Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁) → l1(0, X₁)
t₁: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 1
t₅: l1(X₀, X₁) → l2(X₀, 0) :|: 2 ≤ X₀
t₂: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 1
t₃: l2(X₀, X₁) → l3(X₀, X₁) :|: 2 ≤ X₁ ∧ C+1 ≤ 0
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: 2 ≤ X₁

Preprocessing

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l2

Found invariant X₀ ≤ 2 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁) → l1(0, X₁)
t₁: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 1 ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
t₅: l1(X₀, X₁) → l2(X₀, 0) :|: 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
t₂: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 1 ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₃: l2(X₀, X₁) → l3(X₀, X₁) :|: 2 ≤ X₁ ∧ C+1 ≤ 0 ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: 2 ≤ X₁ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l2

Found invariant X₀ ≤ 2 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 6 {O(1)}

TWN-Loops:

entry: t₀: l0(X₀, X₁) → l1(0, X₁)
results in twn-loop: twn:Inv: [X₀ ≤ 2 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ 1
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 1
alphas_abs: 1
M: 0
N: 1
Bound: 4 {O(1)}

relevant size-bounds w.r.t. t₀:
Runtime-bound of t₀: 1 {O(1)}
Results in: 6 {O(1)}

6 {O(1)}

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l2

Found invariant X₀ ≤ 2 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 6 {O(1)}

TWN-Loops:

entry: t₅: l1(X₀, X₁) → l2(X₀, 0) :|: 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+1) :|: X₁ ≤ 1
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁

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

relevant size-bounds w.r.t. t₅:
X₁: 0 {O(1)}
Runtime-bound of t₅: 1 {O(1)}
Results in: 6 {O(1)}

6 {O(1)}

All Bounds

Timebounds

Overall timebound:16 {O(1)}
t₀: 1 {O(1)}
t₁: 6 {O(1)}
t₅: 1 {O(1)}
t₂: 6 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 16 {O(1)}
t₀: 1 {O(1)}
t₁: 6 {O(1)}
t₅: 1 {O(1)}
t₂: 6 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2 {O(1)}
t₁, X₁: X₁ {O(n)}
t₅, X₀: 2 {O(1)}
t₅, X₁: 0 {O(1)}
t₂, X₀: 2 {O(1)}
t₂, X₁: 2 {O(1)}
t₃, X₀: 2 {O(1)}
t₃, X₁: 2 {O(1)}
t₄, X₀: 2 {O(1)}
t₄, X₁: 2 {O(1)}