MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f4(0, 99)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Fresh_1, Ar_1)) [ Ar_1 >= Ar_0 + 1 /\ C >= D + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Fresh_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f11(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(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: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f4(0, 99)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Fresh_1, Ar_1)) [ Ar_1 >= Ar_0 + 1 /\ C >= D + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Fresh_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f11(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 1 Pol(f4) = 1 Pol(f11) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f4(Ar_0, Ar_1) -> Com_1(f11(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f4(0, 99)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Fresh_1, Ar_1)) [ Ar_1 >= Ar_0 + 1 /\ C >= D + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Fresh_0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1) -> Com_1(f11(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.467 sec (SMT: 0.439 sec)