WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0 - 1, Ar_1 - 1, Ar_0, Ar_1, Ar_0 - 2, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Fresh_1, Ar_2, Ar_3, Ar_4, Fresh_2)) [ 0 >= Ar_1 /\ 0 >= Fresh_1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0 - 1, Ar_1 - 1, Ar_0, Ar_1, Ar_0 - 2, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Fresh_1, Ar_2, Ar_3, Ar_4, Fresh_2)) [ 0 >= Ar_1 /\ 0 >= Fresh_1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 1 Pol(f3) = 1 Pol(f4) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transitions f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Fresh_1, Ar_2, Ar_3, Ar_4, Fresh_2)) [ 0 >= Ar_1 /\ 0 >= Fresh_1 ] f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0 - 1, Ar_1 - 1, Ar_0, Ar_1, Ar_0 - 2, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Fresh_1, Ar_2, Ar_3, Ar_4, Fresh_2)) [ 0 >= Ar_1 /\ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = V_1 Pol(f3) = V_1 Pol(f4) = V_1 Pol(koat_start) = V_1 orients all transitions weakly and the transition f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0 - 1, Ar_1 - 1, Ar_0, Ar_1, Ar_0 - 2, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] strictly and produces the following problem: 4: T: (Comp: Ar_0, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0 - 1, Ar_1 - 1, Ar_0, Ar_1, Ar_0 - 2, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Fresh_1, Ar_2, Ar_3, Ar_4, Fresh_2)) [ 0 >= Ar_1 /\ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound Ar_0 + 3 Time: 1.060 sec (SMT: 1.034 sec)