Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(2⋅X₀+X₁, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(2⋅X₀+X₁, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___1
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l1___1 [X₂-X₁ ]
new bound:
X₁+X₂+1 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, n_l1___1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁₆: l1(X₀, X₁, X₂) → n_l1___1(2⋅X₀+X₁, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
t₁₅: n_l1___1(X₀, X₁, X₂) → n_l1___1(2⋅X₀+X₁, X₁+1, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₁+2⋅X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀
Overall timebound:X₁+X₂+3 {O(n)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: X₁+X₂+1 {O(n)}
Overall costbound: X₁+X₂+3 {O(n)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: X₁+X₂+1 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁₆, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₁₆, X₁: X₁+1 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₅, X₀: 11⋅2^(X₁+X₂+1)⋅X₁+2⋅2^(X₁+X₂+1)⋅X₀+2^(X₁+X₂+1)⋅3⋅X₁⋅X₁+2^(X₁+X₂+1)⋅4⋅X₁⋅X₂+2^(X₁+X₂+1)⋅5⋅X₂+2^(X₁+X₂+1)⋅6+2^(X₁+X₂+1)⋅X₂⋅X₂ {O(EXP)}
t₁₅, X₁: 2⋅X₁+X₂+2 {O(n)}
t₁₅, X₂: X₂ {O(n)}