MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_6 - 1, Ar_1)) [ 0 >= C /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_5 + 1, Ar_1)) [ C >= 2 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_4 - 1, Ar_1)) [ 0 >= C + 2 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_3 + 1, Ar_1)) [ C >= 0 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_2)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_1)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Fresh_0)) [ Ar_0 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f3(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) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_6 - 1, Ar_1)) [ 0 >= C /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_5 + 1, Ar_1)) [ C >= 2 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_4 - 1, Ar_1)) [ 0 >= C + 2 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_3 + 1, Ar_1)) [ C >= 0 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_2)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_1)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Fresh_0)) [ Ar_0 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f2) = 1 Pol(f3) = 1 Pol(f300) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transitions f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Fresh_0)) [ Ar_0 = 0 ] f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_2)) [ 0 >= Ar_0 + 1 ] f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_1)) [ Ar_0 >= 1 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_6 - 1, Ar_1)) [ 0 >= C /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_5 + 1, Ar_1)) [ C >= 2 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_4 - 1, Ar_1)) [ 0 >= C + 2 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_3 + 1, Ar_1)) [ C >= 0 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) (Comp: 1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_2)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(0, Fresh_1)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Fresh_0)) [ Ar_0 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.121 sec (SMT: 1.080 sec)