Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
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, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1
t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆)
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁
t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅
t₁₈: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₁₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₆
t₂₀: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ 0 ≤ X₆
t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 1
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅

Preprocessing

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l11

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

Found invariant X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l7

Found invariant X₄ ≤ 1 ∧ X₄ ≤ X₃ for location l13

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l8

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l10

Found invariant X₄ ≤ X₃ for location l4

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l9

Found invariant X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
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, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1
t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₈: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0 ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₁₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₂₀: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ 0 ≤ X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄ ∧ X₄ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 1 ∧ X₄ ≤ X₃
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0 ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄ ∧ X₄ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0 ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+2 {O(n)} for transition t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+2 {O(n)} for transition t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+2 {O(n)} for transition t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

MPRF for transition t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}

MPRF for transition t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}

Chain transitions t₈: l12→l10 and t₁₀: l10→l11 to t₂₆₂: l12→l11

Chain transitions t₂₆₂: l12→l11 and t₁₁: l11→l9 to t₂₆₃: l12→l9

Chain transitions t₅: l4→l12 and t₂₆₃: l12→l9 to t₂₆₄: l4→l9

Chain transitions t₉: l14→l12 and t₂₆₃: l12→l9 to t₂₆₅: l14→l9

Chain transitions t₉: l14→l12 and t₇: l12→l14 to t₂₆₆: l14→l14

Chain transitions t₅: l4→l12 and t₇: l12→l14 to t₂₆₇: l4→l14

Chain transitions t₉: l14→l12 and t₂₆₂: l12→l11 to t₂₆₈: l14→l11

Chain transitions t₅: l4→l12 and t₂₆₂: l12→l11 to t₂₆₉: l4→l11

Chain transitions t₉: l14→l12 and t₈: l12→l10 to t₂₇₀: l14→l10

Chain transitions t₅: l4→l12 and t₈: l12→l10 to t₂₇₁: l4→l10

Chain transitions t₁₇: l6→l4 and t₂₆₄: l4→l9 to t₂₇₂: l6→l9

Chain transitions t₄: l1→l4 and t₂₆₄: l4→l9 to t₂₇₃: l1→l9

Chain transitions t₄: l1→l4 and t₂₆₇: l4→l14 to t₂₇₄: l1→l14

Chain transitions t₁₇: l6→l4 and t₂₆₇: l4→l14 to t₂₇₅: l6→l14

Chain transitions t₄: l1→l4 and t₆: l4→l13 to t₂₇₆: l1→l13

Chain transitions t₁₇: l6→l4 and t₆: l4→l13 to t₂₇₇: l6→l13

Chain transitions t₄: l1→l4 and t₅: l4→l12 to t₂₇₈: l1→l12

Chain transitions t₁₇: l6→l4 and t₅: l4→l12 to t₂₇₉: l6→l12

Chain transitions t₄: l1→l4 and t₂₆₉: l4→l11 to t₂₈₀: l1→l11

Chain transitions t₁₇: l6→l4 and t₂₆₉: l4→l11 to t₂₈₁: l6→l11

Chain transitions t₄: l1→l4 and t₂₇₁: l4→l10 to t₂₈₂: l1→l10

Chain transitions t₁₇: l6→l4 and t₂₇₁: l4→l10 to t₂₈₃: l6→l10

Chain transitions t₁₆: l8→l6 and t₂₇₂: l6→l9 to t₂₈₄: l8→l9

Chain transitions t₁₆: l8→l6 and t₁₇: l6→l4 to t₂₈₅: l8→l4

Chain transitions t₁₆: l8→l6 and t₂₇₅: l6→l14 to t₂₈₆: l8→l14

Chain transitions t₁₆: l8→l6 and t₂₇₇: l6→l13 to t₂₈₇: l8→l13

Chain transitions t₁₆: l8→l6 and t₂₇₉: l6→l12 to t₂₈₈: l8→l12

Chain transitions t₁₆: l8→l6 and t₂₈₁: l6→l11 to t₂₈₉: l8→l11

Chain transitions t₁₆: l8→l6 and t₂₈₃: l6→l10 to t₂₉₀: l8→l10

Chain transitions t₁₄: l9→l7 and t₁₅: l7→l8 to t₂₉₁: l9→l8

Chain transitions t₁₃: l9→l7 and t₁₅: l7→l8 to t₂₉₂: l9→l8

Chain transitions t₁₂: l9→l7 and t₁₅: l7→l8 to t₂₉₃: l9→l8

Chain transitions t₂₉₃: l9→l8 and t₂₈₄: l8→l9 to t₂₉₄: l9→l9

Chain transitions t₂₉₂: l9→l8 and t₂₈₄: l8→l9 to t₂₉₅: l9→l9

Chain transitions t₂₉₂: l9→l8 and t₁₆: l8→l6 to t₂₉₆: l9→l6

Chain transitions t₂₉₃: l9→l8 and t₁₆: l8→l6 to t₂₉₇: l9→l6

Chain transitions t₂₉₁: l9→l8 and t₁₆: l8→l6 to t₂₉₈: l9→l6

Chain transitions t₂₉₁: l9→l8 and t₂₈₄: l8→l9 to t₂₉₉: l9→l9

Chain transitions t₂₉₁: l9→l8 and t₂₈₅: l8→l4 to t₃₀₀: l9→l4

