Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)²
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l1
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)² ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
new bound:
X₂ {O(n)}
MPRF:
l1 [X₂ ]
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₂:
X₁: 2⋅X₁ {O(n)}
X₂: 2⋅X₂ {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 32⋅X₁⋅X₁+8⋅X₂⋅X₂+14 {O(n^2)}
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2
Found invariant X₂ ≤ 0 for location n_l2___1
Found invariant 1 ≤ X₀ for location l1
new bound:
X₂ {O(n)}
MPRF:
l1 [X₂ ]
Overall timebound:32⋅X₁⋅X₁+8⋅X₂⋅X₂+X₂+16 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 32⋅X₁⋅X₁+8⋅X₂⋅X₂+14 {O(n^2)}
Overall costbound: 32⋅X₁⋅X₁+8⋅X₂⋅X₂+X₂+16 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 32⋅X₁⋅X₁+8⋅X₂⋅X₂+14 {O(n^2)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₂⋅X₂+2⋅X₂+X₀ {O(n^2)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₂⋅X₂+2⋅X₀+2⋅X₂ {O(n^2)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₃, X₁: 2⋅2^(32⋅X₁⋅X₁+8⋅X₂⋅X₂+14)⋅X₁ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}