Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, X₃)
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
Preprocessing
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ for location l11
Found invariant 1+X₃ ≤ 0 for location l6
Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location l12
Found invariant 1+X₃ ≤ 0 for location l7
Found invariant 0 ≤ X₃ ∧ X₁ ≤ X₂ for location l5
Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ for location l13
Found invariant 1+X₃ ≤ 0 for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l10
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1) :|: X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₅: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
MPRF for transition t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₁-X₃-1, X₁, X₂, X₃, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l13 [X₁-1 ]
l12 [X₁-1 ]
l5 [X₁ ]
l10 [X₁ ]
MPRF for transition t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF:
l13 [X₀+X₃+X₄ ]
l12 [X₀+X₃+X₄+1 ]
l5 [X₁+X₃ ]
l10 [X₁+X₃ ]
MPRF for transition t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l13 [X₁ ]
l12 [X₁ ]
l5 [X₁ ]
l10 [X₁ ]
MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1) :|: X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF:
l13 [X₀+X₃+X₄ ]
l12 [X₀+X₃+X₄ ]
l5 [X₁+X₃ ]
l10 [X₁+X₃ ]
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF:
l13 [X₀ ]
l12 [X₀ ]
l5 [X₁-X₃ ]
l10 [X₁-X₃-1 ]
All Bounds
Timebounds
Overall timebound:3⋅X₃+5⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₉: X₂+X₃ {O(n)}
t₁₀: X₂ {O(n)}
t₁₁: X₂+X₃ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+X₃ {O(n)}
t₇: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₄: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₃+5⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₉: X₂+X₃ {O(n)}
t₁₀: X₂ {O(n)}
t₁₁: X₂+X₃ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+X₃ {O(n)}
t₇: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₄: 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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₃ {O(n)}
t₁₂, X₀: 2⋅X₂+X₀ {O(n)}
t₁₂, X₁: 2⋅X₂ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₉, X₀: X₂ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₃ {O(n)}
t₁₀, X₀: 2⋅X₂ {O(n)}
t₁₀, X₁: X₂ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 0 {O(1)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₂+X₀ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: 2⋅X₂+X₀ {O(n)}
t₇, X₁: 2⋅X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}