Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, 1, 1, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+2, X₂+X₁+2, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂
Eliminate variables {X₀} that do not contribute to the problem
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l2
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Start: l0
Program_Vars: X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₁, X₂, X₃) → l1(1, 1, X₃)
t₈: l1(X₁, X₂, X₃) → l1(X₁+2, X₂+X₁+2, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉: l1(X₁, X₂, X₃) → l2(X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
new bound:
X₃+2 {O(n)}
MPRF:
l1 [X₃+1-X₂ ]
Overall timebound:X₃+4 {O(n)}
t₇: 1 {O(1)}
t₈: X₃+2 {O(n)}
t₉: 1 {O(1)}
Overall costbound: X₃+4 {O(n)}
t₇: 1 {O(1)}
t₈: X₃+2 {O(n)}
t₉: 1 {O(1)}
t₇, X₁: 1 {O(1)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}
t₈, X₁: 2⋅X₃+5 {O(n)}
t₈, X₂: 2^(X₃+2)⋅3+2^(X₃+2)⋅X₃ {O(EXP)}
t₈, X₃: X₃ {O(n)}
t₉, X₁: 2⋅X₃+6 {O(n)}
t₉, X₂: 2^(X₃+2)⋅3+2^(X₃+2)⋅X₃+1 {O(EXP)}
t₉, X₃: 2⋅X₃ {O(n)}