Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: L, M, N, O
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, M, N, N, M)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, M, N, L, O, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ L ∧ 1+X₀ ≤ X₁
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, M, N, L, O, X₆, X₇, X₈, X₉, X₁₀) :|: L+1 ≤ 0 ∧ 1+X₀ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, M, N, 0, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, M, N, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀

Preprocessing

Eliminate variables {M,N,O,X₂,X₃,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀} that do not contribute to the problem

Found invariant X₁ ≤ X₀ for location l2

Problem after Preprocessing

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

Analysing control-flow refined program

Found invariant X₁ ≤ X₀ for location l2

Found invariant 1+X₀ ≤ X₁ for location n_l1___1

Found invariant X₁ ≤ X₀ for location l2

Found invariant 1+X₀ ≤ X₁ 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)}