WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 1 Pol(f300) = 1 Pol(f1) = 0 Pol(f3) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 2*V_2 - 31 Pol(f300) = 2*V_2 - 30 Pol(f1) = 2*V_2 - 30 Pol(f3) = 2*V_2 Pol(koat_start) = 2*V_2 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: 2*Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 1 Pol(f300) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ]", 0-0) = Ar_0 S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ]", 0-1) = ? S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ]", 0-2) = ? S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ]", 0-0) = Ar_0 S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ]", 0-1) = ? S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ]", 0-2) = Ar_2 S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ]", 0-0) = Ar_0 S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ]", 0-1) = ? S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ]", 0-2) = Ar_2 S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ]", 0-0) = Ar_0 S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ]", 0-1) = ? S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ]", 0-2) = Ar_2 orients the transitions f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] weakly and the transition f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: 2*Ar_1, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: 2*Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = V_1 Pol(f300) = V_1 Pol(f1) = V_1 Pol(f3) = V_1 Pol(koat_start) = V_1 orients all transitions weakly and the transition f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] strictly and produces the following problem: 6: T: (Comp: Ar_0, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= 31 ] (Comp: 2*Ar_1, Cost: 1) f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ 30 >= Ar_0 ] (Comp: 2*Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 21 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ 20 >= Ar_1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound Ar_0 + 4*Ar_1 + 2 Time: 0.639 sec (SMT: 0.614 sec)