Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₁ ∧ 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0
t₁₇: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄-X₁, X₅, X₆, X₇, X₈)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₆, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ < 0
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₁, X₃, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ < X₁
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ X₃
t₁₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₁, X₄, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₄
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < 0
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, -X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ < 0
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₁
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₂
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₂, X₅, X₆, X₇, X₈) :|: X₂ ≤ 0
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Cut unsatisfiable transition t₅: l3→l8

Cut unsatisfiable transition t₆: l3→l7

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

Found invariant X₁ ≤ X₆ for location l11

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8

Found invariant X₁ ≤ X₆ for location l1

Found invariant 1 ≤ 0 for location l10

Found invariant X₁ ≤ X₆ for location l4

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l9

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₄₂: l10→l6

Cut unsatisfiable transition t₄₈: l6→l1

Cut unsatisfiable transition t₄₉: l6→l10

Cut unsatisfiable transition t₅₀: l7→l8

Cut unsatisfiable transition t₅₃: l8→l6

Cut unreachable locations [l10; l6] from the program graph

Eliminate variables {X₄} that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l11, l2, l3, l4, l5, l7, l8, l9
Transitions:
t₇₈: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₇₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₀
t₈₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0
t₈₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₈₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₈₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁
t₈₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅)
t₈₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₃, X₂, X₃, X₄, X₅) :|: X₃ < X₁
t₈₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃
t₈₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 ≤ X₁
t₈₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₂, X₄, X₅) :|: 0 < X₂
t₈₉: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅)

MPRF for transition t₇₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₈₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₈₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 ≤ X₁ of depth 1:

new bound:

X₅+1 {O(n)}

knowledge_propagation leads to new time bound X₅+1 {O(n)} for transition t₈₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₂, X₄, X₅) :|: 0 < X₂

MPRF for transition t₈₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₃, X₂, X₃, X₄, X₅) :|: X₃ < X₁ of depth 1:

new bound:

