Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I, J, K
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, J, J)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, J, I, K, X₅, X₆, X₇) :|: 1 ≤ I ∧ 1+X₁ ≤ X₀
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, J, I, K, X₅, X₆, X₇) :|: I+1 ≤ 0 ∧ 1+X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, J, 0, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, J, X₃, X₄, I, X₆, X₇) :|: X₀ ≤ X₁

Preprocessing

Eliminate variables {J,K,X₂,X₃,X₄,X₅,X₆,X₇} that do not contribute to the problem

Found invariant X₀ ≤ X₁ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: I
Locations: l0, l1, l2
Transitions:
t₁₄: l0(X₀, X₁) → l1(X₀, X₁)
t₁₅: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ I ∧ 1+X₁ ≤ X₀
t₁₆: l1(X₀, X₁) → l1(X₀, X₁) :|: I+1 ≤ 0 ∧ 1+X₁ ≤ X₀
t₁₇: l1(X₀, X₁) → l1(X₀, X₁) :|: 1+X₁ ≤ X₀
t₁₈: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁

Analysing control-flow refined program

Found invariant X₀ ≤ X₁ for location l2

Found invariant 1+X₁ ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: 3⋅X₀ {O(n)}
t₁₅, X₁: 3⋅X₁ {O(n)}
t₁₆, X₀: 3⋅X₀ {O(n)}
t₁₆, X₁: 3⋅X₁ {O(n)}
t₁₇, X₀: 3⋅X₀ {O(n)}
t₁₇, X₁: 3⋅X₁ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}