Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)²
Found invariant 1 ≤ X₀ for location l1
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)² ∧ 1 ≤ X₀
Found invariant 1 ≤ X₀ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₀:
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₂⋅X₂+8⋅X₁⋅X₁+14 {O(n^2)}
Eliminate variables {X₁,X₂} that do not contribute to the problem
Overall timebound:2⋅X₂⋅X₂+8⋅X₁⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 2⋅X₂⋅X₂+8⋅X₁⋅X₁+14 {O(n^2)}
Overall costbound: 2⋅X₂⋅X₂+8⋅X₁⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 2⋅X₂⋅X₂+8⋅X₁⋅X₁+14 {O(n^2)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₁: 2^(2⋅X₂⋅X₂+8⋅X₁⋅X₁+14)⋅X₁ {O(EXP)}
t₁, X₂: X₂ {O(n)}