X₅+1 {O(n)}

Chain transitions t₈₅: l5→l1 and t₈₁: l1→l4 to t₁₂₇: l5→l4

Chain transitions t₈₂: l2→l1 and t₈₁: l1→l4 to t₁₂₈: l2→l4

Chain transitions t₈₂: l2→l1 and t₈₀: l1→l4 to t₁₂₉: l2→l4

Chain transitions t₈₅: l5→l1 and t₈₀: l1→l4 to t₁₃₀: l5→l4

Chain transitions t₈₂: l2→l1 and t₇₉: l1→l3 to t₁₃₁: l2→l3

Chain transitions t₈₅: l5→l1 and t₇₉: l1→l3 to t₁₃₂: l5→l3

Chain transitions t₁₃₂: l5→l3 and t₈₃: l3→l7 to t₁₃₃: l5→l7

Chain transitions t₁₃₁: l2→l3 and t₈₃: l3→l7 to t₁₃₄: l2→l7

Chain transitions t₈₉: l9→l5 and t₈₆: l5→l9 to t₁₃₅: l9→l9

Chain transitions t₈₈: l8→l5 and t₈₆: l5→l9 to t₁₃₆: l8→l9

Chain transitions t₈₈: l8→l5 and t₁₃₃: l5→l7 to t₁₃₇: l8→l7

Chain transitions t₈₉: l9→l5 and t₁₃₃: l5→l7 to t₁₃₈: l9→l7

Chain transitions t₈₈: l8→l5 and t₁₃₀: l5→l4 to t₁₃₉: l8→l4

Chain transitions t₈₉: l9→l5 and t₁₃₀: l5→l4 to t₁₄₀: l9→l4

Chain transitions t₈₈: l8→l5 and t₁₂₇: l5→l4 to t₁₄₁: l8→l4

Chain transitions t₈₉: l9→l5 and t₁₂₇: l5→l4 to t₁₄₂: l9→l4

Chain transitions t₈₈: l8→l5 and t₁₃₂: l5→l3 to t₁₄₃: l8→l3

Chain transitions t₈₉: l9→l5 and t₁₃₂: l5→l3 to t₁₄₄: l9→l3

Chain transitions t₈₈: l8→l5 and t₈₅: l5→l1 to t₁₄₅: l8→l1

Chain transitions t₈₉: l9→l5 and t₈₅: l5→l1 to t₁₄₆: l9→l1

Chain transitions t₁₃₈: l9→l7 and t₈₇: l7→l8 to t₁₄₇: l9→l8

Chain transitions t₁₃₇: l8→l7 and t₈₇: l7→l8 to t₁₄₈: l8→l8

Chain transitions t₁₃₄: l2→l7 and t₈₇: l7→l8 to t₁₄₉: l2→l8

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃₉: l8→l4

Cut unsatisfiable transition t₁₄₁: l8→l4

Cut unsatisfiable transition t₁₄₂: l9→l4

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

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

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ for location l5

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ for location l8

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ for location l9

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location l3

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₉₉: l8(X₀, X₁, X₂, X₃, X₄) -{5}> l8(X₁, X₀, X₁, X₃, X₄) :|: 0 < X₁ ∧ X₁ < X₀ ∧ 0 < X₁ ∧ 0 < X₀ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁

MPRF for transition t₂₀₀: l8(X₀, X₁, X₂, X₃, X₄) -{2}> l9(X₀, X₁, X₁, X₃, X₄) :|: 0 < X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₃+X₄+1 {O(n)}

MPRF for transition t₂₀₆: l9(X₀, X₁, X₂, X₃, X₄) -{5}> l8(X₂-X₀, X₀, X₂-X₀, X₃, X₄) :|: X₂ < 2⋅X₀ ∧ X₀ < X₂ ∧ 0 < X₀ ∧ X₀ < X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₁ ≤ X₅ for location l11

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l9___1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8

Found invariant X₁ ≤ X₅ for location l1

Found invariant X₁ ≤ X₅ for location l4

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₂₉₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₅+X₄+3 {O(n)}

MPRF for transition t₂₉₁: n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+X₅ {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l11, l2, l3, l4, l5, l7, l8, n_l9___1
Transitions:
t₇₈: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₇₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₅
t₈₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₁ ≤ X₅
t₈₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₁ ≤ X₅
t₈₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₈₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₅
t₈₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₃, X₂, X₃, X₄, X₅) :|: X₃ < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₂, X₄, X₅) :|: 0 < X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉₁: n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₄+9⋅X₅+6 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l11, l2, l3, l4, l5, l7, l8, n_l9___1
Transitions:
t₇₈: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₇₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₅
t₈₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₁ ≤ X₅
t₈₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₁ ≤ X₅
t₈₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₈₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₅
t₈₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₃, X₂, X₃, X₄, X₅) :|: X₃ < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₂, X₄, X₅) :|: 0 < X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉₁: n_l9___1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅) :|: X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:2⋅X₄+9⋅X₅+11 {O(n)}
t₇₈: 1 {O(1)}
t₇₉: X₅ {O(n)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: X₅ {O(n)}
t₈₄: 1 {O(1)}
t₈₅: X₅+1 {O(n)}
t₈₇: X₅+1 {O(n)}
t₈₈: X₅+1 {O(n)}
t₂₉₀: 3⋅X₅+X₄+3 {O(n)}
t₂₉₁: X₄+X₅ {O(n)}

Costbounds

Overall costbound: 2⋅X₄+9⋅X₅+11 {O(n)}
t₇₈: 1 {O(1)}
t₇₉: X₅ {O(n)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: X₅ {O(n)}
t₈₄: 1 {O(1)}
t₈₅: X₅+1 {O(n)}
t₈₇: X₅+1 {O(n)}
t₈₈: X₅+1 {O(n)}
t₂₉₀: 3⋅X₅+X₄+3 {O(n)}
t₂₉₁: X₄+X₅ {O(n)}