Chain transitions t₂₉₂: l9→l8 and t₂₈₅: l8→l4 to t₃₀₁: l9→l4

Chain transitions t₂₉₃: l9→l8 and t₂₈₅: l8→l4 to t₃₀₂: l9→l4

Chain transitions t₂₉₁: l9→l8 and t₂₈₆: l8→l14 to t₃₀₃: l9→l14

Chain transitions t₂₉₂: l9→l8 and t₂₈₆: l8→l14 to t₃₀₄: l9→l14

Chain transitions t₂₉₃: l9→l8 and t₂₈₆: l8→l14 to t₃₀₅: l9→l14

Chain transitions t₂₉₁: l9→l8 and t₂₈₇: l8→l13 to t₃₀₆: l9→l13

Chain transitions t₂₉₂: l9→l8 and t₂₈₇: l8→l13 to t₃₀₇: l9→l13

Chain transitions t₂₉₃: l9→l8 and t₂₈₇: l8→l13 to t₃₀₈: l9→l13

Chain transitions t₂₉₁: l9→l8 and t₂₈₈: l8→l12 to t₃₀₉: l9→l12

Chain transitions t₂₉₂: l9→l8 and t₂₈₈: l8→l12 to t₃₁₀: l9→l12

Chain transitions t₂₉₃: l9→l8 and t₂₈₈: l8→l12 to t₃₁₁: l9→l12

Chain transitions t₂₉₁: l9→l8 and t₂₈₉: l8→l11 to t₃₁₂: l9→l11

Chain transitions t₂₉₂: l9→l8 and t₂₈₉: l8→l11 to t₃₁₃: l9→l11

Chain transitions t₂₉₃: l9→l8 and t₂₈₉: l8→l11 to t₃₁₄: l9→l11

Chain transitions t₂₉₁: l9→l8 and t₂₉₀: l8→l10 to t₃₁₅: l9→l10

Chain transitions t₂₉₂: l9→l8 and t₂₉₀: l8→l10 to t₃₁₆: l9→l10

Chain transitions t₂₉₃: l9→l8 and t₂₉₀: l8→l10 to t₃₁₇: l9→l10

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃: l9→l7

Cut unsatisfiable transition t₂₇₃: l1→l9

Cut unsatisfiable transition t₂₇₆: l1→l13

Cut unsatisfiable transition t₂₈₀: l1→l11

Cut unsatisfiable transition t₂₈₂: l1→l10

Cut unsatisfiable transition t₂₉₂: l9→l8

Cut unsatisfiable transition t₂₉₄: l9→l9

Cut unsatisfiable transition t₂₉₅: l9→l9

Cut unsatisfiable transition t₂₉₆: l9→l6

Cut unsatisfiable transition t₂₉₉: l9→l9

Cut unsatisfiable transition t₃₀₁: l9→l4

Cut unsatisfiable transition t₃₀₄: l9→l14

Cut unsatisfiable transition t₃₀₆: l9→l13

Cut unsatisfiable transition t₃₀₇: l9→l13

Cut unsatisfiable transition t₃₁₀: l9→l12

Cut unsatisfiable transition t₃₁₂: l9→l11

Cut unsatisfiable transition t₃₁₃: l9→l11

Cut unsatisfiable transition t₃₁₄: l9→l11

Cut unsatisfiable transition t₃₁₅: l9→l10

Cut unsatisfiable transition t₃₁₆: l9→l10

Cut unsatisfiable transition t₃₁₇: l9→l10

Eliminate variables {X₀} that do not contribute to the problem

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l11

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l6

Found invariant X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l7

Found invariant 1+X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₃+X₄ ≤ 1 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ X₀+X₄ ≤ 1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 2 ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l13

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l8

Found invariant X₅ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l10

Found invariant X₅ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location l4

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l9

Found invariant X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l14

MPRF for transition t₄₈₆: l14(X₀, X₁, X₂, X₃, X₄, X₅) -{4}> l9(X₀, X₅-X₀, X₂, X₃, X₄-X₀, X₅) :|: X₄ < 2⋅X₀ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₄₉₃: l9(X₀, X₁, X₂, X₃, X₄, X₅) -{6}> l14(X₀-1, X₁, X₂, X₀, X₂, X₅) :|: 0 < X₄ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₂ ∧ X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₄₉₄: l9(X₀, X₁, X₂, X₃, X₄, X₅) -{6}> l14(X₀-1, X₁, X₂, X₀, X₂, X₁) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₂ ∧ X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₄₈₅: l14(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l14(X₀, X₁, X₂, X₃, X₄-X₀, X₅) :|: 2⋅X₀ ≤ X₄ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

12⋅X₂⋅X₂+20⋅X₂+3 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l12→l10

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l11

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

Found invariant X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l14___3

Found invariant 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l12___2

Found invariant X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l7

Found invariant X₄ ≤ 1 ∧ X₄ ≤ X₃ for location l13

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l8

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l10

Found invariant X₄ ≤ X₃ for location l4

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l9

Found invariant 1+X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l14___1

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₅₉₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___3(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆) :|: X₄ ≤ 1+X₅ ∧ X₁+1 ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₅₉₆: n_l14___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l12___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆) :|: X₁+1 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁

