Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1)
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃)
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₃, X₂)

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location l2

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1+X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₃, X₂)

Analysing control-flow refined program

Cut unsatisfiable transition t₂₅₁: n_l1___5→l5

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___6

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___3

Found invariant X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___1

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___5

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___7

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___6

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___3

Found invariant X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___1

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___5

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃₂ 8⋅X₂+8⋅X₃+11 {O(n)}

TWN-Loops:

entry: t₂₃₇: n_l2___8(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃+1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃+1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2+X₃ ≤ X₂
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1

Termination: true
Formula:

1+X₁ < X₀ ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₀ ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ < X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ < X₂ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 < 0
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₃ ≤ X₂ ∧ X₂ ≤ 2+X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃

Stabilization-Threshold for: 2+X₃ ≤ X₂
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}
Stabilization-Threshold for: 1+X₃ ≤ X₂
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}
Stabilization-Threshold for: X₃+1 ≤ X₂
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}
Stabilization-Threshold for: 1+X₃ ≤ X₂
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}

relevant size-bounds w.r.t. t₂₃₇:
X₂: X₃ {O(n)}
X₃: X₂ {O(n)}
Runtime-bound of t₂₃₇: 1 {O(1)}
Results in: 8⋅X₂+8⋅X₃+11 {O(n)}

8⋅X₂+8⋅X₃+11 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃₅ 8⋅X₂+8⋅X₃+11 {O(n)}

relevant size-bounds w.r.t. t₂₃₇:
X₂: X₃ {O(n)}
X₃: X₂ {O(n)}
Runtime-bound of t₂₃₇: 1 {O(1)}
Results in: 8⋅X₂+8⋅X₃+11 {O(n)}

8⋅X₂+8⋅X₃+11 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃₉ 8⋅X₂+8⋅X₃+11 {O(n)}

relevant size-bounds w.r.t. t₂₃₇:
X₂: X₃ {O(n)}
X₃: X₂ {O(n)}
Runtime-bound of t₂₃₇: 1 {O(1)}
Results in: 8⋅X₂+8⋅X₃+11 {O(n)}

8⋅X₂+8⋅X₃+11 {O(n)}

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___6

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___3

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___1

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___5

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___7

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___6

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___3

Found invariant X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___1

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___5

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃₁ 10⋅X₀+10⋅X₁+22 {O(n)}

TWN-Loops:

entry: t₂₄₀: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃) :|: X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃
entry: t₂₃₈: n_l2___8(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₁+1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ 2+X₁ ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,1+X₁,X₂,X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₁+1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ 2+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 2+X₁ ≤ X₀ ∧ 2+X₁ ≤ X₀ ∧ X₂ ≤ X₃
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃

Termination: true
Formula:

X₂ < X₃ ∧ 1 < 0
∨ X₂ < X₃ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₃ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ < X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₄₀:
X₀: X₁ {O(n)}
X₁: X₀+1 {O(n)}
Runtime-bound of t₂₄₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+13 {O(n)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃

Termination: true
Formula:

X₂ < X₃ ∧ 1 < 0
∨ X₂ < X₃ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 1 < 0 ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 1 < 0 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 1 < 0 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ < X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₃ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 < 0 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ < X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < 0
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁

Stabilization-Threshold for: 2+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₃₈:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₂₃₈: 1 {O(1)}
Results in: 6⋅X₀+6⋅X₁+9 {O(n)}

10⋅X₀+10⋅X₁+22 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃₄ 10⋅X₀+10⋅X₁+22 {O(n)}

relevant size-bounds w.r.t. t₂₄₀:
X₀: X₁ {O(n)}
X₁: X₀+1 {O(n)}
Runtime-bound of t₂₄₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+13 {O(n)}

relevant size-bounds w.r.t. t₂₃₈:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₂₃₈: 1 {O(1)}
Results in: 6⋅X₀+6⋅X₁+9 {O(n)}

10⋅X₀+10⋅X₁+22 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₄₁ 10⋅X₀+10⋅X₁+22 {O(n)}

relevant size-bounds w.r.t. t₂₄₀:
X₀: X₁ {O(n)}
X₁: X₀+1 {O(n)}
Runtime-bound of t₂₄₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+13 {O(n)}

relevant size-bounds w.r.t. t₂₃₈:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₂₃₈: 1 {O(1)}
Results in: 6⋅X₀+6⋅X₁+9 {O(n)}

10⋅X₀+10⋅X₁+22 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

24⋅X₂+24⋅X₃+30⋅X₀+30⋅X₁+99 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___2, n_l1___5, n_l2___1, n_l2___4, n_l2___8, n_l3___7, n_l4___3, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₂₃₃: l1(X₀, X₁, X₂, X₃) → n_l2___8(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₃, X₂)
t₂₅₀: n_l1___2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀
t₂₃₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀
t₂₃₂: n_l1___5(X₀, X₁, X₂, X₃) → n_l2___4(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₃₄: n_l2___1(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₂₃₅: n_l2___4(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₃₆: n_l2___4(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₃₇: n_l2___8(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₃₈: n_l2___8(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₂₃₉: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₄₀: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₂₄₁: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁+1, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀

