Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1
t₁₄: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0
t₁₂: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₁₃: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0
t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃-X₀, X₄)

Preprocessing

Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ for location l5

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ for location l1

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₁₄: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁
t₁₂: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁
t₁₃: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l6 [X₀-1 ]
l1 [X₂-1 ]
l7 [X₀-1 ]
l4 [X₀-1 ]

MPRF for transition t₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l6 [X₂-2 ]
l1 [X₂-1 ]
l7 [X₂-1 ]
l4 [X₂-1 ]

MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l6 [X₀ ]
l1 [X₂-1 ]
l7 [X₀ ]
l4 [X₀ ]

MPRF for transition t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l6 [X₂-2 ]
l1 [X₂-2 ]
l7 [X₂-2 ]
l4 [X₂-2 ]

Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l5

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l1

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l5

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l1

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₉: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₁⋅X₁+16⋅X₁+10 {O(n^2)}

MPRF:

l1 [X₁+2-X₂ ]
l6 [X₃-X₀ ]
l7 [X₃-X₀ ]
l4 [X₃+1-X₀ ]

MPRF for transition t₇: l7(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₁⋅X₁+10⋅X₁ {O(n^2)}

MPRF:

l1 [X₁+X₂ ]
l6 [X₀+X₃-1 ]
l7 [X₃ ]
l4 [X₀+X₃-1 ]

Analysing control-flow refined program

Cut unsatisfiable transition t₆: l4→l6

Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l7___3

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l5

Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₁ for location l1

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l7___1

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₅₂: l4(X₀, X₁, X₂, X₃, X₄) → n_l7___3(X₀, X₁, X₀+1, X₃, X₄) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₅₄: n_l7___3(X₀, X₁, X₂, X₃, X₄) → n_l4___2(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₅₁: n_l4___2(X₀, X₁, X₂, X₃, X₄) → n_l7___1(X₀, X₁, X₀+1, X₃, X₄) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₀+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

5⋅X₁⋅X₁+8⋅X₁+1 {O(n^2)}

MPRF:

l4 [X₁-X₂ ]
n_l7___3 [X₃-X₀-1 ]
l1 [X₁-X₂ ]
l6 [X₁+1-X₂ ]
n_l7___1 [X₁+X₃-2 ]
n_l4___2 [X₁+X₃-1 ]

MPRF for transition t₁₅₈: n_l4___2(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l4 [X₀ ]
l1 [X₂-1 ]
l6 [X₂-2 ]
n_l7___1 [X₀ ]
n_l7___3 [X₀ ]
n_l4___2 [X₀ ]

MPRF for transition t₁₅₃: n_l7___1(X₀, X₁, X₂, X₃, X₄) → n_l4___2(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₀+X₃ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

5⋅X₁⋅X₁+6⋅X₁+1 {O(n^2)}

MPRF:

l4 [0 ]
n_l7___3 [0 ]
l1 [0 ]
l6 [0 ]
n_l7___1 [X₃ ]
n_l4___2 [X₀+X₃-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:12⋅X₁⋅X₁+31⋅X₁+24 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 6⋅X₁⋅X₁+16⋅X₁+10 {O(n^2)}
t₆: X₁+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₈: X₁+1 {O(n)}
t₉: X₁+1 {O(n)}
t₁₀: X₁+2 {O(n)}
t₇: 6⋅X₁⋅X₁+10⋅X₁ {O(n^2)}

Costbounds

Overall costbound: 12⋅X₁⋅X₁+31⋅X₁+24 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 6⋅X₁⋅X₁+16⋅X₁+10 {O(n^2)}
t₆: X₁+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₈: X₁+1 {O(n)}
t₉: X₁+1 {O(n)}
t₁₀: X₁+2 {O(n)}
t₇: 6⋅X₁⋅X₁+10⋅X₁ {O(n^2)}

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: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 4⋅X₁ {O(n)}
t₃, X₃: 4⋅X₁ {O(n)}
t₃, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄, X₀: 2⋅X₁ {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₁ {O(n)}
t₄, X₃: 4⋅X₁ {O(n)}
t₄, X₄: 2⋅X₁⋅X₁+6⋅X₁ {O(n^2)}
t₁₄, X₀: 6⋅X₁+X₀ {O(n)}
t₁₄, X₁: 7⋅X₁ {O(n)}
t₁₄, X₂: 6⋅X₁+X₂ {O(n)}
t₁₄, X₃: 12⋅X₁+X₃ {O(n)}
t₁₄, X₄: 4⋅X₁⋅X₁+12⋅X₁+X₄ {O(n^2)}
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: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₁ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 4⋅X₁ {O(n)}
t₅, X₃: 4⋅X₁ {O(n)}
t₅, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 4⋅X₁ {O(n)}
t₆, X₃: 4⋅X₁ {O(n)}
t₆, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₁, X₀: 2⋅X₁ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₁ {O(n)}
t₁₁, X₃: 4⋅X₁ {O(n)}
t₁₁, X₄: 2⋅X₁⋅X₁+6⋅X₁ {O(n^2)}
t₁₂, X₀: 2⋅X₁ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₂, X₂: 2⋅X₁ {O(n)}
t₁₂, X₃: 4⋅X₁ {O(n)}
t₁₂, X₄: 2⋅X₁⋅X₁+6⋅X₁ {O(n^2)}
t₁₃, X₀: 2⋅X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: 2⋅X₁ {O(n)}
t₁₃, X₃: 4⋅X₁ {O(n)}
t₁₃, X₄: 0 {O(1)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: 4⋅X₁ {O(n)}
t₉, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 4⋅X₁ {O(n)}
t₁₀, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 4⋅X₁ {O(n)}
t₇, X₃: 4⋅X₁ {O(n)}
t₇, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}