Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂, X₃, X₄) → l1(1000, X₁, X₂, X₃, X₄)
t₀: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 101 ≤ X₀ ∧ X₁ ≤ 9
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, 0, 0, 0) :|: X₀ ≤ 100 ∧ X₁ ≤ 9
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, 0, 0, 0) :|: 10 ≤ X₁

Preprocessing

Eliminate variables {X₂,X₃,X₄} that do not contribute to the problem

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₀: l0(X₀, X₁) → l1(1000, X₁)
t₁₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 101 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 100 ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₃: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 2005 {O(1)}

TWN-Loops:

entry: t₁₀: l0(X₀, X₁) → l1(1000, X₁)
results in twn-loop: twn:Inv: [X₀ ≤ 1000 ∧ 100 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 101 ≤ X₀ ∧ X₁ ≤ 9
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁

Termination: true
Formula:

X₁ < 9 ∧ 1 < 0
∨ X₁ < 9 ∧ 101 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 101 ≤ X₀ ∧ X₀ ≤ 101
∨ X₁ ≤ 9 ∧ 9 ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ 9 ∧ 9 ≤ X₁ ∧ 101 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ 9 ∧ 9 ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 101 ≤ X₀ ∧ X₀ ≤ 101

Stabilization-Threshold for: 101 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₁₀:
X₀: 1000 {O(1)}
Runtime-bound of t₁₀: 1 {O(1)}
Results in: 2005 {O(1)}

2005 {O(1)}

All Bounds

Timebounds

Overall timebound:2008 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 2005 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 2008 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 2005 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Sizebounds

t₁₀, X₀: 1000 {O(1)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 999 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 100 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 1000 {O(1)}
t₁₃, X₁: X₁ {O(n)}