WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_0, Ar_2)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_0, Ar_2)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Fresh_1)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Fresh_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2) -> Com_1(f23(Ar_0 + 1, Ar_1, Ar_2)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f28(Ar_0, Ar_1, Ar_2) -> Com_1(f23(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f28(Ar_0, Ar_1, Ar_2) -> Com_1(f23(Ar_0 + 1, Ar_1, Ar_2)) [ 98 >= D ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2) -> Com_1(f38(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 1, Ar_0, Ar_2)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_2)) [ 98 >= D ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f23(0, Ar_1, Ar_2)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: ?, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f0) = 1 Pol(f8) = 1 Pol(f23) = 1 Pol(f14) = 1 Pol(f38) = 0 Pol(f28) = 1 orients all transitions weakly and the transition f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f0) = 1 Pol(f8) = 1 Pol(f23) = 0 Pol(f14) = 1 Pol(f38) = 0 Pol(f28) = 0 orients all transitions weakly and the transition f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 297 Pol(f0) = 297 Pol(f8) = 297 Pol(f23) = -2*V_1 + 297 Pol(f14) = 297 Pol(f38) = -2*V_1 + 297 Pol(f28) = -2*V_1 + 296 orients all transitions weakly and the transitions f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: ?, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 198 Pol(f0) = 198 Pol(f8) = 198 Pol(f23) = -V_1 + 100 Pol(f14) = 198 Pol(f38) = -V_1 + 100 Pol(f28) = -V_1 + 99 orients all transitions weakly and the transition f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: 198, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f8) = -2*V_1 + 298 Pol(f14) = -2*V_1 + 297 and size complexities S("f0(Ar_0) -> Com_1(f8(0))", 0-0) = 0 S("f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\\ 99 >= D ]", 0-0) = ? S("f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ]", 0-0) = ? S("f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\\ 0 >= E + 1 ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ]", 0-0) = 1288 S("f28(Ar_0) -> Com_1(f23(Ar_0 + 1))", 0-0) = 1288 S("f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ]", 0-0) = 1288 S("f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ]", 0-0) = ? S("f14(Ar_0) -> Com_1(f8(Ar_0 + 1))", 0-0) = ? S("f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ]", 0-0) = ? S("f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ]", 0-0) = 0 S("koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ]", 0-0) = Ar_0 orients the transitions f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) weakly and the transition f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: 198, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: 298, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f14) = -2*V_1 + 198 Pol(f8) = -2*V_1 + 199 and size complexities S("f0(Ar_0) -> Com_1(f8(0))", 0-0) = 0 S("f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\\ 99 >= D ]", 0-0) = ? S("f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ]", 0-0) = ? S("f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\\ 0 >= E + 1 ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ]", 0-0) = 1288 S("f28(Ar_0) -> Com_1(f23(Ar_0 + 1))", 0-0) = 1288 S("f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ]", 0-0) = 1288 S("f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ]", 0-0) = 1288 S("f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ]", 0-0) = ? S("f14(Ar_0) -> Com_1(f8(Ar_0 + 1))", 0-0) = ? S("f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ]", 0-0) = ? S("f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ]", 0-0) = 0 S("koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ]", 0-0) = Ar_0 orients the transitions f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] weakly and the transitions f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: ?, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: 199, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: 198, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: 199, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: 298, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 10 produces the following problem: 11: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f8(Ar_0) -> Com_1(f23(0)) [ Ar_0 >= 100 ] (Comp: 497, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 98 >= D ] (Comp: 497, Cost: 1) f14(Ar_0) -> Com_1(f8(Ar_0 + 1)) (Comp: 199, Cost: 1) f8(Ar_0) -> Com_1(f8(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 1, Cost: 1) f23(Ar_0) -> Com_1(f38(Ar_0)) [ Ar_0 >= 100 ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 98 >= D ] (Comp: 594, Cost: 1) f28(Ar_0) -> Com_1(f23(Ar_0 + 1)) (Comp: 198, Cost: 1) f23(Ar_0) -> Com_1(f23(Ar_0 + 1)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 ] (Comp: 297, Cost: 1) f23(Ar_0) -> Com_1(f28(Ar_0)) [ 99 >= Ar_0 /\ 0 >= E + 1 ] (Comp: 199, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 ] (Comp: 298, Cost: 1) f8(Ar_0) -> Com_1(f14(Ar_0)) [ 99 >= Ar_0 /\ 99 >= D ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f8(0)) start location: koat_start leaf cost: 0 Complexity upper bound 3673 Time: 1.327 sec (SMT: 1.274 sec)