Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, C) :|: X₀+1 ≤ 0

Preprocessing

Eliminate variables {C,X₁} that do not contribute to the problem

Found invariant 1+X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀) → l1(X₀)
t₈: l1(X₀) → l1(X₀-1) :|: 0 ≤ X₀
t₉: l1(X₀) → l2(X₀) :|: X₀+1 ≤ 0

Found invariant 1+X₀ ≤ 0 for location l2

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 2⋅X₀+4 {O(n)}

TWN-Loops:

entry: t₇: l0(X₀) → l1(X₀)
results in twn-loop: twn: (X₀) -> (X₀-1) :|: 0 ≤ X₀
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₇:
X₀: X₀ {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}

2⋅X₀+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+6 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₀+4 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+6 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₀+4 {O(n)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₈, X₀: X₀+1 {O(n)}
t₉, X₀: 2⋅X₀+1 {O(n)}