Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(I, 0, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁+1 ≤ X₂
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₂, 0, X₅, X₆, X₇) :|: X₂ ≤ X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₄, X₄+1, X₇) :|: 2+X₄ ≤ X₃
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, 0, X₅, X₆, X₇) :|: X₃ ≤ X₄+1
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, I) :|: X₃ ≤ X₆
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1, X₇) :|: X₆+1 ≤ X₃
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₆, X₆+1, X₇) :|: X₆+1 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇) :|: 2+X₄ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ X₄+1

Preprocessing

Eliminate variables {I,X₀,X₅,X₇} that do not contribute to the problem

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l2

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ 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:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, X₁, X₂, X₃, X₄)
t₂₃: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₂₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁, 0, X₄) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₃+1) :|: 2+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₂₆: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ X₃+1 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₂₇: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃+1, X₄) :|: X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₈: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₉: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₀: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: 2+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀
t₃₁: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃+1 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₂₅: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₃+1) :|: 2+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃+1, X₄) :|: X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF for transition t₂₈: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}

MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}

Chain transitions t₂₇: l3→l2 and t₂₆: l2→l4 to t₇₈: l3→l4

Chain transitions t₂₄: l1→l2 and t₂₆: l2→l4 to t₇₉: l1→l4

Chain transitions t₂₄: l1→l2 and t₂₅: l2→l3 to t₈₀: l1→l3

Chain transitions t₂₇: l3→l2 and t₂₅: l2→l3 to t₈₁: l3→l3

Analysing control-flow refined program

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l2

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3

knowledge_propagation leads to new time bound 32⋅X₁⋅X₁+32⋅X₁ {O(n^2)} for transition t₈₁: l3(X₀, X₁, X₂, X₃, X₄) -{2}> l3(X₀, X₁, X₂, 1+X₃, 2+X₃) :|: X₂ ≤ X₄ ∧ 3+X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₀+X₃+1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₂₇: l3→l2

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l2

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₅₃: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₁, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₅₄: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₁, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₅₁: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₁, X₃, X₄+1) :|: 2+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

6⋅X₁⋅X₁+19⋅X₁+10 {O(n^2)}

MPRF for transition t₁₅₂: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₁, X₃, X₄+1) :|: 2+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

6⋅X₁⋅X₁+19⋅X₁+10 {O(n^2)}

MPRF for transition t₁₆₁: n_l3___1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃+1, X₄) :|: X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

MPRF for transition t₃₀: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: 2+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

All Bounds

Timebounds

Overall timebound:32⋅X₁⋅X₁+38⋅X₁+7 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₁+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₁+1 {O(n)}
t₂₈: 16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₂₉: 16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₃₀: 2⋅X₁+1 {O(n)}
t₃₁: 1 {O(1)}

Costbounds

Overall costbound: 32⋅X₁⋅X₁+38⋅X₁+7 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₁+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₁+1 {O(n)}
t₂₈: 16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₂₉: 16⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₃₀: 2⋅X₁+1 {O(n)}
t₃₁: 1 {O(1)}

Sizebounds

t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₀: X₁ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: X₁ {O(n)}
t₂₄, X₁: 2⋅X₁ {O(n)}
t₂₄, X₂: 2⋅X₁ {O(n)}
t₂₄, X₃: 0 {O(1)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₅, X₀: X₁ {O(n)}
t₂₅, X₁: 2⋅X₁ {O(n)}
t₂₅, X₂: 2⋅X₁ {O(n)}
t₂₅, X₃: 2⋅X₁+1 {O(n)}
t₂₅, X₄: 2⋅X₁+3 {O(n)}
t₂₆, X₀: 2⋅X₁ {O(n)}
t₂₆, X₁: 4⋅X₁ {O(n)}
t₂₆, X₂: 4⋅X₁ {O(n)}
t₂₆, X₃: 0 {O(1)}
t₂₆, X₄: 64⋅X₁⋅X₁+2⋅X₄+68⋅X₁+6 {O(n^2)}
t₂₇, X₀: X₁ {O(n)}
t₂₇, X₁: 2⋅X₁ {O(n)}
t₂₇, X₂: 2⋅X₁ {O(n)}
t₂₇, X₃: 2⋅X₁+1 {O(n)}
t₂₇, X₄: 64⋅X₁⋅X₁+68⋅X₁+6 {O(n^2)}
t₂₈, X₀: X₁ {O(n)}
t₂₈, X₁: 2⋅X₁ {O(n)}
t₂₈, X₂: 2⋅X₁ {O(n)}
t₂₈, X₃: 2⋅X₁+1 {O(n)}
t₂₈, X₄: 32⋅X₁⋅X₁+34⋅X₁+3 {O(n^2)}
t₂₉, X₀: X₁ {O(n)}
t₂₉, X₁: 2⋅X₁ {O(n)}
t₂₉, X₂: 2⋅X₁ {O(n)}
t₂₉, X₃: 2⋅X₁+1 {O(n)}
t₂₉, X₄: 32⋅X₁⋅X₁+34⋅X₁+3 {O(n^2)}
t₃₀, X₀: 2⋅X₁ {O(n)}
t₃₀, X₁: 4⋅X₁ {O(n)}
t₃₀, X₂: 4⋅X₁ {O(n)}
t₃₀, X₃: 2⋅X₁+1 {O(n)}
t₃₀, X₄: 64⋅X₁⋅X₁+2⋅X₄+68⋅X₁+6 {O(n^2)}
t₃₁, X₀: 4⋅X₁ {O(n)}
t₃₁, X₁: 8⋅X₁ {O(n)}
t₃₁, X₂: 8⋅X₁ {O(n)}
t₃₁, X₃: 2⋅X₁+1 {O(n)}
t₃₁, X₄: 128⋅X₁⋅X₁+136⋅X₁+4⋅X₄+12 {O(n^2)}