)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfbbin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 2, Cost: 1) evalfbb1in(Ar_0, Ar_1) -> Com_1(evalfreturnin(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbbin(Ar_0, Ar_1) -> Com_1(evalfbb1in(Ar_0, Ar_1 + 1)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1) -> Com_1(evalfstop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfstart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_0 + 4*Ar_1 + 10 Time: 0.366 sec (SMT: 0.352 sec)