WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: ?, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(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) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: ?, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalDis2start) = 2 Pol(evalDis2entryin) = 2 Pol(evalDis2bb3in) = 2 Pol(evalDis2bbin) = 2 Pol(evalDis2returnin) = 1 Pol(evalDis2bb1in) = 2 Pol(evalDis2bb2in) = 2 Pol(evalDis2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(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 evalDis2bb1in: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 For symbol evalDis2bb2in: X_1 - X_3 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalDis2bbin: X_1 - X_3 - 1 >= 0 For symbol evalDis2returnin: -X_1 + X_3 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -3*V_1 + 5*V_2 - 2*V_3 Pol(evalDis2start) = -3*V_1 + 5*V_2 - 2*V_3 Pol(evalDis2returnin) = 5*V_1 - 2*V_2 - 3*V_3 Pol(evalDis2stop) = 5*V_1 - 2*V_2 - 3*V_3 Pol(evalDis2bb2in) = 5*V_1 - 2*V_2 - 3*V_3 - 1 Pol(evalDis2bb3in) = 5*V_1 - 2*V_2 - 3*V_3 Pol(evalDis2bb1in) = 5*V_1 - 2*V_2 - 3*V_3 - 2 Pol(evalDis2bbin) = 5*V_1 - 2*V_2 - 3*V_3 - 1 Pol(evalDis2entryin) = -3*V_1 + 5*V_2 - 2*V_3 orients all transitions weakly and the transition evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalDis2bbin) = 1 Pol(evalDis2bb2in) = 0 Pol(evalDis2bb1in) = 1 Pol(evalDis2bb3in) = 1 and size complexities S("evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0))", 0-0) = Ar_1 S("evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0))", 0-1) = Ar_2 S("evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0))", 0-2) = Ar_0 S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]", 0-2) = ? S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]", 0-0) = Ar_1 S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]", 0-2) = ? S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-2) = ? S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-0) = Ar_1 S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-2) = ? S("evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 ]", 0-0) = Ar_1 S("evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 ]", 0-2) = ? S("evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-0) = Ar_1 S("evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 ]", 0-2) = ? S("evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ]", 0-0) = Ar_1 S("evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ]", 0-1) = 6*Ar_0 + 6*Ar_1 + 6*Ar_2 S("evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ]", 0-2) = ? S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] weakly and the transition evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2 + 1, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -2*V_1 + 2*V_2 + 3 Pol(evalDis2start) = -2*V_1 + 2*V_2 + 3 Pol(evalDis2returnin) = 4*V_1 - 4*V_3 + 3 Pol(evalDis2stop) = 4*V_1 - 4*V_3 + 3 Pol(evalDis2bb2in) = 2*V_1 - 2*V_3 + 3 Pol(evalDis2bb3in) = 2*V_1 - 2*V_3 + 3 Pol(evalDis2bb1in) = 2*V_1 - 2*V_3 + 2 Pol(evalDis2bbin) = 2*V_1 - 2*V_3 + 3 Pol(evalDis2entryin) = -2*V_1 + 2*V_2 + 3 orients all transitions weakly and the transition evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2 + 1, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 2*Ar_0 + 2*Ar_1 + 3, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(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(evalDis2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalDis2returnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2stop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_2 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2, Cost: 1) evalDis2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 2*Ar_0 + 2*Ar_1 + 3, Cost: 1) evalDis2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 ] (Comp: 3*Ar_0 + 5*Ar_1 + 2*Ar_2 + 1, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 2*Ar_0 + 2*Ar_1 + 3, Cost: 1) evalDis2bbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb1in(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2returnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: 5*Ar_0 + 7*Ar_1 + 2*Ar_2 + 4, Cost: 1) evalDis2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bbin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 1, Cost: 1) evalDis2entryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2bb3in(Ar_1, Ar_2, Ar_0)) (Comp: 1, Cost: 1) evalDis2start(Ar_0, Ar_1, Ar_2) -> Com_1(evalDis2entryin(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 15*Ar_0 + 21*Ar_1 + 6*Ar_2 + 17 Time: 1.568 sec (SMT: 1.510 sec)