MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] (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 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] (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 A polynomial rank function with Pol(f0) = 1 Pol(f15) = 1 Pol(f18) = 1 Pol(f28) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] (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 A polynomial rank function with Pol(f0) = 17 Pol(f15) = -2*V_1 + 21 Pol(f18) = -2*V_1 + 20 Pol(f28) = -2*V_1 + 21 Pol(koat_start) = 17 orients all transitions weakly and the transition f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) (Comp: 17, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] (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 A polynomial rank function with Pol(f18) = 1 Pol(f15) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ]", 0-0) = ? S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ]", 0-1) = ? S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ]", 0-2) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2))", 0-0) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2))", 0-1) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2))", 0-2) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ]", 0-0) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ]", 0-1) = ? S("f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ]", 0-2) = ? S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ]", 0-0) = ? S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ]", 0-1) = ? S("f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ]", 0-2) = ? S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2))", 0-0) = 2 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) weakly and the transition f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) (Comp: 17, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ 10 >= Ar_0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ D >= E + 1 ] (Comp: 17, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 11 ] (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 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol f15: X_1 - 2 >= 0 For symbol f18: -X_2 + 10 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 + 20 >= 0 /\ -X_1 + 10 >= 0 /\ X_1 - 2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f28(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 2 >= 0 /\ Ar_0 >= 11 ] (Comp: 17, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_1 + 10 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 20 >= 0 /\ -Ar_0 + 10 >= 0 /\ Ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_1 - 1, Fresh_0)) [ -Ar_1 + 10 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 20 >= 0 /\ -Ar_0 + 10 >= 0 /\ Ar_0 - 2 >= 0 /\ D >= E + 1 ] (Comp: 17, Cost: 1) f15(Ar_0, Ar_1, Ar_2) -> Com_1(f18(Ar_0, Ar_0, Ar_2)) [ Ar_0 - 2 >= 0 /\ 10 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f15(2, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.711 sec (SMT: 1.653 sec)