MPRF for transition t₅₉₃: n_l12___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___1(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆) :|: X₁+1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₄+X₅ ≤ 1+X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF for transition t₅₉₅: n_l14___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l12___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆) :|: X₄+X₅ ≤ 1+X₃ ∧ X₁+1 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₅ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 1+X₁ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

3⋅X₃⋅X₃+4⋅X₃ {O(n^2)}

MPRF for transition t₆₀₀: n_l12___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:12⋅X₃⋅X₃+28⋅X₃+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₈: X₃+1 {O(n)}
t₉: 6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₀: X₃+1 {O(n)}
t₁₁: X₃+1 {O(n)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃+1 {O(n)}
t₁₄: X₃ {O(n)}
t₁₅: 3⋅X₃+2 {O(n)}
t₁₆: 3⋅X₃+2 {O(n)}
t₁₇: 3⋅X₃+2 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₃⋅X₃+28⋅X₃+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₈: X₃+1 {O(n)}
t₉: 6⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₀: X₃+1 {O(n)}
t₁₁: X₃+1 {O(n)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃+1 {O(n)}
t₁₄: X₃ {O(n)}
t₁₅: 3⋅X₃+2 {O(n)}
t₁₆: 3⋅X₃+2 {O(n)}
t₁₇: 3⋅X₃+2 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 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)}
t₀, X₆: X₆ {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)}
t₁, X₆: X₆ {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)}
t₂, X₆: X₆ {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)}
t₃, X₆: X₆ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₃ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₃ {O(n)}
t₅, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₅, X₁: X₃ {O(n)}
t₅, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₃ {O(n)}
t₅, X₅: 2⋅X₃ {O(n)}
t₅, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₆, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₃ {O(n)}
t₆, X₅: 4⋅X₃ {O(n)}
t₆, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₇, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 2⋅X₃ {O(n)}
t₇, X₅: 2⋅X₃ {O(n)}
t₇, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₈, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 2⋅X₃ {O(n)}
t₈, X₅: 2⋅X₃ {O(n)}
t₈, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₉, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₉, X₁: X₃ {O(n)}
t₉, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 2⋅X₃ {O(n)}
t₉, X₅: 2⋅X₃ {O(n)}
t₉, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₀, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 2⋅X₃ {O(n)}
t₁₀, X₅: 2⋅X₃ {O(n)}
t₁₀, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₁, X₀: X₃⋅X₃+3⋅X₃+X₀ {O(n^2)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: 2⋅X₃ {O(n)}
t₁₁, X₅: 2⋅X₃ {O(n)}
t₁₁, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₂, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: 2⋅X₃ {O(n)}
t₁₂, X₅: 0 {O(1)}
t₁₂, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₃, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₃, X₁: X₃ {O(n)}
t₁₃, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: 2⋅X₃ {O(n)}
t₁₃, X₅: 2⋅X₃ {O(n)}
t₁₃, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₄, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: 2⋅X₃ {O(n)}
t₁₄, X₅: 2⋅X₃ {O(n)}
t₁₄, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₅, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₅, X₁: X₃ {O(n)}
t₁₅, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: 6⋅X₃ {O(n)}
t₁₅, X₅: 4⋅X₃ {O(n)}
t₁₅, X₆: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₆, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₆, X₁: X₃ {O(n)}
t₁₆, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: 6⋅X₃ {O(n)}
t₁₆, X₅: 4⋅X₃ {O(n)}
t₁₆, X₆: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₇, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₃ {O(n)}
t₁₇, X₅: 4⋅X₃ {O(n)}
t₁₇, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₈, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₈, X₁: X₃ {O(n)}
t₁₈, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₃ {O(n)}
t₁₈, X₅: 4⋅X₃ {O(n)}
t₁₈, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₉, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₉, X₁: X₃ {O(n)}
t₁₉, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₃ {O(n)}
t₁₉, X₅: 4⋅X₃ {O(n)}
t₁₉, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₂₀, X₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₂₀, X₁: X₃ {O(n)}
t₂₀, X₂: 3⋅X₃⋅X₃+9⋅X₃ {O(n^2)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₃ {O(n)}
t₂₀, X₅: 4⋅X₃ {O(n)}
t₂₀, X₆: 0 {O(1)}
t₂₁, X₀: 3⋅X₃⋅X₃+9⋅X₃+X₀ {O(n^2)}
t₂₁, X₁: 3⋅X₃+X₁ {O(n)}
t₂₁, X₂: 9⋅X₃⋅X₃+27⋅X₃+X₂ {O(n^2)}
t₂₁, X₃: 4⋅X₃ {O(n)}
t₂₁, X₄: 3⋅X₃+X₄ {O(n)}
t₂₁, X₅: 12⋅X₃+X₅ {O(n)}
t₂₁, X₆: 2⋅X₃⋅X₃+6⋅X₃+X₆ {O(n^2)}