MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(1, Ar_2, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0, Fresh_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_0 + 2 /\ Fresh_1^2 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_0 + 2 /\ Ar_2 >= Fresh_0^2 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f16(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 + 1 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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, Ar_2, Ar_3) -> Com_1(f6(1, Ar_2, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0, Fresh_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_0 + 2 /\ Fresh_1^2 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_0 + 2 /\ Ar_2 >= Fresh_0^2 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f16(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 + 1 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 1 Pol(f6) = 1 Pol(f16) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f16(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 + 1 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(1, Ar_2, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0, Fresh_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_0 + 2 /\ Fresh_1^2 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_0 + 2 /\ Ar_2 >= Fresh_0^2 ] (Comp: 1, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f16(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 + 1 >= Ar_1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.608 sec (SMT: 0.574 sec)