MAYBE Initial complexity problem: 1: T: (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) -> Com_1(f1(Fresh_44, Fresh_44, Fresh_44, Fresh_44, Fresh_44, Fresh_44, Fresh_44, Fresh_44, Fresh_44, 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)) (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) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_38, Fresh_39, Fresh_40, Fresh_41, Fresh_42, Fresh_43, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ 0 >= Y /\ 0 >= Ar_9 + 1 ] (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) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_31, Fresh_32, Fresh_33, Fresh_34, Ar_14, Ar_15, Fresh_35, Fresh_36, Fresh_37, Ar_19, Ar_20, Ar_21, Ar_22)) [ 0 >= Ar_9 + 1 /\ E1 >= 1 /\ F1 >= 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) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_24, Ar_11, Ar_12, Fresh_25, Fresh_26, Fresh_27, Ar_16, Ar_17, Ar_18, Fresh_28, Fresh_29, Fresh_30, Ar_22)) [ 0 >= E1 + 2 /\ Ar_9 >= 1 ] (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) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_16, Ar_11, Ar_12, Fresh_17, Ar_14, Ar_15, Fresh_18, Fresh_19, Fresh_20, Fresh_21, Fresh_22, Fresh_23, Ar_22)) [ Ar_9 >= 1 /\ F1 >= 0 /\ G1 + 1 >= 0 ] (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) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_10, Fresh_11, Fresh_12, Fresh_13, Ar_14, Ar_15, Fresh_14, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Fresh_15)) [ 1 >= Y /\ 0 >= Ar_9 + 1 /\ E1 >= 1 ] (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) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_3, Ar_11, Ar_12, Fresh_4, Ar_14, Ar_15, Fresh_5, Ar_17, Ar_18, Fresh_6, Fresh_7, Fresh_8, Fresh_9)) [ 0 >= E1 + 1 /\ Ar_9 >= 1 /\ F1 + 1 >= 0 ] (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) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_0, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Fresh_1, Ar_20, Ar_21, Fresh_2)) [ Ar_9 = 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) -> Com_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)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_9]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_9) -> Com_1(f2(Ar_9)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ Ar_9 = 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 0 >= E1 + 1 /\ Ar_9 >= 1 /\ F1 + 1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 1 >= Y /\ 0 >= Ar_9 + 1 /\ E1 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ Ar_9 >= 1 /\ F1 >= 0 /\ G1 + 1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= E1 + 2 /\ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Ar_9 + 1 /\ E1 >= 1 /\ F1 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Y /\ 0 >= Ar_9 + 1 ] (Comp: ?, Cost: 1) f2(Ar_9) -> Com_1(f1(Ar_9)) 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_9) -> Com_1(f2(Ar_9)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ Ar_9 = 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 0 >= E1 + 1 /\ Ar_9 >= 1 /\ F1 + 1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 1 >= Y /\ 0 >= Ar_9 + 1 /\ E1 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ Ar_9 >= 1 /\ F1 >= 0 /\ G1 + 1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= E1 + 2 /\ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Ar_9 + 1 /\ E1 >= 1 /\ F1 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Y /\ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f2(Ar_9) -> Com_1(f1(Ar_9)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f2) = 1 Pol(f1) = 1 Pol(f300) = 0 orients all transitions weakly and the transitions f1(Ar_9) -> Com_1(f300(Ar_9)) [ 1 >= Y /\ 0 >= Ar_9 + 1 /\ E1 >= 1 ] f1(Ar_9) -> Com_1(f300(Ar_9)) [ 0 >= E1 + 1 /\ Ar_9 >= 1 /\ F1 + 1 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_9) -> Com_1(f2(Ar_9)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ Ar_9 = 0 ] (Comp: 1, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 0 >= E1 + 1 /\ Ar_9 >= 1 /\ F1 + 1 >= 0 ] (Comp: 1, Cost: 1) f1(Ar_9) -> Com_1(f300(Ar_9)) [ 1 >= Y /\ 0 >= Ar_9 + 1 /\ E1 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ Ar_9 >= 1 /\ F1 >= 0 /\ G1 + 1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= E1 + 2 /\ Ar_9 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Ar_9 + 1 /\ E1 >= 1 /\ F1 >= 2 ] (Comp: ?, Cost: 1) f1(Ar_9) -> Com_1(f1(Ar_9)) [ 0 >= Y /\ 0 >= Ar_9 + 1 ] (Comp: 1, Cost: 1) f2(Ar_9) -> Com_1(f1(Ar_9)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.066 sec (SMT: 1.019 sec)