MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Fresh_8, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2 - 1, Fresh_6, 0, Fresh_7)) [ Ar_0 >= 1 /\ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_3, Fresh_4, Fresh_5, Ar_5)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_0, Fresh_1, Fresh_2, Ar_5)) [ Fresh_2 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f1(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Fresh_8, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2 - 1, Fresh_6, 0, Fresh_7)) [ Ar_0 >= 1 /\ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_3, Fresh_4, Fresh_5, Ar_5)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_0, Fresh_1, Fresh_2, Ar_5)) [ Fresh_2 >= 1 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f1(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(f0) = 1 Pol(f2) = 0 Pol(f1) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Fresh_8, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Fresh_8, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2 - 1, Fresh_6, 0, Fresh_7)) [ Ar_0 >= 1 /\ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_3, Fresh_4, Fresh_5, Ar_5)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_0, Fresh_1, Fresh_2, Ar_5)) [ Fresh_2 >= 1 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f1(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(f0) = V_1 Pol(f2) = V_1 Pol(f1) = V_1 Pol(koat_start) = V_1 orients all transitions weakly and the transitions f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_3, Fresh_4, Fresh_5, Ar_5)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 1 ] f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_0, Fresh_1, Fresh_2, Ar_5)) [ Fresh_2 >= 1 /\ Ar_0 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Fresh_8, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2 - 1, Fresh_6, 0, Fresh_7)) [ Ar_0 >= 1 /\ Ar_2 >= 3 ] (Comp: Ar_0, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_3, Fresh_4, Fresh_5, Ar_5)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 1 ] (Comp: Ar_0, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0 - 1, Ar_1, Fresh_0, Fresh_1, Fresh_2, Ar_5)) [ Fresh_2 >= 1 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.644 sec (SMT: 1.574 sec)