Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100)
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃

Preprocessing

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ for location l11

Found invariant 1+X₃ ≤ 0 for location l6

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l12

Found invariant 1+X₃ ≤ 0 for location l7

Found invariant 1+X₃ ≤ 0 for location l5

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

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l10

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂
t₉: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂

MPRF for transition t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

TWN: t₉: l12→l13

cycle: [t₉: l12→l13; t₁₁: l13→l12]
loop: (0 < X₄,(X₄) -> (X₄-1)
order: [X₄]
closed-form:
X₄: X₄ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₄
alphas_abs: X₄
M: 0
N: 1
Bound: 2⋅X₄+2 {O(n)}

TWN - Lifting for t₉: l12→l13 of 2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₈:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₈: X₂ {O(n)}
Results in: 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}

TWN: t₁₁: l13→l12

TWN - Lifting for t₁₁: l13→l12 of 2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₈:
X₄: 2⋅X₃+100 {O(n)}
Runtime-bound of t₈: X₂ {O(n)}
Results in: 4⋅X₂⋅X₃+204⋅X₂ {O(n^2)}

Chain transitions t₆: l9→l10 and t₈: l10→l12 to t₈₈: l9→l12

Chain transitions t₈₈: l9→l12 and t₁₀: l12→l9 to t₈₉: l9→l9

Chain transitions t₁₁: l13→l12 and t₁₀: l12→l9 to t₉₀: l13→l9

Chain transitions t₁₁: l13→l12 and t₉: l12→l13 to t₉₁: l13→l13

Chain transitions t₈₈: l9→l12 and t₉: l12→l13 to t₉₂: l9→l13

Analysing control-flow refined program

Cut unsatisfiable transition t₈₉: l9→l9

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ for location l11

Found invariant 1+X₃ ≤ 0 for location l6

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l12

Found invariant 1+X₃ ≤ 0 for location l7

Found invariant 1+X₃ ≤ 0 for location l5

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

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l10

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l9

MPRF for transition t₉₀: l13(X₀, X₁, X₂, X₃, X₄) -{2}> l9(X₁, X₁, X₂, X₃, X₄-1) :|: X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₉₁: l13(X₀, X₁, X₂, X₃, X₄) -{2}> l13(X₀, X₁, X₂, X₃, X₄-1) :|: 1 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃+99⋅X₂+1 {O(n)}

MPRF for transition t₉₂: l9(X₀, X₁, X₂, X₃, X₄) -{3}> l13(X₀, X₀-1-X₃, X₂, X₃, 100+2⋅X₃) :|: X₃ < X₀ ∧ 0 < 100+2⋅X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2+X₃ ≤ X₀+X₂ ∧ X₀ ≤ X₃+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2+X₃ ≤ 2⋅X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀: l12→l9

Cut unsatisfiable transition t₁₇₆: n_l12___4→l9

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ for location l11

Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___3

Found invariant 1+X₃ ≤ 0 for location l6

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___1

Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___5

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l12___2

Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l12

Found invariant 1+X₃ ≤ 0 for location l7

Found invariant 1+X₃ ≤ 0 for location l5

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l10

Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l9

Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l12___4

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₆₈: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1 ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₇₁: n_l13___5(X₀, X₁, X₂, X₃, X₄) → n_l12___4(X₀, X₁, X₂, X₃, X₄-1) :|: 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₆₇: n_l12___4(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₇₀: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₆₆: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

98⋅X₂+98 {O(n)}

MPRF for transition t₁₆₉: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

99⋅X₂+99⋅X₃+98 {O(n)}

MPRF for transition t₁₇₅: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

CFR did not improve the program. Rolling back

CFR: Improvement to new bound with the following program:

new bound:

204⋅X₂+99⋅X₃+197 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9, n_l12___2, n_l12___4, n_l13___1, n_l13___3, n_l13___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₈: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₂: l11(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂
t₁₆₈: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1 ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l9(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₁₄: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ 0 ∧ 1+X₃ ≤ 0
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₁₇₅: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₆₆: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₆₇: n_l12___4(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₆₉: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 0 < X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₇₀: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₇₁: n_l13___5(X₀, X₁, X₂, X₃, X₄) → n_l12___4(X₀, X₁, X₂, X₃, X₄-1) :|: 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:204⋅X₂+99⋅X₃+208 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+1 {O(n)}
t₇: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆₆: 98⋅X₂+98 {O(n)}
t₁₆₇: X₂ {O(n)}
t₁₆₈: X₂ {O(n)}
t₁₆₉: 99⋅X₂+99⋅X₃+98 {O(n)}
t₁₇₀: X₂ {O(n)}
t₁₇₁: X₂ {O(n)}
t₁₇₅: X₂ {O(n)}

Costbounds

Overall costbound: 204⋅X₂+99⋅X₃+208 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+1 {O(n)}
t₇: 1 {O(1)}
t₈: X₂ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆₆: 98⋅X₂+98 {O(n)}
t₁₆₇: X₂ {O(n)}
t₁₆₈: X₂ {O(n)}
t₁₆₉: 99⋅X₂+99⋅X₃+98 {O(n)}
t₁₇₀: X₂ {O(n)}
t₁₇₁: X₂ {O(n)}
t₁₇₅: X₂ {O(n)}

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)}
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: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {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)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₁+X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: 2⋅X₂ {O(n)}
t₇, X₁: X₁+X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 2⋅X₃+100 {O(n)}
t₁₂, X₀: 2⋅X₂ {O(n)}
t₁₂, X₁: X₁+X₂ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆₆, X₀: X₂ {O(n)}
t₁₆₆, X₁: X₂ {O(n)}
t₁₆₆, X₂: X₂ {O(n)}
t₁₆₆, X₃: X₃ {O(n)}
t₁₆₆, X₄: 2⋅X₃+100 {O(n)}
t₁₆₇, X₀: X₂ {O(n)}
t₁₆₇, X₁: X₂ {O(n)}
t₁₆₇, X₂: X₂ {O(n)}
t₁₆₇, X₃: X₃ {O(n)}
t₁₆₇, X₄: 2⋅X₃+100 {O(n)}
t₁₆₈, X₀: X₂ {O(n)}
t₁₆₈, X₁: X₂ {O(n)}
t₁₆₈, X₂: X₂ {O(n)}
t₁₆₈, X₃: X₃ {O(n)}
t₁₆₈, X₄: 2⋅X₃+100 {O(n)}
t₁₆₉, X₀: X₂ {O(n)}
t₁₆₉, X₁: X₂ {O(n)}
t₁₆₉, X₂: X₂ {O(n)}
t₁₆₉, X₃: X₃ {O(n)}
t₁₆₉, X₄: 2⋅X₃+100 {O(n)}
t₁₇₀, X₀: X₂ {O(n)}
t₁₇₀, X₁: X₂ {O(n)}
t₁₇₀, X₂: X₂ {O(n)}
t₁₇₀, X₃: X₃ {O(n)}
t₁₇₀, X₄: 2⋅X₃+100 {O(n)}
t₁₇₁, X₀: X₂ {O(n)}
t₁₇₁, X₁: X₂ {O(n)}
t₁₇₁, X₂: X₂ {O(n)}
t₁₇₁, X₃: X₃ {O(n)}
t₁₇₁, X₄: 2⋅X₃+100 {O(n)}
t₁₇₅, X₀: X₂ {O(n)}
t₁₇₅, X₁: X₂ {O(n)}
t₁₇₅, X₂: X₂ {O(n)}
t₁₇₅, X₃: X₃ {O(n)}
t₁₇₅, X₄: 0 {O(1)}