Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀) → l1(X₀)
t₀: l1(X₀) → l1(X₀) :|: (X₀)²+1 ≤ 0

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀) → l1(X₀)
t₀: l1(X₀) → l1(X₀) :|: (X₀)²+1 ≤ 0

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 3 {O(1)}

TWN-Loops:

entry: t₁: l0(X₀) → l1(X₀)
results in twn-loop: twn: (X₀) -> (X₀) :|: (X₀)²+1 ≤ 0
order: [X₀]
closed-form:
X₀: X₀

Termination: true
Formula:

(X₀)²+1 < 0
∨ (X₀)²+1 ≤ 0 ∧ 0 ≤ (X₀)²+1

relevant size-bounds w.r.t. t₁:
Runtime-bound of t₁: 1 {O(1)}
Results in: 3 {O(1)}

3 {O(1)}

All Bounds

Timebounds

Overall timebound:4 {O(1)}
t₁: 1 {O(1)}
t₀: 3 {O(1)}

Costbounds

Overall costbound: 4 {O(1)}
t₁: 1 {O(1)}
t₀: 3 {O(1)}

Sizebounds

t₁, X₀: X₀ {O(n)}
t₀, X₀: X₀ {O(n)}