Sizebounds

t₇₈, X₀: X₀ {O(n)}
t₇₈, X₁: X₁ {O(n)}
t₇₈, X₂: X₂ {O(n)}
t₇₈, X₃: X₃ {O(n)}
t₇₈, X₄: X₄ {O(n)}
t₇₈, X₅: X₅ {O(n)}
t₇₉, X₀: X₄+X₅ {O(n)}
t₇₉, X₁: X₄+X₅ {O(n)}
t₇₉, X₂: 2⋅X₄+2⋅X₅+X₂ {O(n)}
t₇₉, X₃: 2⋅X₄+2⋅X₅+X₃ {O(n)}
t₇₉, X₄: X₄ {O(n)}
t₇₉, X₅: X₅ {O(n)}
t₈₀, X₀: 2⋅X₄+X₅ {O(n)}
t₈₀, X₁: 2⋅X₅+X₄ {O(n)}
t₈₀, X₂: 2⋅X₄+2⋅X₅+X₂ {O(n)}
t₈₀, X₃: 2⋅X₄+2⋅X₅+X₃ {O(n)}
t₈₀, X₄: 2⋅X₄ {O(n)}
t₈₀, X₅: 2⋅X₅ {O(n)}
t₈₁, X₀: X₄ {O(n)}
t₈₁, X₁: X₅ {O(n)}
t₈₁, X₂: X₂ {O(n)}
t₈₁, X₃: X₃ {O(n)}
t₈₁, X₄: X₄ {O(n)}
t₈₁, X₅: X₅ {O(n)}
t₈₂, X₀: X₄ {O(n)}
t₈₂, X₁: X₅ {O(n)}
t₈₂, X₂: X₂ {O(n)}
t₈₂, X₃: X₃ {O(n)}
t₈₂, X₄: X₄ {O(n)}
t₈₂, X₅: X₅ {O(n)}
t₈₃, X₀: X₄+X₅ {O(n)}
t₈₃, X₁: X₄+X₅ {O(n)}
t₈₃, X₂: 2⋅X₄+2⋅X₅+X₂ {O(n)}
t₈₃, X₃: 2⋅X₄+2⋅X₅+X₃ {O(n)}
t₈₃, X₄: X₄ {O(n)}
t₈₃, X₅: X₅ {O(n)}
t₈₄, X₀: 3⋅X₄+X₅ {O(n)}
t₈₄, X₁: 3⋅X₅+X₄ {O(n)}
t₈₄, X₂: 2⋅X₂+2⋅X₄+2⋅X₅ {O(n)}
t₈₄, X₃: 2⋅X₃+2⋅X₄+2⋅X₅ {O(n)}
t₈₄, X₄: 3⋅X₄ {O(n)}
t₈₄, X₅: 3⋅X₅ {O(n)}
t₈₅, X₀: X₄+X₅ {O(n)}
t₈₅, X₁: X₄+X₅ {O(n)}
t₈₅, X₂: 2⋅X₄+2⋅X₅ {O(n)}
t₈₅, X₃: 2⋅X₄+2⋅X₅ {O(n)}
t₈₅, X₄: X₄ {O(n)}
t₈₅, X₅: X₅ {O(n)}
t₈₇, X₀: X₄+X₅ {O(n)}
t₈₇, X₁: X₄+X₅ {O(n)}
t₈₇, X₂: X₄+X₅ {O(n)}
t₈₇, X₃: 2⋅X₄+2⋅X₅+X₃ {O(n)}
t₈₇, X₄: X₄ {O(n)}
t₈₇, X₅: X₅ {O(n)}
t₈₈, X₀: X₄+X₅ {O(n)}
t₈₈, X₁: X₄+X₅ {O(n)}
t₈₈, X₂: X₄+X₅ {O(n)}
t₈₈, X₃: X₄+X₅ {O(n)}
t₈₈, X₄: X₄ {O(n)}
t₈₈, X₅: X₅ {O(n)}
t₂₉₀, X₀: X₄+X₅ {O(n)}
t₂₉₀, X₁: X₄+X₅ {O(n)}
t₂₉₀, X₂: X₄+X₅ {O(n)}
t₂₉₀, X₃: X₄+X₅ {O(n)}
t₂₉₀, X₄: X₄ {O(n)}
t₂₉₀, X₅: X₅ {O(n)}
t₂₉₁, X₀: X₄+X₅ {O(n)}
t₂₉₁, X₁: X₄+X₅ {O(n)}
t₂₉₁, X₂: X₄+X₅ {O(n)}
t₂₉₁, X₃: X₄+X₅ {O(n)}
t₂₉₁, X₄: X₄ {O(n)}
t₂₉₁, X₅: X₅ {O(n)}