Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(30, 30, 1, 0, 2, X₅, X₆, X₇, X₈)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀, X₁, X₂+X₃, X₂, X₄+1, X₂, X₆, X₇, X₈) :|: X₄ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₂, X₂) :|: 1+X₁ ≤ X₄

Preprocessing

Eliminate variables {X₀,X₂,X₃,X₅,X₆,X₇,X₈} that do not contribute to the problem

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 31 ≤ X₄ ∧ 61 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l2

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₁, X₄
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₁, X₄) → l1(30, 2)
t₈: l1(X₁, X₄) → l1(X₁, X₄+1) :|: X₄ ≤ X₁ ∧ X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁
t₉: l1(X₁, X₄) → l2(X₁, X₄) :|: 1+X₁ ≤ X₄ ∧ X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 31 ≤ X₄ ∧ 61 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l2

Found invariant X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 68 {O(1)}

TWN-Loops:

entry: t₇: l0(X₁, X₄) → l1(30, 2)
results in twn-loop: twn:Inv: [X₄ ≤ 31 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 61 ∧ 2 ≤ X₄ ∧ 32 ≤ X₁+X₄ ∧ X₁ ≤ 28+X₄ ∧ X₁ ≤ 30 ∧ 30 ≤ X₁] , (X₁,X₄) -> (X₁,X₄+1) :|: X₄ ≤ X₁
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄

Stabilization-Threshold for: X₄ ≤ X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}

relevant size-bounds w.r.t. t₇:
X₁: 30 {O(1)}
X₄: 2 {O(1)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 68 {O(1)}

68 {O(1)}

All Bounds

Timebounds

Overall timebound:70 {O(1)}
t₇: 1 {O(1)}
t₈: 68 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 70 {O(1)}
t₇: 1 {O(1)}
t₈: 68 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₁: 30 {O(1)}
t₇, X₄: 2 {O(1)}
t₈, X₁: 30 {O(1)}
t₈, X₄: 31 {O(1)}
t₉, X₁: 30 {O(1)}
t₉, X₄: 31 {O(1)}