Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ < 0
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₀ < 0
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition t₆: l3→l1

Cut unsatisfiable transition t₇: l3→l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂

Chain transitions t₈: l3→l1 and t₄: l1→l4 to t₇₂: l3→l4

Chain transitions t₅: l3→l1 and t₄: l1→l4 to t₇₃: l3→l4

Chain transitions t₅: l3→l1 and t₃: l1→l3 to t₇₄: l3→l3

Chain transitions t₈: l3→l1 and t₃: l1→l3 to t₇₅: l3→l3

Chain transitions t₁: l2→l1 and t₃: l1→l3 to t₇₆: l2→l3

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₇₇: l2→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₇₈: l2→l3

Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₇₉: l3→l3

Chain transitions t₈: l3→l1 and t₂: l1→l3 to t₈₀: l3→l3

Analysing control-flow refined program

Cut unsatisfiable transition t₈₀: l3→l3

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

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

MPRF for transition t₇₄: l3(X₀, X₁, X₂, X₃) -{2}> l3(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

MPRF for transition t₇₅: l3(X₀, X₁, X₂, X₃) -{2}> l3(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1+X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₃ {O(n)}

MPRF for transition t₇₉: l3(X₀, X₁, X₂, X₃) -{2}> l3(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

Analysing control-flow refined program

Cut unsatisfiable transition t₂₂₁: n_l1___6→l4

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l1___6

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___4

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ for location n_l1___9

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l3___3

Found invariant 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l1___2

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___11

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___8

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l1___5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___1

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l3___10

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l3___7

MPRF for transition t₁₉₄: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₃+3 {O(n)}

MPRF for transition t₂₀₀: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₃+2 {O(n)}

MPRF for transition t₁₉₉: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF for transition t₂₀₈: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF for transition t₁₉₆: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₂+5 {O(n)}

MPRF for transition t₁₉₇: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₂+7 {O(n)}

MPRF for transition t₂₀₅: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₂+5 {O(n)}

MPRF for transition t₂₀₇: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₂+6 {O(n)}

MPRF for transition t₁₉₅: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

5⋅X₃+3 {O(n)}

MPRF for transition t₂₀₄: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

5⋅X₃+3 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l1___5, n_l1___6, n_l1___9, n_l3___1, n_l3___10, n_l3___11, n_l3___3, n_l3___4, n_l3___7, n_l3___8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₉₂: l1(X₀, X₁, X₂, X₃) → n_l3___10(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₉₃: l1(X₀, X₁, X₂, X₃) → n_l3___11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0
t₂₁₉: n_l1___2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₉₄: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₂₀: n_l1___5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₉₅: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₉₆: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₁₉₇: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₂₂: n_l1___9(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₁₉₈: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₁₉₉: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₂₀₀: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₀₁: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ < 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₂₀₂: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₂₀₃: n_l3___11(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₂₀₄: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₀₅: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₀₆: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₀₇: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₀₈: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