All Bounds

Timebounds

Overall timebound:24⋅X₂+24⋅X₃+30⋅X₀+30⋅X₁+109 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₂₃₃: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂₃₁: 10⋅X₀+10⋅X₁+22 {O(n)}
t₂₅₀: 1 {O(1)}
t₂₃₂: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₃₄: 10⋅X₀+10⋅X₁+22 {O(n)}
t₂₃₅: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₃₆: 1 {O(1)}
t₂₃₇: 1 {O(1)}
t₂₃₈: 1 {O(1)}
t₂₃₉: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₄₀: 1 {O(1)}
t₂₄₁: 10⋅X₀+10⋅X₁+22 {O(n)}

Costbounds

Overall costbound: 24⋅X₂+24⋅X₃+30⋅X₀+30⋅X₁+109 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₂₃₃: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂₃₁: 10⋅X₀+10⋅X₁+22 {O(n)}
t₂₅₀: 1 {O(1)}
t₂₃₂: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₃₄: 10⋅X₀+10⋅X₁+22 {O(n)}
t₂₃₅: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₃₆: 1 {O(1)}
t₂₃₇: 1 {O(1)}
t₂₃₈: 1 {O(1)}
t₂₃₉: 8⋅X₂+8⋅X₃+11 {O(n)}
t₂₄₀: 1 {O(1)}
t₂₄₁: 10⋅X₀+10⋅X₁+22 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₃ {O(n)}
t₃, X₃: X₂ {O(n)}
t₂₃₃, X₀: X₁ {O(n)}
t₂₃₃, X₁: X₀ {O(n)}
t₂₃₃, X₂: X₃ {O(n)}
t₂₃₃, X₃: X₂ {O(n)}
t₈, X₀: 4⋅X₁ {O(n)}
t₈, X₁: 10⋅X₁+14⋅X₀+24 {O(n)}
t₈, X₂: 4⋅X₃ {O(n)}
t₈, X₃: 16⋅X₃+20⋅X₂+22 {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₂ {O(n)}
t₂₃₁, X₀: 2⋅X₁ {O(n)}
t₂₃₁, X₁: 10⋅X₁+12⋅X₀+23 {O(n)}
t₂₃₁, X₂: 2⋅X₃ {O(n)}
t₂₃₁, X₃: 10⋅X₂+8⋅X₃+11 {O(n)}
t₂₅₀, X₀: 3⋅X₁ {O(n)}
t₂₅₀, X₁: 10⋅X₁+13⋅X₀+24 {O(n)}
t₂₅₀, X₂: 3⋅X₃ {O(n)}
t₂₅₀, X₃: 16⋅X₃+19⋅X₂+22 {O(n)}
t₂₃₂, X₀: X₁ {O(n)}
t₂₃₂, X₁: X₀ {O(n)}
t₂₃₂, X₂: X₃ {O(n)}
t₂₃₂, X₃: 8⋅X₃+9⋅X₂+11 {O(n)}
t₂₃₄, X₀: 2⋅X₁ {O(n)}
t₂₃₄, X₁: 10⋅X₁+12⋅X₀+23 {O(n)}
t₂₃₄, X₂: 2⋅X₃ {O(n)}
t₂₃₄, X₃: 10⋅X₂+8⋅X₃+11 {O(n)}
t₂₃₅, X₀: X₁ {O(n)}
t₂₃₅, X₁: X₀ {O(n)}
t₂₃₅, X₂: X₃ {O(n)}
t₂₃₅, X₃: 8⋅X₃+9⋅X₂+11 {O(n)}
t₂₃₆, X₀: X₁ {O(n)}
t₂₃₆, X₁: X₀ {O(n)}
t₂₃₆, X₂: X₃ {O(n)}
t₂₃₆, X₃: 8⋅X₃+9⋅X₂+11 {O(n)}
t₂₃₇, X₀: X₁ {O(n)}
t₂₃₇, X₁: X₀ {O(n)}
t₂₃₇, X₂: X₃ {O(n)}
t₂₃₇, X₃: X₂ {O(n)}
t₂₃₈, X₀: X₁ {O(n)}
t₂₃₈, X₁: X₀ {O(n)}
t₂₃₈, X₂: X₃ {O(n)}
t₂₃₈, X₃: X₂ {O(n)}
t₂₃₉, X₀: X₁ {O(n)}
t₂₃₉, X₁: X₀ {O(n)}
t₂₃₉, X₂: X₃ {O(n)}
t₂₃₉, X₃: 8⋅X₃+9⋅X₂+11 {O(n)}
t₂₄₀, X₀: X₁ {O(n)}
t₂₄₀, X₁: X₀+1 {O(n)}
t₂₄₀, X₂: X₃ {O(n)}
t₂₄₀, X₃: 8⋅X₃+9⋅X₂+11 {O(n)}
t₂₄₁, X₀: 2⋅X₁ {O(n)}
t₂₄₁, X₁: 10⋅X₁+12⋅X₀+23 {O(n)}
t₂₄₁, X₂: 2⋅X₃ {O(n)}
t₂₄₁, X₃: 10⋅X₂+8⋅X₃+11 {O(n)}