Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₁+1
t₁: l2(X₀, X₁, X₂, X₃) → l1(10000, 1, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

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

Found invariant X₀+X₁ ≤ 10001 ∧ 5001 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5000 for location l5

Found invariant X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 for location l1

Found invariant X₀+X₁ ≤ 10001 ∧ 5001 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5000 for location l4

Found invariant X₁ ≤ 5000 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ 5001 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁) → l2(X₀, X₁)
t₁₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000
t₁₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < X₁+1 ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000
t₁₅: l2(X₀, X₁) → l1(10000, 1)
t₁₆: l3(X₀, X₁) → l1(X₀-1, X₁+1) :|: X₁ ≤ 5000 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ 5001 ≤ X₀
t₁₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀+X₁ ≤ 10001 ∧ 5001 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5000

Found invariant X₁ ≤ 5001 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 10001 ∧ 5001 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5000 ∧ 5000 ≤ X₀ for location l5

Found invariant X₁ ≤ 5001 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ 5000 ≤ X₀ for location l1

Found invariant X₁ ≤ 5001 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 10001 ∧ 5001 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5000 ∧ 5000 ≤ X₀ for location l4

Found invariant X₁ ≤ 5000 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ 5001 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 20008 {O(1)}

TWN-Loops:

entry: t₁₅: l2(X₀, X₁) → l1(10000, 1)
results in twn-loop: twn:Inv: [X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ X₁ ≤ 5000 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10001 ∧ 1 ≤ X₁ ∧ 10001 ≤ X₀+X₁ ∧ X₀ ≤ 9999+X₁ ∧ X₀ ≤ 10000 ∧ 5001 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁+1) :|: 1+X₁ ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

2 < 0
∨ 1+X₁ < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁

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

relevant size-bounds w.r.t. t₁₅:
X₀: 10000 {O(1)}
X₁: 1 {O(1)}
Runtime-bound of t₁₅: 1 {O(1)}
Results in: 20008 {O(1)}

20008 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₆ 20008 {O(1)}

relevant size-bounds w.r.t. t₁₅:
X₀: 10000 {O(1)}
X₁: 1 {O(1)}
Runtime-bound of t₁₅: 1 {O(1)}
Results in: 20008 {O(1)}

20008 {O(1)}

All Bounds

Timebounds

Overall timebound:40020 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 20008 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 20008 {O(1)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 40020 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 20008 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 20008 {O(1)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 10000 {O(1)}
t₁₃, X₁: 20009 {O(1)}
t₁₄, X₀: 10000 {O(1)}
t₁₄, X₁: 20009 {O(1)}
t₁₅, X₀: 10000 {O(1)}
t₁₅, X₁: 1 {O(1)}
t₁₆, X₀: 10000 {O(1)}
t₁₆, X₁: 20009 {O(1)}
t₁₇, X₀: 10000 {O(1)}
t₁₇, X₁: 20009 {O(1)}