MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f11(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_3, Fresh_72, Ar_3, Fresh_73, Ar_1, Ar_8, 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_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f2(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_70, Fresh_71, Ar_9, Fresh_71, Ar_9, Ar_16, Ar_16, Ar_8, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f2(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_68, Fresh_69, Ar_9, Fresh_69, Ar_9, Ar_16, Ar_16, Ar_8, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f5(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, 1, Fresh_67, Ar_9, Fresh_67, Ar_9, Ar_15, Ar_16, Ar_17, Ar_8, Ar_20, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f5(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, 1, Fresh_66, Ar_9, Fresh_66, Ar_9, Ar_15, Ar_16, Ar_17, Ar_8, Ar_20, Ar_20, Ar_21, Ar_22, Ar_23, Ar_24, Ar_25, Ar_26, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f0(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f11(Fresh_61, 2, Fresh_62, Fresh_63, Fresh_62, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_61, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Fresh_64, Fresh_62, Fresh_65, Ar_24, Ar_25, Ar_26, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ Fresh_61 >= 2 ] (Comp: ?, Cost: 1) f0(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_42, Fresh_43, Fresh_44, Ar_5, Ar_6, Ar_7, Ar_8, Fresh_45, Fresh_46, Fresh_47, Fresh_48, Ar_13, Fresh_49, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Fresh_50, Fresh_51, Ar_23, Fresh_52, Fresh_53, Fresh_54, Fresh_55, Fresh_56, Fresh_57, Fresh_58, Fresh_59, Fresh_60, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: ?, Cost: 1) f0(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Fresh_32, Fresh_33, Fresh_34, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, 1, Fresh_35, Ar_9, Fresh_35, Ar_9, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Fresh_36, Fresh_37, Ar_23, Ar_24, Fresh_38, Fresh_39, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f0(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Fresh_22, Fresh_23, Fresh_24, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, 1, Fresh_25, Ar_9, Fresh_25, Ar_9, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Fresh_26, Fresh_27, Ar_23, Ar_24, Fresh_28, Fresh_29, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f11(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Fresh_12, Fresh_13, Fresh_14, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_15, Fresh_16, Ar_9, Fresh_16, Ar_9, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Fresh_17, Ar_23, Ar_24, Fresh_18, Fresh_19, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: ?, Cost: 1) f11(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Fresh_2, Fresh_3, Fresh_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_5, Fresh_6, Ar_9, Fresh_6, Ar_9, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Fresh_7, Ar_23, Ar_24, Fresh_8, Fresh_9, Ar_27, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33) -> Com_1(f0(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, Ar_28, Ar_29, Ar_30, Ar_31, Ar_32, Ar_33)) [ 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_1, Ar_9, Ar_24, Ar_33]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_45, Fresh_52, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Fresh_61, 2, Ar_9, Ar_24, Ar_33)) [ Fresh_61 >= 2 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_9, Ar_24, Ar_33)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] 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_1, Ar_9, Ar_24, Ar_33) -> Com_1(f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_45, Fresh_52, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Fresh_61, 2, Ar_9, Ar_24, Ar_33)) [ Fresh_61 >= 2 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_9, Ar_24, Ar_33)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f0) = 1 Pol(f11) = 1 Pol(f2) = 0 Pol(f5) = 1 Pol(f1) = 1 orients all transitions weakly and the transition f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_45, Fresh_52, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Fresh_61, 2, Ar_9, Ar_24, Ar_33)) [ Fresh_61 >= 2 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_9, Ar_24, Ar_33)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f0) = 1 Pol(f11) = 1 Pol(f2) = 0 Pol(f5) = 1 Pol(f1) = 1 orients all transitions weakly and the transition f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_45, Fresh_52, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Fresh_61, 2, Ar_9, Ar_24, Ar_33)) [ Fresh_61 >= 2 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_9, Ar_24, Ar_33)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol f11: X_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0 For symbol f2: X_5 - 2 >= 0 This yielded the following problem: 6: T: (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Ar_0, Ar_1 + 1, Ar_9, Ar_24, Ar_33)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_33 - 2 >= 0 /\ 0 >= Ar_9 + 1 /\ Fresh_70 >= 2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_33 - 2 >= 0 /\ Ar_9 >= 1 /\ Fresh_68 >= 2 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f11(Fresh_61, 2, Ar_9, Ar_24, Ar_33)) [ Fresh_61 >= 2 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f1(Fresh_40, Fresh_41, Fresh_45, Fresh_52, Ar_33)) [ 0 >= N1 /\ 0 >= Fresh_46 /\ 0 >= O1 /\ Ar_24 = 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_30, Fresh_31, Ar_9, Ar_24, Ar_33)) [ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f5(Fresh_20, Fresh_21, Ar_9, Ar_24, Ar_33)) [ Ar_9 >= 1 ] (Comp: 1, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_10, Fresh_11, Ar_9, Ar_24, Ar_33)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_15 >= 2 /\ 0 >= Ar_9 + 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 1) f11(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f2(Fresh_0, Fresh_1, Ar_9, Ar_24, Ar_33)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ U1 >= 2 /\ Ar_33 >= U1 /\ V1 >= 2 /\ Ar_33 >= V1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_5 >= 2 /\ Ar_9 >= 1 /\ Ar_33 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33) -> Com_1(f0(Ar_0, Ar_1, Ar_9, Ar_24, Ar_33)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 3.239 sec (SMT: 3.087 sec)