Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₂ ≤ X₅ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ X₅ for location l1

Found invariant X₂ ≤ X₅ ∧ X₀ ≤ 0 for location l4

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₂ ≤ X₅
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₂ ≤ X₅
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ X₀ ≤ 0

Found invariant X₂ ≤ X₅ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ X₅ for location l1

Found invariant X₂ ≤ X₅ ∧ X₀ ≤ 0 for location l4

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

TWN-Loops:

entry: t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
results in twn-loop: twn:Inv: [X₂ ≤ X₅ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₁,X₁+X₂,X₂-1,X₃,X₄,X₅) :|: 0 < X₀
order: [X₂; X₁; X₀; X₅]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₀: X₀ + [[n != 0]] * X₁ * n^1 + [[n != 0, n != 1]] * 1/2⋅X₂ * n^2 + [[n != 0, n != 1]] * -1/2⋅X₂ * n^1 + [[n != 0, n != 1, n != 2]] * -1/6 * n^3 + [[n != 0, n != 1, n != 2]] * 1/2 * n^2 + [[n != 0, n != 1, n != 2]] * -1/3 * n^1
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0
∨ 1 < 0 ∧ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 3⋅X₂+3 ∧ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0
∨ 0 < 3⋅X₂+3 ∧ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 1 < 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6
∨ 0 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 1 < 0
∨ 0 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 6⋅X₀ ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0
∨ 0 < 6⋅X₀ ∧ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2
∨ 0 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6

Stabilization-Threshold for: 0 < X₀
alphas_abs: 3+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+10 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₄ {O(n)}
X₂: X₅ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₄ {O(n)}
X₂: X₅ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}

All Bounds

Timebounds

Overall timebound:12⋅X₅+24⋅X₃+24⋅X₄+28 {O(n)}
t₀: 1 {O(1)}
t₂: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₅+24⋅X₃+24⋅X₄+28 {O(n)}
t₀: 1 {O(1)}
t₂: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 12⋅X₃+12⋅X₄+6⋅X₅+12 {O(n)}
t₅: 1 {O(1)}

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)}
t₀, X₅: X₅ {O(n)}
t₂, X₀: 1440⋅X₃⋅X₅⋅X₅+1440⋅X₄⋅X₅⋅X₅+1728⋅X₃⋅X₃⋅X₃+1728⋅X₄⋅X₄⋅X₄+252⋅X₅⋅X₅⋅X₅+2736⋅X₃⋅X₃⋅X₅+2736⋅X₄⋅X₄⋅X₅+5184⋅X₃⋅X₃⋅X₄+5184⋅X₃⋅X₄⋅X₄+5472⋅X₃⋅X₄⋅X₅+10956⋅X₃⋅X₄+1524⋅X₅⋅X₅+5472⋅X₃⋅X₃+5484⋅X₄⋅X₄+5784⋅X₃⋅X₅+5790⋅X₄⋅X₅+3055⋅X₅+5773⋅X₃+5785⋅X₄+2028 {O(n^3)}
t₂, X₁: 144⋅X₃⋅X₃+144⋅X₄⋅X₄+156⋅X₃⋅X₅+156⋅X₄⋅X₅+288⋅X₃⋅X₄+42⋅X₅⋅X₅+163⋅X₅+300⋅X₃+301⋅X₄+156 {O(n^2)}
t₂, X₂: 12⋅X₃+12⋅X₄+7⋅X₅+12 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 1440⋅X₃⋅X₅⋅X₅+1440⋅X₄⋅X₅⋅X₅+1728⋅X₃⋅X₃⋅X₃+1728⋅X₄⋅X₄⋅X₄+252⋅X₅⋅X₅⋅X₅+2736⋅X₃⋅X₃⋅X₅+2736⋅X₄⋅X₄⋅X₅+5184⋅X₃⋅X₃⋅X₄+5184⋅X₃⋅X₄⋅X₄+5472⋅X₃⋅X₄⋅X₅+10956⋅X₃⋅X₄+1524⋅X₅⋅X₅+5472⋅X₃⋅X₃+5484⋅X₄⋅X₄+5784⋅X₃⋅X₅+5790⋅X₄⋅X₅+3055⋅X₅+5774⋅X₃+5785⋅X₄+2028 {O(n^3)}
t₃, X₁: 144⋅X₃⋅X₃+144⋅X₄⋅X₄+156⋅X₃⋅X₅+156⋅X₄⋅X₅+288⋅X₃⋅X₄+42⋅X₅⋅X₅+163⋅X₅+300⋅X₃+302⋅X₄+156 {O(n^2)}
t₃, X₂: 12⋅X₃+12⋅X₄+8⋅X₅+12 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₅ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₄, X₀: 1440⋅X₃⋅X₅⋅X₅+1440⋅X₄⋅X₅⋅X₅+1728⋅X₃⋅X₃⋅X₃+1728⋅X₄⋅X₄⋅X₄+252⋅X₅⋅X₅⋅X₅+2736⋅X₃⋅X₃⋅X₅+2736⋅X₄⋅X₄⋅X₅+5184⋅X₃⋅X₃⋅X₄+5184⋅X₃⋅X₄⋅X₄+5472⋅X₃⋅X₄⋅X₅+10956⋅X₃⋅X₄+1524⋅X₅⋅X₅+5472⋅X₃⋅X₃+5484⋅X₄⋅X₄+5784⋅X₃⋅X₅+5790⋅X₄⋅X₅+3055⋅X₅+5773⋅X₃+5785⋅X₄+2028 {O(n^3)}
t₄, X₁: 144⋅X₃⋅X₃+144⋅X₄⋅X₄+156⋅X₃⋅X₅+156⋅X₄⋅X₅+288⋅X₃⋅X₄+42⋅X₅⋅X₅+163⋅X₅+300⋅X₃+301⋅X₄+156 {O(n^2)}
t₄, X₂: 12⋅X₃+12⋅X₄+7⋅X₅+12 {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 1440⋅X₃⋅X₅⋅X₅+1440⋅X₄⋅X₅⋅X₅+1728⋅X₃⋅X₃⋅X₃+1728⋅X₄⋅X₄⋅X₄+252⋅X₅⋅X₅⋅X₅+2736⋅X₃⋅X₃⋅X₅+2736⋅X₄⋅X₄⋅X₅+5184⋅X₃⋅X₃⋅X₄+5184⋅X₃⋅X₄⋅X₄+5472⋅X₃⋅X₄⋅X₅+10956⋅X₃⋅X₄+1524⋅X₅⋅X₅+5472⋅X₃⋅X₃+5484⋅X₄⋅X₄+5784⋅X₃⋅X₅+5790⋅X₄⋅X₅+3055⋅X₅+5774⋅X₃+5785⋅X₄+2028 {O(n^3)}
t₅, X₁: 144⋅X₃⋅X₃+144⋅X₄⋅X₄+156⋅X₃⋅X₅+156⋅X₄⋅X₅+288⋅X₃⋅X₄+42⋅X₅⋅X₅+163⋅X₅+300⋅X₃+302⋅X₄+156 {O(n^2)}
t₅, X₂: 12⋅X₃+12⋅X₄+8⋅X₅+12 {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}