12⋅X₃+14⋅X₂+38 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l1___5, n_l1___6, n_l1___9, n_l3___1, n_l3___10, n_l3___11, n_l3___3, n_l3___4, n_l3___7, n_l3___8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₉₂: l1(X₀, X₁, X₂, X₃) → n_l3___10(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₉₃: l1(X₀, X₁, X₂, X₃) → n_l3___11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0
t₂₁₉: n_l1___2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₉₄: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₂₀: n_l1___5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₉₅: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₉₆: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₁₉₇: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₂₂: n_l1___9(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₁₉₈: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₁₉₉: n_l1___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀
t₂₀₀: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₀₁: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁-1, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ < 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₂₀₂: n_l3___10(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₂₀₃: n_l3___11(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₂₀₄: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₀ < 0 ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₂₀₅: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₀₆: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₀₇: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₀
t₂₀₈: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___9(X₀-1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:12⋅X₃+14⋅X₂+52 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁₉₂: 1 {O(1)}
t₁₉₃: 1 {O(1)}
t₁₉₄: X₃+3 {O(n)}
t₁₉₅: 5⋅X₃+3 {O(n)}
t₁₉₆: 3⋅X₂+5 {O(n)}
t₁₉₇: 3⋅X₂+7 {O(n)}
t₁₉₈: 1 {O(1)}
t₁₉₉: X₂+2 {O(n)}
t₂₀₀: X₃+2 {O(n)}
t₂₀₁: 1 {O(1)}
t₂₀₂: 1 {O(1)}
t₂₀₃: 1 {O(1)}
t₂₀₄: 5⋅X₃+3 {O(n)}
t₂₀₅: 3⋅X₂+5 {O(n)}
t₂₀₆: 1 {O(1)}
t₂₀₇: 3⋅X₂+6 {O(n)}
t₂₀₈: X₂+2 {O(n)}
t₂₁₉: 1 {O(1)}
t₂₂₀: 1 {O(1)}
t₂₂₂: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₃+14⋅X₂+52 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁₉₂: 1 {O(1)}
t₁₉₃: 1 {O(1)}
t₁₉₄: X₃+3 {O(n)}
t₁₉₅: 5⋅X₃+3 {O(n)}
t₁₉₆: 3⋅X₂+5 {O(n)}
t₁₉₇: 3⋅X₂+7 {O(n)}
t₁₉₈: 1 {O(1)}
t₁₉₉: X₂+2 {O(n)}
t₂₀₀: X₃+2 {O(n)}
t₂₀₁: 1 {O(1)}
t₂₀₂: 1 {O(1)}
t₂₀₃: 1 {O(1)}
t₂₀₄: 5⋅X₃+3 {O(n)}
t₂₀₅: 3⋅X₂+5 {O(n)}
t₂₀₆: 1 {O(1)}
t₂₀₇: 3⋅X₂+6 {O(n)}
t₂₀₈: X₂+2 {O(n)}
t₂₁₉: 1 {O(1)}
t₂₂₀: 1 {O(1)}
t₂₂₂: 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: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₉, X₀: 3⋅X₂+2 {O(n)}
t₉, X₁: 3⋅X₃+2 {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₉, X₃: 3⋅X₃ {O(n)}
t₁₉₂, X₀: X₂ {O(n)}
t₁₉₂, X₁: X₃ {O(n)}
t₁₉₂, X₂: X₂ {O(n)}
t₁₉₂, X₃: X₃ {O(n)}
t₁₉₃, X₀: X₂ {O(n)}
t₁₉₃, X₁: X₃ {O(n)}
t₁₉₃, X₂: X₂ {O(n)}
t₁₉₃, X₃: X₃ {O(n)}
t₁₉₄, X₀: X₂ {O(n)}
t₁₉₄, X₁: X₃+2 {O(n)}
t₁₉₄, X₂: X₂ {O(n)}
t₁₉₄, X₃: X₃ {O(n)}
t₁₉₅, X₀: 1 {O(1)}
t₁₉₅, X₁: 5⋅X₃+3 {O(n)}
t₁₉₅, X₂: 5⋅X₂ {O(n)}
t₁₉₅, X₃: 5⋅X₃ {O(n)}
t₁₉₆, X₀: 3⋅X₂+5 {O(n)}
t₁₉₆, X₁: 3⋅X₃ {O(n)}
t₁₉₆, X₂: 3⋅X₂ {O(n)}
t₁₉₆, X₃: 3⋅X₃ {O(n)}
t₁₉₇, X₀: 3⋅X₂+5 {O(n)}
t₁₉₇, X₁: 3⋅X₃ {O(n)}
t₁₉₇, X₂: 3⋅X₂ {O(n)}
t₁₉₇, X₃: 3⋅X₃ {O(n)}
t₁₉₈, X₀: 2⋅X₂+3 {O(n)}
t₁₉₈, X₁: 2⋅X₃ {O(n)}
t₁₉₈, X₂: 2⋅X₂ {O(n)}
t₁₉₈, X₃: 2⋅X₃ {O(n)}
t₁₉₉, X₀: X₂+2 {O(n)}
t₁₉₉, X₁: X₃ {O(n)}
t₁₉₉, X₂: X₂ {O(n)}
t₁₉₉, X₃: X₃ {O(n)}
t₂₀₀, X₀: X₂ {O(n)}
t₂₀₀, X₁: X₃+2 {O(n)}
t₂₀₀, X₂: X₂ {O(n)}
t₂₀₀, X₃: X₃ {O(n)}
t₂₀₁, X₀: X₂ {O(n)}
t₂₀₁, X₁: X₃+1 {O(n)}
t₂₀₁, X₂: X₂ {O(n)}
t₂₀₁, X₃: X₃ {O(n)}
t₂₀₂, X₀: X₂+1 {O(n)}
t₂₀₂, X₁: X₃ {O(n)}
t₂₀₂, X₂: X₂ {O(n)}
t₂₀₂, X₃: X₃ {O(n)}
t₂₀₃, X₀: X₂+1 {O(n)}
t₂₀₃, X₁: X₃ {O(n)}
t₂₀₃, X₂: X₂ {O(n)}
t₂₀₃, X₃: X₃ {O(n)}
t₂₀₄, X₀: 1 {O(1)}
t₂₀₄, X₁: 5⋅X₃+3 {O(n)}
t₂₀₄, X₂: 5⋅X₂ {O(n)}
t₂₀₄, X₃: 5⋅X₃ {O(n)}
t₂₀₅, X₀: 3⋅X₂+5 {O(n)}
t₂₀₅, X₁: 3⋅X₃ {O(n)}
t₂₀₅, X₂: 3⋅X₂ {O(n)}
t₂₀₅, X₃: 3⋅X₃ {O(n)}
t₂₀₆, X₀: 1 {O(1)}
t₂₀₆, X₁: 5⋅X₃+2 {O(n)}
t₂₀₆, X₂: 5⋅X₂ {O(n)}
t₂₀₆, X₃: 5⋅X₃ {O(n)}
t₂₀₇, X₀: 3⋅X₂+5 {O(n)}
t₂₀₇, X₁: 3⋅X₃ {O(n)}
t₂₀₇, X₂: 3⋅X₂ {O(n)}
t₂₀₇, X₃: 3⋅X₃ {O(n)}
t₂₀₈, X₀: X₂+2 {O(n)}
t₂₀₈, X₁: X₃ {O(n)}
t₂₀₈, X₂: X₂ {O(n)}
t₂₀₈, X₃: X₃ {O(n)}
t₂₁₉, X₀: 2⋅X₂ {O(n)}
t₂₁₉, X₁: 1 {O(1)}
t₂₁₉, X₂: 2⋅X₂ {O(n)}
t₂₁₉, X₃: 2⋅X₃ {O(n)}
t₂₂₀, X₀: 1 {O(1)}
t₂₂₀, X₁: 1 {O(1)}
t₂₂₀, X₂: 10⋅X₂ {O(n)}
t₂₂₀, X₃: 10⋅X₃ {O(n)}
t₂₂₂, X₀: 1 {O(1)}
t₂₂₂, X₁: 2⋅X₃ {O(n)}
t₂₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂₂, X₃: 2⋅X₃ {O(n)}