WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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(f4(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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(f4) = 1 Pol(f7) = 1 Pol(f19) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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(f4(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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) = 3*V_2 - 2 Pol(f4) = -3*V_1 + 3*V_2 - 2 Pol(f7) = -3*V_1 + 3*V_2 - 4 Pol(f19) = -3*V_1 + 3*V_2 - 2 Pol(koat_start) = 3*V_2 - 2 orients all transitions weakly and the transition f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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(f7) = 1 Pol(f4) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-0) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-1) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-2) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-0) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-1) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-2) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-0) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-1) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-2) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ]", 0-0) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ]", 0-1) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ]", 0-2) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ]", 0-3) = 0 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-0) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 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 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol f4: X_1 >= 0 For symbol f7: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 This yielded the following problem: 6: T: (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 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_2 Pol(f0) = V_2 Pol(f4) = V_2 Pol(f19) = V_2 Pol(f7) = V_2 orients all transitions weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] strictly and produces the following problem: 7: T: (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 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: Ar_1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_2 Pol(f0) = V_2 Pol(f4) = V_2 Pol(f19) = V_2 Pol(f7) = V_2 orients all transitions weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] strictly and produces the following problem: 8: T: (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 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: Ar_1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: Ar_1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f7) = V_2 - V_3 + 1 and size complexities S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-0) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_1 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-2) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-3) = 0 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-0) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-1) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-2) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ 0 >= Fresh_1 + 1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-0) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-1) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-2) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Fresh_0 >= 1 ]", 0-3) = ? S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-0) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-1) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-2) = Ar_1 S("f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-3) = ? S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_1 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] strictly and produces the following problem: 9: T: (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 ] (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: Ar_1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Fresh_0 >= 1 ] (Comp: Ar_1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1 - 1, Ar_2, Fresh_1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ 0 >= Fresh_1 + 1 ] (Comp: 10*Ar_1^2 + 9*Ar_1 + 2, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 3*Ar_1 + 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_0 + 1, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 17*Ar_1 + 10*Ar_1^2 + 8 Time: 3.361 sec (SMT: 3.260 sec)