Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₃: l0(X₀, X₁, X₂) → l3(X₀, X₁, 1) :|: 1 ≤ X₀
t₄: l1(X₀, X₁, X₂) → l3(-1-X₀, X₁, 1) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0
t₅: l1(X₀, X₁, X₂) → l3(-1-X₀, X₁, 1) :|: X₀+1 ≤ 0 ∧ 2 ≤ X₂
t₆: l1(X₀, X₁, X₂) → l3(-1-X₀, X₁, 1) :|: 1 ≤ X₀ ∧ X₂ ≤ 0
t₇: l1(X₀, X₁, X₂) → l3(-1-X₀, X₁, 1) :|: 1 ≤ X₀ ∧ 2 ≤ X₂
t₁: l1(X₀, X₁, X₂) → l4(0, D, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₀: l2(X₀, X₁, X₂) → l1(-X₀, X₁, X₂)
t₈: l3(X₀, X₁, X₂) → l1(1-X₀, X₁, 0) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 1 ∧ 1 ≤ X₂
t₉: l3(X₀, X₁, X₂) → l1(1-X₀, X₁, 0) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂
t₂: l3(X₀, X₁, X₂) → l4(0, D, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₀: l5(X₀, X₁, X₂) → l1(1-X₀, X₁, 0) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 1 ∧ 1 ≤ X₂
t₁₁: l5(X₀, X₁, X₂) → l1(1-X₀, X₁, 0) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂
Preprocessing
Cut unreachable locations [l2; l5] from the program graph
Cut unsatisfiable transition t₅: l1→l3
Cut unsatisfiable transition t₇: l1→l3
Eliminate variables {D,X₁} that do not contribute to the problem
Found invariant X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l1
Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location l3
Cut unsatisfiable transition t₃₁: l1→l3
Cut unsatisfiable transition t₃₃: l3→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₂
Temp_Vars:
Locations: l0, l1, l3, l4
Transitions:
t₂₈: l0(X₀, X₂) → l3(X₀, 1) :|: 1 ≤ X₀
t₃₀: l1(X₀, X₂) → l3(-1-X₀, 1) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0
t₂₉: l1(X₀, X₂) → l4(0, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0
t₃₄: l3(X₀, X₂) → l1(1-X₀, 0) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₀
t₃₂: l3(X₀, X₂) → l4(0, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₀
Found invariant X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l1
Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₃₀ 4⋅X₀+12 {O(n)}
TWN-Loops:
entry: t₂₈: l0(X₀, X₂) → l3(X₀, 1) :|: 1 ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀] , (X₀,X₂) -> (X₀-2,1) :|: 1 ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 0 ≤ 0
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -2 * n^1
X₂: [[n == 0]] * X₂ + [[n != 0]]
Termination: true
Formula:
2 < 0
∨ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < X₀ ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < 0 ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < 0 ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 2 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 2 ≤ X₀
alphas_abs: 2+X₀
M: 0
N: 1
Bound: 2⋅X₀+6 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+X₀
M: 0
N: 1
Bound: 2⋅X₀+4 {O(n)}
relevant size-bounds w.r.t. t₂₈:
X₀: X₀ {O(n)}
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 4⋅X₀+12 {O(n)}
4⋅X₀+12 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₃₄ 4⋅X₀+12 {O(n)}
relevant size-bounds w.r.t. t₂₈:
X₀: X₀ {O(n)}
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 4⋅X₀+12 {O(n)}
4⋅X₀+12 {O(n)}
All Bounds
Timebounds
Overall timebound:8⋅X₀+27 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 4⋅X₀+12 {O(n)}
t₃₂: 1 {O(1)}
t₃₄: 4⋅X₀+12 {O(n)}
Costbounds
Overall costbound: 8⋅X₀+27 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 4⋅X₀+12 {O(n)}
t₃₂: 1 {O(1)}
t₃₄: 4⋅X₀+12 {O(n)}
Sizebounds
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₂: 1 {O(1)}
t₂₉, X₀: 0 {O(1)}
t₂₉, X₂: 0 {O(1)}
t₃₀, X₀: X₀ {O(n)}
t₃₀, X₂: 1 {O(1)}
t₃₂, X₀: 0 {O(1)}
t₃₂, X₂: 1 {O(1)}
t₃₄, X₀: X₀ {O(n)}
t₃₄, X₂: 0 {O(1)}