Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀)
t₁: l1(X₀) → l1(2⋅X₀+10) :|: 1 ≤ X₀ ∧ X₀ ≤ 99

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀)
t₁: l1(X₀) → l1(2⋅X₀+10) :|: 1 ≤ X₀ ∧ X₀ ≤ 99

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 246 {O(1)}

TWN-Loops:

entry: t₀: l0(X₀) → l1(X₀)
results in twn-loop: twn: (X₀) -> (2⋅X₀+10) :|: 1 ≤ X₀ ∧ X₀ ≤ 99
order: [X₀]
closed-form:
X₀: X₀ * 2^n + [[n != 0]] * 10 * 2^n + [[n != 0]] * -10

Termination: true
Formula:

X₀+10 < 0 ∧ 0 < X₀+10
∨ X₀+10 < 0 ∧ 11 < 0 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0
∨ X₀+10 < 0 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0 ∧ 11 ≤ 0 ∧ 0 ≤ 11
∨ 0 < 109 ∧ X₀+10 ≤ 0 ∧ 0 ≤ X₀+10 ∧ 0 < X₀+10
∨ 0 < 109 ∧ 11 < 0 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0
∨ 0 < 109 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0 ∧ 11 ≤ 0 ∧ 0 ≤ 11
∨ X₀+10 ≤ 0 ∧ 0 ≤ X₀+10 ∧ 0 ≤ 109 ∧ 109 ≤ 0 ∧ 0 < X₀+10
∨ 0 ≤ 109 ∧ 109 ≤ 0 ∧ 11 < 0 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0
∨ 0 ≤ 109 ∧ 109 ≤ 0 ∧ 0 ≤ X₀+10 ∧ X₀+10 ≤ 0 ∧ 11 ≤ 0 ∧ 0 ≤ 11

Stabilization-Threshold for: X₀ ≤ 99
alphas_abs: 109
M: 0
N: 1
Bound: 220 {O(1)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 11
M: 0
N: 1
Bound: 24 {O(1)}

relevant size-bounds w.r.t. t₀:
Runtime-bound of t₀: 1 {O(1)}
Results in: 246 {O(1)}

246 {O(1)}

All Bounds

Timebounds

Overall timebound:247 {O(1)}
t₀: 1 {O(1)}
t₁: 246 {O(1)}

Costbounds

Overall costbound: 247 {O(1)}
t₀: 1 {O(1)}
t₁: 246 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: 208 {O(1)}