MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f2(Fresh_1, Ar_1 - 1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (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: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f2(Fresh_1, Ar_1 - 1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (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(f2) = V_2 Pol(f0) = V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f2(Fresh_1, Ar_1 - 1)) [ Ar_1 >= 1 ] (Comp: Ar_1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ 0 >= Ar_0 ] (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 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f2: X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: Ar_1, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Fresh_0, Ar_1 - 1)) [ Ar_1 >= 0 /\ Ar_1 >= 1 /\ 0 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f2(Fresh_1, Ar_1 - 1)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 1 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.490 sec (SMT: 1.441 sec)