Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l3(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 0 < X₀
t₇: l2(X₀, X₁) → l5(X₀, X₁)
t₁: l3(X₀, X₁) → l1(X₁, X₁) :|: 0 < X₁
t₂: l3(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₆: l4(X₀, X₁) → l1(X₀-1, X₁)

Preprocessing

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Cut unsatisfiable transition t₃: l1→l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l3(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 0 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁) → l5(X₀, X₁)
t₁: l3(X₀, X₁) → l1(X₁, X₁) :|: 0 < X₁
t₂: l3(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₆: l4(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 2⋅X₁+4 {O(n)}

TWN-Loops:

entry: t₁: l3(X₀, X₁) → l1(X₁, X₁) :|: 0 < X₁
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 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. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

2⋅X₁+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆ 2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

2⋅X₁+4 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₁+13 {O(n)}
t₀: 1 {O(1)}
t₄: 2⋅X₁+4 {O(n)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 2⋅X₁+4 {O(n)}

Costbounds

Overall costbound: 4⋅X₁+13 {O(n)}
t₀: 1 {O(1)}
t₄: 2⋅X₁+4 {O(n)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 2⋅X₁+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}