WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 /\ Ar_1 + Ar_0 + 2 >= 2*Ar_2 /\ Ar_1 >= Ar_0 + 1 /\ 2*Ar_2 >= Ar_1 + Ar_0 /\ Ar_3 >= 0 /\ Ar_4 + 1 = Ar_2 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_6, Ar_3, Ar_4, Fresh_7)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_4 + 1 /\ Ar_1 + 1 >= Fresh_7 /\ Ar_2 + 1 >= Fresh_6 /\ Fresh_6 >= Ar_2 + 1 /\ Ar_5 + 1 >= Fresh_7 /\ Fresh_7 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_4, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_5)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_4 + 1 >= Fresh_4 /\ Ar_2 >= Ar_1 + 1 /\ Ar_5 + 1 >= Fresh_5 /\ Fresh_5 >= Ar_5 + 1 /\ Ar_0 + 1 >= Fresh_4 /\ Fresh_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_2, Ar_3, Ar_4, Fresh_3)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 + 1 >= Fresh_2 /\ Ar_4 >= Ar_0 /\ Ar_5 + 1 >= Fresh_3 /\ Fresh_3 >= Ar_5 + 1 /\ Ar_2 + 1 >= Fresh_2 /\ Fresh_2 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 >= Ar_2 /\ Ar_4 + 1 >= Fresh_0 /\ Ar_0 + 1 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ Ar_5 + 1 >= Fresh_1 /\ Fresh_1 >= Ar_5 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(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: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 /\ Ar_1 + Ar_0 + 2 >= 2*Ar_2 /\ Ar_1 >= Ar_0 + 1 /\ 2*Ar_2 >= Ar_1 + Ar_0 /\ Ar_3 >= 0 /\ Ar_4 + 1 = Ar_2 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_6, Ar_3, Ar_4, Fresh_7)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_4 + 1 /\ Ar_1 + 1 >= Fresh_7 /\ Ar_2 + 1 >= Fresh_6 /\ Fresh_6 >= Ar_2 + 1 /\ Ar_5 + 1 >= Fresh_7 /\ Fresh_7 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_4, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_5)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_4 + 1 >= Fresh_4 /\ Ar_2 >= Ar_1 + 1 /\ Ar_5 + 1 >= Fresh_5 /\ Fresh_5 >= Ar_5 + 1 /\ Ar_0 + 1 >= Fresh_4 /\ Fresh_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_2, Ar_3, Ar_4, Fresh_3)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 + 1 >= Fresh_2 /\ Ar_4 >= Ar_0 /\ Ar_5 + 1 >= Fresh_3 /\ Fresh_3 >= Ar_5 + 1 /\ Ar_2 + 1 >= Fresh_2 /\ Fresh_2 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 >= Ar_2 /\ Ar_4 + 1 >= Fresh_0 /\ Ar_0 + 1 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ Ar_5 + 1 >= Fresh_1 /\ Fresh_1 >= Ar_5 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(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(start) = V_2 + V_3 - V_5 - V_6 Pol(m1) = V_2 - V_6 + 1 Pol(koat_start) = V_2 + V_3 - V_5 - V_6 orients all transitions weakly and the transitions m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_4, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_5)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_4 + 1 >= Fresh_4 /\ Ar_2 >= Ar_1 + 1 /\ Ar_5 + 1 >= Fresh_5 /\ Fresh_5 >= Ar_5 + 1 /\ Ar_0 + 1 >= Fresh_4 /\ Fresh_4 >= Ar_0 + 1 ] m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 >= Ar_2 /\ Ar_4 + 1 >= Fresh_0 /\ Ar_0 + 1 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ Ar_5 + 1 >= Fresh_1 /\ Fresh_1 >= Ar_5 + 1 ] m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_6, Ar_3, Ar_4, Fresh_7)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_4 + 1 /\ Ar_1 + 1 >= Fresh_7 /\ Ar_2 + 1 >= Fresh_6 /\ Fresh_6 >= Ar_2 + 1 /\ Ar_5 + 1 >= Fresh_7 /\ Fresh_7 >= Ar_5 + 1 ] m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_2, Ar_3, Ar_4, Fresh_3)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 + 1 >= Fresh_2 /\ Ar_4 >= Ar_0 /\ Ar_5 + 1 >= Fresh_3 /\ Fresh_3 >= Ar_5 + 1 /\ Ar_2 + 1 >= Fresh_2 /\ Fresh_2 >= Ar_2 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 /\ Ar_1 + Ar_0 + 2 >= 2*Ar_2 /\ Ar_1 >= Ar_0 + 1 /\ 2*Ar_2 >= Ar_1 + Ar_0 /\ Ar_3 >= 0 /\ Ar_4 + 1 = Ar_2 /\ Ar_5 = Ar_0 ] (Comp: Ar_1 + Ar_2 + Ar_4 + Ar_5, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_6, Ar_3, Ar_4, Fresh_7)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_4 + 1 /\ Ar_1 + 1 >= Fresh_7 /\ Ar_2 + 1 >= Fresh_6 /\ Fresh_6 >= Ar_2 + 1 /\ Ar_5 + 1 >= Fresh_7 /\ Fresh_7 >= Ar_5 + 1 ] (Comp: Ar_1 + Ar_2 + Ar_4 + Ar_5, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_4, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_5)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_4 + 1 >= Fresh_4 /\ Ar_2 >= Ar_1 + 1 /\ Ar_5 + 1 >= Fresh_5 /\ Fresh_5 >= Ar_5 + 1 /\ Ar_0 + 1 >= Fresh_4 /\ Fresh_4 >= Ar_0 + 1 ] (Comp: Ar_1 + Ar_2 + Ar_4 + Ar_5, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Ar_0, Ar_1, Fresh_2, Ar_3, Ar_4, Fresh_3)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 + 1 >= Fresh_2 /\ Ar_4 >= Ar_0 /\ Ar_5 + 1 >= Fresh_3 /\ Fresh_3 >= Ar_5 + 1 /\ Ar_2 + 1 >= Fresh_2 /\ Fresh_2 >= Ar_2 + 1 ] (Comp: Ar_1 + Ar_2 + Ar_4 + Ar_5, Cost: 1) m1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(m1(Fresh_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1)) [ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_1 >= Ar_5 /\ Ar_1 >= Ar_2 /\ Ar_4 + 1 >= Fresh_0 /\ Ar_0 + 1 >= Fresh_0 /\ Fresh_0 >= Ar_0 + 1 /\ Ar_5 + 1 >= Fresh_1 /\ Fresh_1 >= Ar_5 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_1 + 4*Ar_2 + 4*Ar_4 + 4*Ar_5 + 1 Time: 2.505 sec (SMT: 2.451 sec)