WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval1(Ar_1, Ar_1, 1, Ar_3)) (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(end(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0, Ar_1, Ar_2, Ar_0 - 10)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval11(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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, Ar_1, Ar_2]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) 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, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(eval0) = 1 Pol(eval11) = -1 Pol(eval5) = -1 Pol(eval9) = -1 Pol(eval7) = -1 Pol(eval3) = 1 Pol(eval1) = 1 Pol(end) = 1 orients all transitions weakly and the transition eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval3) = -V_1 + 101 and size complexities S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = 1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-2) = ? S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] weakly and the transition eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval9) = 101*V_3 - 100 Pol(eval11) = 101*V_3 - 100 Pol(eval7) = 101*V_3 - 100 Pol(eval5) = 101*V_3 - 201 and size complexities S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = 1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-2) = Ar_1 + 102 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = Ar_1 + 102 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-2) = ? S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) weakly and the transition eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 101*Ar_1 + 10503, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol eval1: -X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 For symbol eval11: X_3 >= 0 /\ -X_2 + X_3 + 100 >= 0 /\ X_1 + X_3 - 91 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval3: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 >= 0 For symbol eval5: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 101 >= 0 For symbol eval7: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval9: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 101*Ar_1 + 10503, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval0) = -4*V_2 + 402 Pol(eval1) = -4*V_1 + 41*V_3 + 361 Pol(end) = -4*V_1 + 41*V_3 + 361 Pol(eval3) = -4*V_1 + 41*V_3 + 361 Pol(eval5) = -4*V_1 + 41*V_3 + 361 Pol(eval7) = -4*V_1 + 41*V_3 + 361 Pol(eval9) = -4*V_1 + 41*V_3 + 360 Pol(eval11) = -4*V_1 + 41*V_3 + 359 Pol(koat_start) = -4*V_2 + 402 orients all transitions weakly and the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 101*Ar_1 + 10503, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 4*Ar_1 + 402, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 4*Ar_1 + 402, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval9) = 4*V_1 - 9 Pol(eval11) = 4*V_1 + 22 Pol(eval7) = 4*V_1 Pol(eval5) = 4*V_1 - 31 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = 100 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-2) = 2 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = 100 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-2) = ? S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-2) = Ar_1 + 102 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = Ar_1 + 102 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-2) = 1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 orients the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] weakly and the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1692*Ar_1 + 170119, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 101*Ar_1 + 10503, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 4*Ar_1 + 402, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 1692*Ar_1 + 170119, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: 1692*Ar_1 + 170119, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: 1692*Ar_1 + 170119, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 4*Ar_1 + 402, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 1692*Ar_1 + 170119, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 8570*Ar_1 + 862007 Time: 4.597 sec (SMT: 4.444 sec)