Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₁: l10(X₀, X₁) → l9(X₀-1, X₁)
t₁₂: l11(X₀, X₁) → l12(X₀, X₁)
t₁: l2(X₀, X₁) → l3(X₀, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, X₁)
t₆: l6(X₀, X₁) → l7(X₀, X₁)
t₇: l7(X₀, X₁) → l8(X₀, X₁)
t₈: l8(X₀, X₁) → l9(X₁, X₁)
t₉: l9(X₀, X₁) → l10(X₀, X₁) :|: 0 < X₀
t₁₀: l9(X₀, X₁) → l11(X₀, X₁) :|: X₀ ≤ 0

Preprocessing

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l11

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l12

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l10

Found invariant X₀ ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₁: l10(X₀, X₁) → l9(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₂: l11(X₀, X₁) → l12(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁: l2(X₀, X₁) → l3(X₀, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, X₁)
t₆: l6(X₀, X₁) → l7(X₀, X₁)
t₇: l7(X₀, X₁) → l8(X₀, X₁)
t₈: l8(X₀, X₁) → l9(X₁, X₁)
t₉: l9(X₀, X₁) → l10(X₀, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁
t₁₀: l9(X₀, X₁) → l11(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l11

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l12

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l10

Found invariant X₀ ≤ X₁ for location l9

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 2⋅X₁+4 {O(n)}

TWN-Loops:

entry: t₈: l8(X₀, X₁) → l9(X₁, X₁)
results in twn-loop: twn:Inv: [X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 0 < X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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

relevant size-bounds w.r.t. t₈:
X₀: X₁ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

2⋅X₁+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₉ 2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₈:
X₀: X₁ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

2⋅X₁+4 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₁+19 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 2⋅X₁+4 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁+19 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 2⋅X₁+4 {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 2⋅X₁ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 2⋅X₁ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}