Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0
t₁₃: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃-1, X₄, X₅)
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < 0
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂
t₁₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂+1, X₃, X₄, X₅)
t₁₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₄, X₅, X₂, X₃, X₄, X₅)
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀+999, X₁+1000, X₂, X₃, X₄, X₅)
Preprocessing
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l11
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l15
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l12
Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l13
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l8
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location l10
Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁
t₁₃: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂+1, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₄, X₅, X₂, X₃, X₄, X₅)
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀+999, X₁+1000, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀
MPRF for transition t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀ of depth 1:
new bound:
X₄+X₅ {O(n)}
MPRF for transition t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀+999, X₁+1000, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₄+X₅ {O(n)}
MPRF for transition t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
1000⋅X₄+1002⋅X₅ {O(n)}
MPRF for transition t₁₃: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
1000⋅X₄+1002⋅X₅ {O(n)}
MPRF for transition t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:
new bound:
1998⋅X₅+2002⋅X₄ {O(n)}
MPRF for transition t₁₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂+1, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
1998⋅X₅+2002⋅X₄ {O(n)}
All Bounds
Timebounds
Overall timebound:6002⋅X₅+6006⋅X₄+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: X₄+X₅ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₄+X₅ {O(n)}
t₁₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₄: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₇: 1 {O(1)}
Costbounds
Overall costbound: 6002⋅X₅+6006⋅X₄+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: X₄+X₅ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₄+X₅ {O(n)}
t₁₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₄: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₇: 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)}
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)}
t₁, X₅: X₅ {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)}
t₂, X₅: X₅ {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)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {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)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₁: X₅ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 1000⋅X₄+999⋅X₅ {O(n)}
t₈, X₁: 1000⋅X₄+1001⋅X₅ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₉, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₉, X₅: 2⋅X₅ {O(n)}
t₁₀, X₀: 1000⋅X₄+999⋅X₅ {O(n)}
t₁₀, X₁: 1000⋅X₄+1001⋅X₅ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₁, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₁₁, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 2⋅X₅ {O(n)}
t₁₂, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₂, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₂, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₂, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₂, X₄: 4⋅X₄ {O(n)}
t₁₂, X₅: 4⋅X₅ {O(n)}
t₁₃, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₁₃, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₄, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₄, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₄, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₄, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₄, X₄: 4⋅X₄ {O(n)}
t₁₄, X₅: 4⋅X₅ {O(n)}
t₁₅, X₀: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₅, X₁: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₅, X₂: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₅, X₃: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₅, X₄: 8⋅X₄ {O(n)}
t₁₅, X₅: 8⋅X₅ {O(n)}
t₁₆, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₆, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₆, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₆, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₆, X₄: 4⋅X₄ {O(n)}
t₁₆, X₅: 4⋅X₅ {O(n)}
t₁₇, X₀: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₇, X₁: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₇, X₂: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₇, X₃: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₇, X₄: 8⋅X₄ {O(n)}
t₁₇, X₅: 8⋅X₅ {O(n)}