Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(1+X₀, 1+X₁, X₂) :|: X₀ ≤ 1
t₁: l1(X₀, X₁, X₂) → l1(1+X₀, 1+X₁, X₂) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: 3 ≤ X₁ ∧ 2 ≤ X₀
Eliminate variables {D,X₂} that do not contribute to the problem
Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l2
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀, X₁) → l1(X₀, X₁)
t₁₂: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₀ ≤ 1
t₁₃: l1(X₀, X₁) → l1(1+X₀, 1+X₁) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₁₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 3 ≤ X₁ ∧ 2 ≤ X₀
Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l2
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₁: 1 {O(1)}
Results in: 2⋅X₁+4⋅X₀+18 {O(n)}
relevant size-bounds w.r.t. t₁₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₁: 1 {O(1)}
Results in: 2⋅X₁+4⋅X₀+18 {O(n)}
Overall timebound:4⋅X₁+8⋅X₀+38 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁+4⋅X₀+18 {O(n)}
t₁₃: 2⋅X₁+4⋅X₀+18 {O(n)}
t₁₄: 1 {O(1)}
Overall costbound: 4⋅X₁+8⋅X₀+38 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁+4⋅X₀+18 {O(n)}
t₁₃: 2⋅X₁+4⋅X₀+18 {O(n)}
t₁₄: 1 {O(1)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 2⋅X₁+5⋅X₀+18 {O(n)}
t₁₂, X₁: 3⋅X₁+4⋅X₀+18 {O(n)}
t₁₃, X₀: 10⋅X₀+4⋅X₁+36 {O(n)}
t₁₃, X₁: 6⋅X₁+8⋅X₀+36 {O(n)}
t₁₄, X₀: 16⋅X₀+6⋅X₁+54 {O(n)}
t₁₄, X₁: 10⋅X₁+12⋅X₀+54 {O(n)}