Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄+1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: F+1 ≤ 0
t₇: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ F
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1)
t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₄, X₄)
t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₃) :|: X₁+1 ≤ X₀
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₁, X₀, X₃, X₂, X₄)
Preprocessing
Found invariant 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l2
Found invariant X₀ ≤ X₁ for location l6
Found invariant X₀ ≤ X₁ for location l8
Found invariant X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location l1
Found invariant X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location l4
Found invariant 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄+1 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: F+1 ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ F ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₄, X₄) :|: X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₃) :|: X₁+1 ≤ X₀
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₁, X₀, X₃, X₂, X₄)
MPRF for transition t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₃) :|: X₁+1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄+1 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+X₂+X₃+1 {O(n)}
MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: F+1 ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ F ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
MPRF for transition t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₄, X₄) :|: X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁ {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₂+4⋅X₃+5⋅X₀+5⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁ {O(n)}
t₅: X₀+X₁+X₂+X₃+1 {O(n)}
t₆: X₂+X₃ {O(n)}
t₇: X₂+X₃ {O(n)}
t₈: X₀+X₁ {O(n)}
t₉: X₂+X₃ {O(n)}
t₁₀: X₀+X₁ {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₂+4⋅X₃+5⋅X₀+5⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁ {O(n)}
t₅: X₀+X₁+X₂+X₃+1 {O(n)}
t₆: X₂+X₃ {O(n)}
t₇: X₂+X₃ {O(n)}
t₈: X₀+X₁ {O(n)}
t₉: X₂+X₃ {O(n)}
t₁₀: X₀+X₁ {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₂ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₀+X₁ {O(n)}
t₂, X₂: X₃ {O(n)}
t₂, X₃: 3⋅X₂+X₃ {O(n)}
t₂, X₄: 2⋅X₂+X₃ {O(n)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 3⋅X₀+X₁ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: 3⋅X₂+X₃ {O(n)}
t₃, X₄: 2⋅X₃+4⋅X₂+X₄ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: 2⋅X₀+X₁ {O(n)}
t₄, X₂: X₃ {O(n)}
t₄, X₃: 2⋅X₃+6⋅X₂ {O(n)}
t₄, X₄: 2⋅X₂+X₃ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: 2⋅X₀+X₁ {O(n)}
t₅, X₂: X₃ {O(n)}
t₅, X₃: 3⋅X₂+X₃ {O(n)}
t₅, X₄: 2⋅X₂+X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: 2⋅X₀+X₁ {O(n)}
t₆, X₂: X₃ {O(n)}
t₆, X₃: 3⋅X₂+X₃ {O(n)}
t₆, X₄: 2⋅X₂+X₃ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: 2⋅X₀+X₁ {O(n)}
t₇, X₂: X₃ {O(n)}
t₇, X₃: 3⋅X₂+X₃ {O(n)}
t₇, X₄: 2⋅X₂+X₃ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: 2⋅X₀+X₁ {O(n)}
t₈, X₂: X₃ {O(n)}
t₈, X₃: 3⋅X₂+X₃ {O(n)}
t₈, X₄: 2⋅X₂+X₃ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: 2⋅X₀+X₁ {O(n)}
t₉, X₂: X₃ {O(n)}
t₉, X₃: 3⋅X₂+X₃ {O(n)}
t₉, X₄: 2⋅X₂+X₃ {O(n)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: 2⋅X₀+X₁ {O(n)}
t₁₀, X₂: X₃ {O(n)}
t₁₀, X₃: 2⋅X₂+X₃ {O(n)}
t₁₀, X₄: 2⋅X₃+4⋅X₂ {O(n)}
t₁₁, X₀: 2⋅X₁ {O(n)}
t₁₁, X₁: 3⋅X₀+X₁ {O(n)}
t₁₁, X₂: 2⋅X₃ {O(n)}
t₁₁, X₃: 3⋅X₂+X₃ {O(n)}
t₁₁, X₄: 2⋅X₃+4⋅X₂+X₄ {O(n)}