WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 /\ Ar_0 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 /\ Ar_0 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 /\ Ar_0 <= 0 ] eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 /\ Ar_0 > 0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > 0 ] (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_cousot9_bb3_in) = 1 Pol(eval_cousot9_stop) = 0 Pol(eval_cousot9_bb2_in) = 2 Pol(eval_cousot9_bb1_in) = 2 Pol(eval_cousot9_6) = 2 Pol(eval_cousot9_5) = 2 Pol(eval_cousot9_4) = 2 Pol(eval_cousot9_3) = 2 Pol(eval_cousot9_2) = 2 Pol(eval_cousot9_1) = 2 Pol(eval_cousot9_0) = 2 Pol(eval_cousot9_bb0_in) = 2 Pol(eval_cousot9_start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= 0 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 > 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > 0 ] (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol eval_cousot9_bb1_in: X_2 - X_3 >= 0 For symbol eval_cousot9_bb2_in: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 For symbol eval_cousot9_bb3_in: -X_3 >= 0 /\ X_2 - X_3 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 <= 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_2 Pol(eval_cousot9_start) = V_2 Pol(eval_cousot9_bb0_in) = V_2 Pol(eval_cousot9_0) = V_2 Pol(eval_cousot9_1) = V_2 Pol(eval_cousot9_2) = V_2 Pol(eval_cousot9_3) = V_2 Pol(eval_cousot9_4) = V_2 Pol(eval_cousot9_5) = V_2 Pol(eval_cousot9_6) = V_2 Pol(eval_cousot9_bb1_in) = V_3 Pol(eval_cousot9_bb2_in) = V_3 Pol(eval_cousot9_bb3_in) = V_3 Pol(eval_cousot9_stop) = V_3 orients all transitions weakly and the transition eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 <= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] (Comp: Ar_1, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 <= 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_cousot9_bb2_in) = 2*V_1 Pol(eval_cousot9_bb1_in) = 2*V_1 + 1 and size complexities S("eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 ]", 0-0) = Ar_1 + Ar_3 S("eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 ]", 0-2) = Ar_1 S("eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 ]", 0-3) = Ar_3 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 <= 0 ]", 0-0) = Ar_1 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 <= 0 ]", 0-1) = Ar_1 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 <= 0 ]", 0-2) = Ar_1 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 <= 0 ]", 0-3) = Ar_3 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 > 0 ]", 0-0) = Ar_1 + Ar_3 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 > 0 ]", 0-1) = Ar_1 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 > 0 ]", 0-2) = Ar_1 S("eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 > 0 ]", 0-3) = Ar_3 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 <= 0 ]", 0-0) = Ar_1 + Ar_3 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 <= 0 ]", 0-1) = Ar_1 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 <= 0 ]", 0-2) = Ar_1 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 <= 0 ]", 0-3) = Ar_3 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 > 0 ]", 0-0) = Ar_1 + Ar_3 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 > 0 ]", 0-1) = Ar_1 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 > 0 ]", 0-2) = Ar_1 S("eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 > 0 ]", 0-3) = Ar_3 S("eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3))", 0-0) = Ar_3 S("eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3))", 0-2) = Ar_1 S("eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > 0 ] weakly and the transition eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: ?, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 <= 0 ] (Comp: 2*Ar_1^2 + Ar_1 + 2*Ar_3 + 1, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] (Comp: Ar_1, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 <= 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 ] 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, Ar_3) -> Com_1(eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_cousot9_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_cousot9_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_3, Ar_1, Ar_1, Ar_3)) (Comp: 2*Ar_1 + 2*Ar_1^2 + 2*Ar_3 + 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 <= 0 ] (Comp: 2*Ar_1^2 + Ar_1 + 2*Ar_3 + 1, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 > 0 ] (Comp: Ar_1, Cost: 1) eval_cousot9_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_bb1_in(Ar_1, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 <= 0 ] (Comp: 2, Cost: 1) eval_cousot9_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_cousot9_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_1 + 4*Ar_1^2 + 4*Ar_3 + 16 Time: 2.895 sec (SMT: 2.800 sec)