Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, 0, X₂, X₃, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂-1, F, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ F
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂-2, F, X₄) :|: 1 ≤ X₂ ∧ F ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, F) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l2(1, X₁, X₂, X₃, F) :|: 1 ≤ X₄
t₅: l2(X₀, X₁, X₂, X₃, X₄) → l2(0, X₁, X₂, X₃, F) :|: X₄ ≤ 0

Preprocessing

Eliminate variables {X₀,X₁,X₃} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
t₁₄: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ F
t₁₅: l1(X₀, X₁) → l1(X₀-2, X₁) :|: 1 ≤ X₀ ∧ F ≤ 0
t₁₆: l1(X₀, X₁) → l2(X₀, F) :|: X₀ ≤ 0
t₁₇: l2(X₀, X₁) → l2(X₀, F) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₈: l2(X₀, X₁) → l2(X₀, F) :|: X₁ ≤ 0 ∧ X₀ ≤ 0

MPRF for transition t₁₄: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ F of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₅: l1(X₀, X₁) → l1(X₀-2, X₁) :|: 1 ≤ X₀ ∧ F ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 3⋅X₀ {O(n)}
t₁₇, X₀: 3⋅X₀ {O(n)}
t₁₈, X₀: 3⋅X₀ {O(n)}