KoAT2 Proof Output

Initial Problem

Start: start
Program_Vars: X₀
Temp_Vars:
Locations: f, start
Transitions:
t₀: f(X₀) → f(X₀) :|: 1+(X₀)² ≤ 0
t₁: start(X₀) → f(X₀)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀
Temp_Vars:
Locations: f, start
Transitions:
t₀: f(X₀) → f(X₀) :|: 1+(X₀)² ≤ 0
t₁: start(X₀) → f(X₀)

TWN: t₀: f→f

cycle: [t₀: f→f]
original loop: (1+(X₀)² ≤ 0,(X₀) -> (X₀))
transformed loop: (1+(X₀)² ≤ 0,(X₀) -> (X₀))
loop: (1+(X₀)² ≤ 0,(X₀) -> (X₀))
order: [X₀]
closed-form:

X₀: X₀

Termination: true
Formula:

1+(X₀)² ≤ 0

TWN - Lifting for [0: f->f] of 2 {O(1)}

relevant size-bounds w.r.t. t₁: start→f:
Runtime-bound of t₁: 1 {O(1)}
Results in: 2 {O(1)}

All Bounds

Timebounds

Overall timebound:3 {O(1)}
t₀: 2 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 3 {O(1)}
t₀: 2 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}