MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Fresh_1, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_1 >= C + 1 /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E + 1 >= Fresh_1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_0 >= C /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E >= Fresh_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Fresh_1, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_1 >= C + 1 /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E + 1 >= Fresh_1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_0 >= C /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E >= Fresh_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval) = 2*V_2 + 1 Pol(start) = 2*V_2 + 1 Pol(koat_start) = 2*V_2 + 1 orients all transitions weakly and the transition eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_0 >= C /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E >= Fresh_0 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Fresh_1, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_1 >= C + 1 /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E + 1 >= Fresh_1 ] (Comp: 2*Ar_1 + 1, Cost: 1) eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2*C /\ 3*C >= Ar_0 + Ar_1 + 1 /\ Fresh_0 >= C /\ Ar_0 + Ar_1 >= 2*E /\ 3*E >= Ar_0 + Ar_1 + 1 /\ E >= Fresh_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.823 sec (SMT: 0.778 sec)