WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(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) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb3in) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb4in) = 2 Pol(evalfbbin) = 2 Pol(evalfbb1in) = 2 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ] (Comp: 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfbb1in: X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfbb3in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfbb4in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfbbin: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfreturnin: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ D >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 9*V_1 Pol(evalfstart) = 9*V_1 Pol(evalfreturnin) = 9*V_2 + 5*V_3 - 12 Pol(evalfstop) = 9*V_2 + 5*V_3 - 12 Pol(evalfbb1in) = 9*V_2 + 5*V_3 - 14 Pol(evalfbb3in) = 9*V_2 + 5*V_3 - 11 Pol(evalfbbin) = 9*V_2 + 5*V_3 - 13 Pol(evalfbb4in) = 9*V_2 + 5*V_3 - 12 Pol(evalfentryin) = 9*V_1 orients all transitions weakly and the transition evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 9*Ar_0, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ D >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= D + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 6*V_1 Pol(evalfstart) = 6*V_1 Pol(evalfreturnin) = 6*V_2 + 2*V_3 - 1 Pol(evalfstop) = 6*V_2 + 2*V_3 - 1 Pol(evalfbb1in) = 6*V_2 + 2*V_3 - 3 Pol(evalfbb3in) = 6*V_2 + 2*V_3 Pol(evalfbbin) = 6*V_2 + 2*V_3 - 2 Pol(evalfbb4in) = 6*V_2 + 2*V_3 - 1 Pol(evalfentryin) = 6*V_1 orients all transitions weakly and the transitions evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ D >= 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= D + 1 ] evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_0, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1 - 1, Ar_2 + 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 9*Ar_0, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: 6*Ar_0, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_0, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ D >= 1 ] (Comp: 6*Ar_0, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= D + 1 ] (Comp: 6*Ar_0, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_1, Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 39*Ar_0 + 8 Time: 2.032 sec (SMT: 1.963 sec)