WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 1 Pol(f300) = 1 Pol(f1) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = -V_1 + V_2 Pol(f300) = -V_1 + V_2 Pol(f1) = -V_1 + V_2 Pol(koat_start) = -V_1 + V_2 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = -V_1 + V_2 Pol(f300) = -V_1 + V_2 Pol(f1) = -V_1 + V_2 Pol(koat_start) = -V_1 + V_2 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = -V_1 + V_2 Pol(f300) = -V_1 + V_2 Pol(f1) = -V_1 + V_2 Pol(koat_start) = -V_1 + V_2 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_2, Ar_3)) [ Fresh_2 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0 + 1, Ar_1, Fresh_1, Ar_3)) [ 0 >= Fresh_1 + 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1 - 1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 3*Ar_0 + 3*Ar_1 + 2 Time: 1.025 sec (SMT: 0.991 sec)