Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₅
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₃
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ X₂
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ < X₄
t₁₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀+1, X₂, X₂, X₃, X₄, X₅, X₆, X₇)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆, X₇)
t₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₆, X₇, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
Preprocessing
Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location l2
Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location l6
Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ for location l7
Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location l5
Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ for location l1
Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ ∧ X₅ ≤ X₀ for location l10
Found invariant X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ for location l4
Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ ∧ X₅ ≤ X₀ for location l9
Found invariant X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₅ ∧ X₇ ≤ X₁ ∧ X₆ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₆ ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0 ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₃ ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ < X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂
t₁₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀+1, X₂, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂
t₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₆, X₇, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₁ ∧ X₆ ≤ X₀ ∧ X₅ ≤ X₀
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₅ ∧ X₇ ≤ X₁ ∧ X₆ ≤ X₀ of depth 1:
new bound:
X₅+X₆ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ < X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₄+X₅+X₆+X₇+1 {O(n)}
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₅+X₆ {O(n)}
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₄+X₅+X₆+X₇+1 {O(n)}
MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₅+2⋅X₆+X₄+X₇ {O(n)}
MPRF for transition t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₃ ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₄+X₅+X₆+X₇ {O(n)}
MPRF for transition t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0 ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₅+X₆+1 {O(n)}
MPRF for transition t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₄+X₇ {O(n)}
MPRF for transition t₁₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀+1, X₂, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₅+X₆ {O(n)}
All Bounds
Timebounds
Overall timebound:5⋅X₄+5⋅X₇+9⋅X₅+9⋅X₆+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅+X₆+X₇+1 {O(n)}
t₅: X₅+X₆ {O(n)}
t₆: X₄+X₅+X₆+X₇+1 {O(n)}
t₈: 2⋅X₅+2⋅X₆+X₄+X₇ {O(n)}
t₉: X₄+X₅+X₆+X₇ {O(n)}
t₁₀: X₅+X₆+1 {O(n)}
t₁₁: X₄+X₇ {O(n)}
t₁₂: X₅+X₆ {O(n)}
t₁₃: 1 {O(1)}
Costbounds
Overall costbound: 5⋅X₄+5⋅X₇+9⋅X₅+9⋅X₆+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅+X₆+X₇+1 {O(n)}
t₅: X₅+X₆ {O(n)}
t₆: X₄+X₅+X₆+X₇+1 {O(n)}
t₈: 2⋅X₅+2⋅X₆+X₄+X₇ {O(n)}
t₉: X₄+X₅+X₆+X₇ {O(n)}
t₁₀: X₅+X₆+1 {O(n)}
t₁₁: X₄+X₇ {O(n)}
t₁₂: X₅+X₆ {O(n)}
t₁₃: 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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₁, X₀: X₆ {O(n)}
t₁, X₁: X₇ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₂, X₀: 2⋅X₆+X₅ {O(n)}
t₂, X₁: 3⋅X₇+X₄ {O(n)}
t₂, X₂: 2⋅X₇+X₄ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: 3⋅X₆+X₅ {O(n)}
t₃, X₁: 3⋅X₇+X₄ {O(n)}
t₃, X₂: 2⋅X₄+4⋅X₇+X₂ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₄, X₀: 2⋅X₆+X₅ {O(n)}
t₄, X₁: 3⋅X₇+X₄ {O(n)}
t₄, X₂: 2⋅X₇+X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₅, X₀: 2⋅X₆+X₅ {O(n)}
t₅, X₁: 2⋅X₄+6⋅X₇ {O(n)}
t₅, X₂: 2⋅X₇+X₄ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₆, X₀: 2⋅X₆+X₅ {O(n)}
t₆, X₁: 3⋅X₇+X₄ {O(n)}
t₆, X₂: 2⋅X₇+X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₈, X₀: 2⋅X₆+X₅ {O(n)}
t₈, X₁: 3⋅X₇+X₄ {O(n)}
t₈, X₂: 2⋅X₇+X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₉, X₀: 2⋅X₆+X₅ {O(n)}
t₉, X₁: 3⋅X₇+X₄ {O(n)}
t₉, X₂: 2⋅X₇+X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₇ {O(n)}
t₁₀, X₀: 2⋅X₆+X₅ {O(n)}
t₁₀, X₁: 3⋅X₇+X₄ {O(n)}
t₁₀, X₂: 2⋅X₇+X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₁, X₀: 2⋅X₆+X₅ {O(n)}
t₁₁, X₁: 3⋅X₇+X₄ {O(n)}
t₁₁, X₂: 2⋅X₇+X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₂, X₀: 2⋅X₆+X₅ {O(n)}
t₁₂, X₁: 2⋅X₇+X₄ {O(n)}
t₁₂, X₂: 2⋅X₄+4⋅X₇ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₃, X₀: 3⋅X₆+X₅ {O(n)}
t₁₃, X₁: 3⋅X₇+X₄ {O(n)}
t₁₃, X₂: 2⋅X₄+4⋅X₇+X₂ {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₃, X₆: 2⋅X₆ {O(n)}
t₁₃, X₇: 2⋅X₇ {O(n)}