Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀+X₁ < 0
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₁: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₃, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀+X₁+X₄, -X₄-1, X₂, X₃, X₄)

Preprocessing

Found invariant 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀+X₁ < 0
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₁: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₃, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀+X₁+X₄, -X₄-1, X₂, X₃, X₄) :|: 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

Found invariant 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

TWN-Loops:

entry: t₁: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₃, X₂, X₃, X₄)
results in twn-loop: twn:Inv: [0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄) -> (X₀+X₁+X₄,-X₄-1,X₂,X₃,X₄) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
order: [X₄; X₁; X₀]
closed-form:
X₄: X₄
X₁: [[n == 0]] * X₁ + [[n != 0]] * -X₄-1
X₀: X₀ + [[n != 0]] * X₄ * n^1 + [[n != 0]] * X₁ + [[n != 0, n != 1]] * -X₄-1 * n^1 + [[n != 0, n != 1]] * X₄+1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < X₀+X₁+X₄+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₄+1 ∧ X₀+X₁+X₄+1 ≤ 0
∨ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < X₀+X₁ ∧ 0 < X₀+X₁+X₄+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₄+1 ∧ X₀+X₁+X₄+1 ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀+X₁+X₄+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₄+1 ∧ X₀+X₁+X₄+1 ≤ 0

Stabilization-Threshold for: 0 ≤ X₀+X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀+X₁+X₄+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅ 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₄+8⋅X₂+8⋅X₃+21 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

Costbounds

Overall costbound: 4⋅X₄+8⋅X₂+8⋅X₃+21 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₄+4⋅X₂+4⋅X₃+8 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₀: 10⋅X₃⋅X₄+4⋅X₂⋅X₃+4⋅X₃⋅X₃+4⋅X₄⋅X₄+8⋅X₂⋅X₄+13⋅X₃+20⋅X₄+5⋅X₂+9 {O(n^2)}
t₂, X₁: X₃+X₄+1 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 10⋅X₃⋅X₄+4⋅X₂⋅X₃+4⋅X₃⋅X₃+4⋅X₄⋅X₄+8⋅X₂⋅X₄+13⋅X₃+20⋅X₄+6⋅X₂+9 {O(n^2)}
t₃, X₁: X₃+X₄+1 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 10⋅X₃⋅X₄+4⋅X₂⋅X₃+4⋅X₃⋅X₃+4⋅X₄⋅X₄+8⋅X₂⋅X₄+13⋅X₃+20⋅X₄+6⋅X₂+9 {O(n^2)}
t₄, X₁: X₃+X₄+1 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 16⋅X₂⋅X₄+20⋅X₃⋅X₄+8⋅X₂⋅X₃+8⋅X₃⋅X₃+8⋅X₄⋅X₄+12⋅X₂+26⋅X₃+40⋅X₄+18 {O(n^2)}
t₆, X₁: 2⋅X₃+2⋅X₄+2 {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₅, X₀: 10⋅X₃⋅X₄+4⋅X₂⋅X₃+4⋅X₃⋅X₃+4⋅X₄⋅X₄+8⋅X₂⋅X₄+13⋅X₃+20⋅X₄+5⋅X₂+9 {O(n^2)}
t₅, X₁: X₄+1 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}