KoAT2 Proof Output

Initial Problem

Start: start
Program_Vars: X₀
Temp_Vars: B
Locations: eval, start
Transitions:
t₀: eval(X₀) → eval(B) :|: B+2⋅X₀ ≤ 10 ∧ 10 ≤ B+2⋅X₀ ∧ 0 ≤ X₀
t₁: start(X₀) → eval(X₀)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀) → eval(10-2⋅X₀) :|: 0 ≤ X₀
t₁: start(X₀) → eval(X₀)

TWN: t₀: eval→eval

cycle: [t₀: eval→eval]
original loop: (0 ≤ X₀,(X₀) -> (10-2⋅X₀))
transformed loop: (0 ≤ X₀,(X₀) -> (10-2⋅X₀))
loop: (0 ≤ X₀,(X₀) -> (10-2⋅X₀))
order: [X₀]
closed-form:

X₀: X₀⋅(4)^n + [[n != 0]]⋅-10/3⋅(4)^n + [[n != 0]]⋅10/3

Termination: true
Formula:

3⋅X₀ ≤ 10 ∧ X₀ ≤ 3 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ 3⋅X₀
∨ 3⋅X₀ ≤ 10 ∧ X₀ ≤ 3 ∧ 0 ≤ 1 ∧ 10 ≤ 3⋅X₀
∨ 3⋅X₀ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ 3⋅X₀
∨ 3⋅X₀ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ 3⋅X₀ ∧ 11 ≤ 3⋅X₀
∨ 3⋅X₀ ≤ 10 ∧ 0 ≤ 1 ∧ 10 ≤ 3⋅X₀
∨ 3⋅X₀ ≤ 10 ∧ 0 ≤ 1 ∧ 10 ≤ 3⋅X₀ ∧ 11 ≤ 3⋅X₀
∨ X₀ ≤ 3 ∧ 11 ≤ 3⋅X₀

Stabilization-Threshold for: X₀ ≤ 5

alphas_abs: 8
M': 1
N: 1
Bound: 5 {O(1)}

Stabilization-Threshold for: 0 ≤ X₀

alphas_abs: 13
M': 1
N: 1
Bound: 6 {O(1)}

TWN - Lifting for [0: eval->eval] of 27 {O(1)}

relevant size-bounds w.r.t. t₁: start→eval:
Runtime-bound of t₁: 1 {O(1)}
Results in: 27 {O(1)}

All Bounds

Timebounds

Overall timebound:28 {O(1)}
t₀: 27 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 28 {O(1)}
t₀: 27 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: 134217728⋅X₀+18119393280 {O(n)}
t₁, X₀: X₀ {O(n)}