Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₀-1, X₂, X₀)
t₁₅: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 < X₀
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁₂: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 0
t₁₃: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₃
t₁₄: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0
t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂
t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃)

Preprocessing

Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location l6

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

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l8

Found invariant 2 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₀-1, X₂, X₀) :|: 2 ≤ X₀
t₁₅: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 < X₀
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₁₃: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₁₄: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

3⋅X₀⋅X₀+X₀ {O(n^2)}

MPRF for transition t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

9⋅X₀⋅X₀+2⋅X₀ {O(n^2)}

Chain transitions t₁₁: l7→l4 and t₅: l4→l6 to t₁₀₄: l7→l6

Chain transitions t₁₀: l7→l4 and t₅: l4→l6 to t₁₀₅: l7→l6

Chain transitions t₁₀: l7→l4 and t₄: l4→l5 to t₁₀₆: l7→l5

Chain transitions t₁₁: l7→l4 and t₄: l4→l5 to t₁₀₇: l7→l5

Chain transitions t₉: l7→l4 and t₄: l4→l5 to t₁₀₈: l7→l5

Chain transitions t₉: l7→l4 and t₅: l4→l6 to t₁₀₉: l7→l6

Chain transitions t₃: l1→l4 and t₄: l4→l5 to t₁₁₀: l1→l5

Chain transitions t₃: l1→l4 and t₅: l4→l6 to t₁₁₁: l1→l6

Chain transitions t₈: l8→l5 and t₆: l5→l8 to t₁₁₂: l8→l8

Chain transitions t₁₀₈: l7→l5 and t₆: l5→l8 to t₁₁₃: l7→l8

Chain transitions t₁₀₈: l7→l5 and t₇: l5→l7 to t₁₁₄: l7→l7

Chain transitions t₈: l8→l5 and t₇: l5→l7 to t₁₁₅: l8→l7

Chain transitions t₁₀₇: l7→l5 and t₇: l5→l7 to t₁₁₆: l7→l7

Chain transitions t₁₀₇: l7→l5 and t₆: l5→l8 to t₁₁₇: l7→l8

Chain transitions t₁₀₆: l7→l5 and t₇: l5→l7 to t₁₁₈: l7→l7

Chain transitions t₁₀₆: l7→l5 and t₆: l5→l8 to t₁₁₉: l7→l8

Chain transitions t₁₁₀: l1→l5 and t₇: l5→l7 to t₁₂₀: l1→l7

Chain transitions t₁₁₀: l1→l5 and t₆: l5→l8 to t₁₂₁: l1→l8

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀: l7→l4

Cut unsatisfiable transition t₁₀₄: l7→l6

Cut unsatisfiable transition t₁₀₅: l7→l6

Cut unsatisfiable transition t₁₀₆: l7→l5

Cut unsatisfiable transition t₁₁₁: l1→l6

Cut unsatisfiable transition t₁₁₄: l7→l7

Cut unsatisfiable transition t₁₁₆: l7→l7

Cut unsatisfiable transition t₁₁₈: l7→l7

Cut unsatisfiable transition t₁₁₉: l7→l8

Cut unsatisfiable transition t₁₂₀: l1→l7

Found invariant 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

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

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l8

Found invariant 2 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4

MPRF for transition t₁₁₃: l7(X₀, X₁, X₂, X₃) -{3}> l8(X₀, X₁-1, X₀, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ X₁ ≤ 1+X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀+X₁ ∧ 0 ≤ 0 ∧ 2 ≤ X₁+X₀ ∧ 2 ≤ 2⋅X₀ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF for transition t₁₁₅: l8(X₀, X₁, X₂, X₃) -{2}> l7(X₀, X₁, X₂-X₁, X₃) :|: X₂ < 2⋅X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀+X₁ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₁₇: l7(X₀, X₁, X₂, X₃) -{3}> l8(X₀, X₁-1, X₀, X₃) :|: 0 < X₂ ∧ 1 < X₁ ∧ X₁ ≤ 1+X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ 0 ∧ 2 ≤ X₁+X₀ ∧ 2 ≤ 2⋅X₀ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₁₂: l8(X₀, X₁, X₂, X₃) -{2}> l8(X₀, X₁, X₂-X₁, X₃) :|: 2⋅X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀+X₁ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀⋅X₀+X₀ {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 t₇: l5→l7

Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___1

Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l6

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___3

Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___2

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

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant 2 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l4

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₂₅₆: l5(X₀, X₁, X₂, X₃) → n_l8___3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₂₅₈: n_l8___3(X₀, X₁, X₂, X₃) → n_l5___2(X₀, X₁, X₂-X₁, X₃) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₂₅₅: n_l5___2(X₀, X₁, X₂, X₃) → n_l8___1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ X₁+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+2⋅X₀ {O(n^2)}

MPRF for transition t₂₅₇: n_l8___1(X₀, X₁, X₂, X₃) → n_l5___2(X₀, X₁, X₂-X₁, X₃) :|: X₁+X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

6⋅X₀⋅X₀+X₀ {O(n^2)}

MPRF for transition t₂₆₂: n_l5___2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:12⋅X₀⋅X₀+8⋅X₀+9 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₇: X₀ {O(n)}
t₈: 9⋅X₀⋅X₀+2⋅X₀ {O(n^2)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₀⋅X₀+8⋅X₀+9 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₇: X₀ {O(n)}
t₈: 9⋅X₀⋅X₀+2⋅X₀ {O(n^2)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 2⋅X₀ {O(n)}
t₄, X₂: 4⋅X₀ {O(n)}
t₄, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 4⋅X₀ {O(n)}
t₅, X₂: 4⋅X₀ {O(n)}
t₅, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 2⋅X₀ {O(n)}
t₆, X₂: 4⋅X₀ {O(n)}
t₆, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2⋅X₀ {O(n)}
t₇, X₂: 4⋅X₀ {O(n)}
t₇, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 2⋅X₀ {O(n)}
t₈, X₂: 4⋅X₀ {O(n)}
t₈, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 2⋅X₀ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 2⋅X₀ {O(n)}
t₁₀, X₂: 4⋅X₀ {O(n)}
t₁₀, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: 2⋅X₀ {O(n)}
t₁₁, X₂: 4⋅X₀ {O(n)}
t₁₁, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 4⋅X₀ {O(n)}
t₁₂, X₂: 4⋅X₀ {O(n)}
t₁₂, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₁₃, X₀: 2⋅X₀ {O(n)}
t₁₃, X₁: 4⋅X₀ {O(n)}
t₁₃, X₂: 4⋅X₀ {O(n)}
t₁₃, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₁₄, X₀: 2⋅X₀ {O(n)}
t₁₄, X₁: 4⋅X₀ {O(n)}
t₁₄, X₂: 4⋅X₀ {O(n)}
t₁₄, X₃: 0 {O(1)}
t₁₅, X₀: 7⋅X₀ {O(n)}
t₁₅, X₁: 12⋅X₀+X₁ {O(n)}
t₁₅, X₂: 12⋅X₀+X₂ {O(n)}
t₁₅, X₃: 8⋅X₀⋅X₀+12⋅X₀+X₃ {O(n^2)}