Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: l0, l1, l2
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: 1 ≤ D ∧ 2 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: D+1 ≤ 0 ∧ 2 ≤ X₀
t₄: l1(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀-1, D, E) :|: 1 ≤ D ∧ X₀ ≤ 1
t₃: l1(X₀, X₁, X₂) → l2(X₀-1, D, E) :|: D+1 ≤ 0 ∧ X₀ ≤ 1
t₅: l1(X₀, X₁, X₂) → l2(X₀, 0, D) :|: X₀ ≤ 0

Preprocessing

Eliminate variables {E,X₁,X₂} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁₇: l0(X₀) → l1(X₀)
t₁₈: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 2 ≤ X₀
t₁₉: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 2 ≤ X₀
t₂₀: l1(X₀) → l1(X₀) :|: 1 ≤ X₀
t₂₁: l1(X₀) → l2(X₀-1) :|: 1 ≤ D ∧ X₀ ≤ 1
t₂₂: l1(X₀) → l2(X₀-1) :|: D+1 ≤ 0 ∧ X₀ ≤ 1
t₂₃: l1(X₀) → l2(X₀) :|: X₀ ≤ 0

MPRF for transition t₁₈: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₉: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location n_l1___1

MPRF for transition t₉₂: n_l1___1(X₀) → n_l1___1(X₀-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀ {O(n)}

MPRF for transition t₉₃: n_l1___1(X₀) → n_l1___1(X₀-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₀ {O(n)}
t₁₉: X₀ {O(n)}
t₂₀: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₀ {O(n)}
t₁₉: X₀ {O(n)}
t₂₀: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₁, X₀: 4⋅X₀+4 {O(n)}
t₂₂, X₀: 4⋅X₀+4 {O(n)}
t₂₃, X₀: X₀ {O(n)}