WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (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) -> Com_1(f7(8, 0, 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)) (Comp: ?, Cost: 1) f7(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) -> Com_1(f7(Ar_0, Ar_1 + 1, Fresh_17 + Fresh_18, Fresh_19, Fresh_20 + Fresh_21, Fresh_22, Fresh_23 + Fresh_24, Fresh_25, Fresh_26 + Fresh_27, Fresh_28, Fresh_17 + Fresh_18 + Fresh_26 + Fresh_27, Fresh_17 + Fresh_18 - Fresh_26 - Fresh_27, Fresh_20 + Fresh_21 + Fresh_23 + Fresh_24, Fresh_20 + Fresh_21 - Fresh_23 - Fresh_24, -3196, Fresh_29, Fresh_30, Fresh_31 + Fresh_32, Fresh_33 + Fresh_32, Fresh_32)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f62(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) -> Com_1(f62(Ar_0, Ar_1 + 1, Fresh_0 + Fresh_1, Fresh_2, Fresh_3 + Fresh_4, Fresh_5, Fresh_6 + Fresh_7, Fresh_8, Fresh_9 + Fresh_10, Fresh_11, Fresh_0 + Fresh_1 + Fresh_9 + Fresh_10, Fresh_0 + Fresh_1 - Fresh_9 - Fresh_10, Fresh_3 + Fresh_4 + Fresh_6 + Fresh_7, Fresh_3 + Fresh_4 - Fresh_6 - Fresh_7, -3196, Fresh_12, Fresh_13, Fresh_14 + Fresh_15, Fresh_16 + Fresh_15, Fresh_15)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f62(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) -> Com_1(f118(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_1 >= 8 ] (Comp: ?, Cost: 1) f7(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) -> Com_1(f62(Ar_0, 0, 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_1 >= 8 ] (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) -> 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)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_1]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] (Comp: ?, Cost: 1) f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] (Comp: ?, Cost: 1) f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f0(Ar_1) -> Com_1(f7(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_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] (Comp: ?, Cost: 1) f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] (Comp: ?, Cost: 1) f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: 1, Cost: 1) f0(Ar_1) -> Com_1(f7(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f0) = 2 Pol(f7) = 2 Pol(f62) = 1 Pol(f118) = 0 orients all transitions weakly and the transitions f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] (Comp: 2, Cost: 1) f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] (Comp: ?, Cost: 1) f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: 1, Cost: 1) f0(Ar_1) -> Com_1(f7(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 14 Pol(f0) = 14 Pol(f7) = 14 Pol(f62) = -V_1 + 14 Pol(f118) = -V_1 + 14 orients all transitions weakly and the transition f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] (Comp: 2, Cost: 1) f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] (Comp: 14, Cost: 1) f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: ?, Cost: 1) f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: 1, Cost: 1) f0(Ar_1) -> Com_1(f7(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f7) = -V_1 + 8 and size complexities S("f0(Ar_1) -> Com_1(f7(0))", 0-0) = 0 S("f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]", 0-0) = 8 S("f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]", 0-0) = 8 S("f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]", 0-0) = 8 S("f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]", 0-0) = 0 S("koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_1 orients the transitions f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] weakly and the transition f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ] (Comp: 2, Cost: 1) f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ] (Comp: 14, Cost: 1) f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: 8, Cost: 1) f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ] (Comp: 1, Cost: 1) f0(Ar_1) -> Com_1(f7(0)) start location: koat_start leaf cost: 0 Complexity upper bound 27 Time: 0.570 sec (SMT: 0.546 sec)