WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(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) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx6start) = 2 Pol(evalEx6entryin) = 2 Pol(evalEx6bb3in) = 2 Pol(evalEx6bbin) = 2 Pol(evalEx6returnin) = 1 Pol(evalEx6bb1in) = 2 Pol(evalEx6bb2in) = 2 Pol(evalEx6stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: ?, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(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 evalEx6bb1in: -X_2 + X_3 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalEx6bb2in: -X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalEx6bbin: -X_2 + X_3 - 1 >= 0 For symbol evalEx6returnin: X_2 - X_3 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -6*V_1 - 2*V_2 + 8*V_3 - 3 Pol(evalEx6start) = -6*V_1 - 2*V_2 + 8*V_3 - 3 Pol(evalEx6returnin) = -2*V_1 - 6*V_2 + 8*V_3 - 3 Pol(evalEx6stop) = -2*V_1 - 6*V_2 + 8*V_3 - 3 Pol(evalEx6bb2in) = -2*V_1 - 6*V_2 + 8*V_3 - 4 Pol(evalEx6bb3in) = -2*V_1 - 6*V_2 + 8*V_3 - 3 Pol(evalEx6bb1in) = -2*V_1 - 6*V_2 + 8*V_3 - 8 Pol(evalEx6bbin) = -2*V_1 - 6*V_2 + 8*V_3 - 4 Pol(evalEx6entryin) = -6*V_1 - 2*V_2 + 8*V_3 - 3 orients all transitions weakly and the transition evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 3, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx6bbin) = 1 Pol(evalEx6bb2in) = 0 Pol(evalEx6bb1in) = 1 Pol(evalEx6bb3in) = 1 and size complexities S("evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2))", 0-0) = Ar_1 S("evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2))", 0-1) = Ar_0 S("evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2))", 0-2) = Ar_2 S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 243 S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-1) = ? S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 2187 S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-1) = ? S("evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-2) = Ar_2 S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 243 S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 243 S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = ? S("evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-2) = Ar_2 S("evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 243 S("evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-1) = ? S("evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-2) = Ar_2 S("evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 243 S("evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-1) = ? S("evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-2) = Ar_2 S("evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ]", 0-0) = 9*Ar_0 + 9*Ar_1 + 9*Ar_2 + 19683 S("evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ]", 0-1) = ? S("evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] weakly and the transition evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 3, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 4, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -3*V_1 + 3*V_3 Pol(evalEx6start) = -3*V_1 + 3*V_3 Pol(evalEx6returnin) = -4*V_2 + 4*V_3 Pol(evalEx6stop) = -4*V_2 + 4*V_3 Pol(evalEx6bb2in) = -3*V_2 + 3*V_3 Pol(evalEx6bb3in) = -3*V_2 + 3*V_3 Pol(evalEx6bb1in) = -3*V_2 + 3*V_3 - 1 Pol(evalEx6bbin) = -3*V_2 + 3*V_3 Pol(evalEx6entryin) = -3*V_1 + 3*V_3 orients all transitions weakly and the transition evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 3, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 4, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 3*Ar_0 + 3*Ar_2, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx6returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6stop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 3, Cost: 1) evalEx6bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 3*Ar_0 + 3*Ar_2, Cost: 1) evalEx6bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 6*Ar_0 + 2*Ar_1 + 8*Ar_2 + 4, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 3*Ar_0 + 3*Ar_2, Cost: 1) evalEx6bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb1in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6returnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: 9*Ar_0 + 11*Ar_2 + 2*Ar_1 + 4, Cost: 1) evalEx6bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bbin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalEx6entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6bb3in(Ar_1, Ar_0, Ar_2)) (Comp: 1, Cost: 1) evalEx6start(Ar_0, Ar_1, Ar_2) -> Com_1(evalEx6entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 27*Ar_0 + 6*Ar_1 + 33*Ar_2 + 17 Time: 1.696 sec (SMT: 1.637 sec)