Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂
Temp_Vars: A1, B1, X, Y, Z
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, 0)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀+1, X₁, 1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, X₁₇, 1, 1, 1, 0, X₂₂) :|: Y ≤ 0 ∧ X₀+1 ≤ X₁
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁ ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 3 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 1
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, 2, X₃+1, X₄, X₅, X₇, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 2 ∧ 2 ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, 0, X, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, 0, X, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ X
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)
t₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)

Preprocessing

Cut unreachable locations [l5; l6] from the program graph

Eliminate variables {A1,Z,X₃,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂} that do not contribute to the problem

Found invariant 1+X₀ ≤ X₁ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: B1, X, Y
Locations: l0, l1, l2, l3, l4
Transitions:
t₂₈: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₂₉: l1(X₀, X₁, X₂) → l1(X₀+1, X₁, 1) :|: Y ≤ 0 ∧ X₀+1 ≤ X₁
t₃₀: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1
t₃₁: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0
t₃₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₃₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁
t₃₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 3 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 1 ∧ 1+X₀ ≤ X₁
t₃₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, 2) :|: X₂ ≤ 2 ∧ 2 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₇: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X ≤ 0
t₃₈: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X
t₃₉: l4(X₀, X₁, X₂) → l4(X₀, X₁, X₂)

MPRF for transition t₂₉: l1(X₀, X₁, X₂) → l1(X₀+1, X₁, 1) :|: Y ≤ 0 ∧ X₀+1 ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

Analysing control-flow refined program

Found invariant 1+X₀ ≤ X₁ 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}
t₂₈: 1 {O(1)}
t₂₉: X₀+X₁ {O(n)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₂₈: 1 {O(1)}
t₂₉: X₀+X₁ {O(n)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: inf {Infinity}

Sizebounds

t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₉, X₀: 2⋅X₀+X₁ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: 1 {O(1)}
t₃₀, X₀: 3⋅X₀+X₁ {O(n)}
t₃₀, X₁: 2⋅X₁ {O(n)}
t₃₁, X₀: 3⋅X₀+X₁ {O(n)}
t₃₁, X₁: 2⋅X₁ {O(n)}
t₃₂, X₀: 3⋅X₀+X₁ {O(n)}
t₃₂, X₁: 2⋅X₁ {O(n)}
t₃₂, X₂: X₂+1 {O(n)}
t₃₃, X₀: 3⋅X₀+X₁ {O(n)}
t₃₃, X₁: 2⋅X₁ {O(n)}
t₃₃, X₂: X₂+1 {O(n)}
t₃₄, X₀: 3⋅X₀+X₁ {O(n)}
t₃₄, X₁: 2⋅X₁ {O(n)}
t₃₅, X₀: 3⋅X₀+X₁ {O(n)}
t₃₅, X₁: 2⋅X₁ {O(n)}
t₃₆, X₀: 3⋅X₀+X₁ {O(n)}
t₃₆, X₁: 2⋅X₁ {O(n)}
t₃₆, X₂: 2 {O(1)}
t₃₇, X₀: 15⋅X₀+5⋅X₁ {O(n)}
t₃₇, X₁: 10⋅X₁ {O(n)}
t₃₈, X₀: 15⋅X₀+5⋅X₁ {O(n)}
t₃₈, X₁: 10⋅X₁ {O(n)}
t₃₉, X₀: 10⋅X₁+30⋅X₀ {O(n)}
t₃₉, X₁: 20⋅X₁ {O(n)}