Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂, X₁, X₂, X₃, X₄) :|: 0 < X₃
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, nondef.0, X₄)
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: 0 < X₀
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁-1, X₃, X₄) :|: 1 < X₁
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₄, X₁, X₂, X₃, X₄)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
Preprocessing
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l2
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 0 for location l7
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 0 for location l8
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1
Found invariant X₀ ≤ X₄ for location l4
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂, X₁, X₂, X₃, X₄) :|: 0 < X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, nondef.0, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₀ ≤ X₄
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₄
t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁-1, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₄, X₁, X₂, X₃, X₄)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₀ ≤ 0
MPRF for transition t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₀ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁-1, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF for transition t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, nondef.0, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF for transition t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂, X₁, X₂, X₃, X₄) :|: 0 < X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
All Bounds
Timebounds
Overall timebound:7⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₈: X₄ {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: X₄+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₈: X₄ {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: X₄+1 {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: X₄ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: 2⋅X₄ {O(n)}
t₂, X₂: 4⋅X₄+X₂ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₄ {O(n)}
t₃, X₁: X₁+1 {O(n)}
t₃, X₂: 2⋅X₂+8⋅X₄ {O(n)}
t₃, X₄: 3⋅X₄ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 2⋅X₄ {O(n)}
t₄, X₂: 4⋅X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: 1 {O(1)}
t₅, X₂: 8⋅X₄+X₂ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: 2⋅X₄ {O(n)}
t₆, X₂: 4⋅X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₁: 2⋅X₄ {O(n)}
t₈, X₂: 4⋅X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: X₄ {O(n)}
t₉, X₁: 2⋅X₄ {O(n)}
t₉, X₂: 4⋅X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: X₄ {O(n)}
t₁₀, X₁: 2⋅X₄ {O(n)}
t₁₀, X₂: 4⋅X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₀: X₄ {O(n)}
t₁₁, X₁: X₁+1 {O(n)}
t₁₁, X₂: 2⋅X₂+8⋅X₄ {O(n)}
t₁₁, X₄: 3⋅X₄ {O(n)}