WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] (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(f8(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] (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(f8) = 1 Pol(f23) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transitions f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] (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) = 4 Pol(f8) = -V_1 + 4 Pol(f23) = -V_1 + 4 Pol(koat_start) = 4 orients all transitions weakly and the transition f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(0, Ar_1, Ar_2, Ar_3)) (Comp: 4, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] (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) = 4 Pol(f8) = -V_1 + 4 Pol(f23) = -V_1 + 4 Pol(koat_start) = 4 orients all transitions weakly and the transition f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(0, Ar_1, Ar_2, Ar_3)) (Comp: 4, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ 3 >= Ar_0 ] (Comp: 4, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_0 + 1, Fresh_0)) [ 3 >= Ar_0 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 /\ 0 >= E + 1 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 4 ] (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 11 Time: 1.186 sec (SMT: 1.158 sec)