Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₇: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: X₁ < 0
t₈: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: 0 < X₁
t₉: l1(X₀, X₁, X₂) → l4(X₀+2, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₆: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₂: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 255
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁: l5(X₀, X₁, X₂) → l4(X₂, X₁, X₂)
t₁₀: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
Preprocessing
Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 for location l2
Found invariant X₂ ≤ X₀ ∧ 255 ≤ X₀ for location l6
Found invariant X₂ ≤ X₀ ∧ 255 ≤ X₀ for location l7
Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 for location l1
Found invariant X₂ ≤ X₀ for location l4
Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₇: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: X₁ < 0 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254
t₈: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: 0 < X₁ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254
t₉: l1(X₀, X₁, X₂) → l4(X₀+2, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254
t₆: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂) :|: X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254
t₂: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 255 ∧ X₂ ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀
t₁: l5(X₀, X₁, X₂) → l4(X₂, X₁, X₂)
t₁₀: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 255 ≤ X₀
MPRF for transition t₂: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 255 ∧ X₂ ≤ X₀ of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₆: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂) :|: X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₇: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: X₁ < 0 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₈: l1(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: 0 < X₁ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₉: l1(X₀, X₁, X₂) → l4(X₀+2, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 of depth 1:
new bound:
X₂+255 {O(n)}
All Bounds
Timebounds
Overall timebound:6⋅X₂+1534 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+255 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+255 {O(n)}
t₆: X₂+255 {O(n)}
t₇: X₂+255 {O(n)}
t₈: X₂+255 {O(n)}
t₉: X₂+255 {O(n)}
t₁₀: 1 {O(1)}
Costbounds
Overall costbound: 6⋅X₂+1534 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+255 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+255 {O(n)}
t₆: X₂+255 {O(n)}
t₇: X₂+255 {O(n)}
t₈: X₂+255 {O(n)}
t₉: X₂+255 {O(n)}
t₁₀: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 5⋅X₂+1020 {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 16⋅X₂+3060 {O(n)}
t₃, X₂: 4⋅X₂ {O(n)}
t₄, X₀: 5⋅X₂+1020 {O(n)}
t₄, X₂: X₂ {O(n)}
t₆, X₀: 5⋅X₂+1020 {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: 5⋅X₂+1020 {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: 5⋅X₂+1020 {O(n)}
t₈, X₂: X₂ {O(n)}
t₉, X₀: 5⋅X₂+1020 {O(n)}
t₉, X₁: 0 {O(1)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₀: 16⋅X₂+3060 {O(n)}
t₁₀, X₂: 4⋅X₂ {O(n)}