MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f12(Ar_0, Fresh_58, Fresh_59, Ar_4, Ar_4, Ar_6, Ar_6, Ar_0, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27)) [ Ar_0 >= 0 /\ Fresh_58 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_11, Fresh_56, Ar_11, Fresh_57, Ar_9, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27)) [ Ar_8 >= Ar_9 + 1 /\ Ar_9 >= 0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f1(Ar_0, Fresh_51, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_51, 2, Fresh_52, Fresh_53, Fresh_52, Ar_13, Ar_14, Fresh_54, Fresh_52, Fresh_55, 2, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27)) [ Fresh_51 >= 2 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f9(Ar_0, Fresh_35, 0, Ar_3, 0, Ar_5, Ar_6, Ar_7, Fresh_36, Fresh_37, Fresh_38, Fresh_39, Fresh_40, Ar_13, Ar_14, Fresh_41, Fresh_42, Ar_17, Ar_18, Fresh_43, Fresh_44, Fresh_45, Fresh_46, Fresh_47, Fresh_48, Fresh_49, Fresh_50, Ar_27)) [ 0 >= H1 /\ 0 >= I1 /\ 0 >= Fresh_35 /\ 0 >= J1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f12(Ar_0, Fresh_24, Fresh_25, Ar_3, Ar_10, Ar_5, Ar_6, Ar_7, Fresh_26, Fresh_27, Fresh_28, Fresh_29, Fresh_30, Ar_13, Ar_14, Ar_15, Fresh_31, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Fresh_32, Fresh_33, Ar_26, Fresh_34)) [ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f9(Ar_0, Fresh_16, 0, Ar_3, 0, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Fresh_17, Fresh_18, Fresh_19, Fresh_20, Fresh_21, Ar_24, Fresh_22, Fresh_23, Ar_27)) [ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f9(Ar_0, 1, Fresh_0, Ar_3, 0, Ar_5, Ar_6, Ar_7, Fresh_1, Fresh_2, Fresh_3, Fresh_4, Fresh_5, Ar_13, Ar_14, Fresh_6, Fresh_7, Ar_17, Ar_18, Fresh_8, Fresh_9, Fresh_10, Fresh_11, Fresh_12, Fresh_13, Fresh_14, Fresh_15, Ar_27)) [ Ar_11 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27) -> Com_1(f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, Fresh_0, 0, Fresh_1, Fresh_2, Fresh_3, Fresh_4)) [ Ar_11 = 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11)) [ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_25, Ar_10, Fresh_26, Fresh_27, Fresh_28, Fresh_29)) [ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Fresh_36, Fresh_37, Fresh_38, Fresh_39)) [ 0 >= H1 /\ 0 >= I1 /\ 0 >= Fresh_35 /\ 0 >= J1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Fresh_51, 2, Fresh_52, Fresh_53)) [ Fresh_51 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9 + 1, Ar_11, Fresh_56)) [ Ar_8 >= Ar_9 + 1 /\ Ar_9 >= 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_59, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ Ar_0 >= 0 /\ Fresh_58 >= 2 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, Fresh_0, 0, Fresh_1, Fresh_2, Fresh_3, Fresh_4)) [ Ar_11 = 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11)) [ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_25, Ar_10, Fresh_26, Fresh_27, Fresh_28, Fresh_29)) [ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Fresh_36, Fresh_37, Fresh_38, Fresh_39)) [ 0 >= H1 /\ 0 >= I1 /\ 0 >= Fresh_35 /\ 0 >= J1 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Fresh_51, 2, Fresh_52, Fresh_53)) [ Fresh_51 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9 + 1, Ar_11, Fresh_56)) [ Ar_8 >= Ar_9 + 1 /\ Ar_9 >= 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_59, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ Ar_0 >= 0 /\ Fresh_58 >= 2 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f8) = 2 Pol(f9) = 0 Pol(f12) = 1 Pol(f1) = 2 orients all transitions weakly and the transitions f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11)) [ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_25, Ar_10, Fresh_26, Fresh_27, Fresh_28, Fresh_29)) [ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, Fresh_0, 0, Fresh_1, Fresh_2, Fresh_3, Fresh_4)) [ Ar_11 = 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11)) [ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_25, Ar_10, Fresh_26, Fresh_27, Fresh_28, Fresh_29)) [ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Fresh_36, Fresh_37, Fresh_38, Fresh_39)) [ 0 >= H1 /\ 0 >= I1 /\ 0 >= Fresh_35 /\ 0 >= J1 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Fresh_51, 2, Fresh_52, Fresh_53)) [ Fresh_51 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9 + 1, Ar_11, Fresh_56)) [ Ar_8 >= Ar_9 + 1 /\ Ar_9 >= 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_59, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ Ar_0 >= 0 /\ Fresh_58 >= 2 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol f1: X_4 - X_5 >= 0 /\ X_5 - 2 >= 0 /\ X_4 + X_5 - 4 >= 0 /\ X_4 - 2 >= 0 For symbol f12: X_5 - 2 >= 0 This yielded the following problem: 5: T: (Comp: ?, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_59, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ Ar_9 - 2 >= 0 /\ Ar_0 >= 0 /\ Fresh_58 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9 + 1, Ar_11, Fresh_56)) [ Ar_8 - Ar_9 >= 0 /\ Ar_9 - 2 >= 0 /\ Ar_8 + Ar_9 - 4 >= 0 /\ Ar_8 - 2 >= 0 /\ Ar_8 >= Ar_9 + 1 /\ Ar_9 >= 0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f1(Ar_0, Ar_2, Ar_4, Fresh_51, 2, Fresh_52, Fresh_53)) [ Fresh_51 >= 2 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Fresh_36, Fresh_37, Fresh_38, Fresh_39)) [ 0 >= H1 /\ 0 >= I1 /\ 0 >= Fresh_35 /\ 0 >= J1 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f12(Ar_0, Fresh_25, Ar_10, Fresh_26, Fresh_27, Fresh_28, Fresh_29)) [ Ar_8 - Ar_9 >= 0 /\ Ar_9 - 2 >= 0 /\ Ar_8 + Ar_9 - 4 >= 0 /\ Ar_8 - 2 >= 0 /\ Ar_9 >= Ar_8 /\ Ar_9 >= 0 /\ Q1 >= 2 /\ Fresh_27 >= Q1 /\ Fresh_27 >= 0 /\ Fresh_24 >= 2 /\ Fresh_34 >= Fresh_24 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11)) [ Ar_9 - 2 >= 0 /\ N1 >= 2 /\ O1 >= 2 /\ Ar_0 >= 0 /\ Fresh_16 >= 2 /\ Ar_4 = 0 /\ Ar_2 = 0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f9(Ar_0, Fresh_0, 0, Fresh_1, Fresh_2, Fresh_3, Fresh_4)) [ Ar_11 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11) -> Com_1(f8(Ar_0, Ar_2, Ar_4, Ar_8, Ar_9, Ar_10, Ar_11)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 2.725 sec (SMT: 2.615 sec)