Initial Problem

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

Preprocessing

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

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

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, 0) :|: X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₄: l4→l2

Cut unsatisfiable transition t₂₀₈: n_l4___3→n_l1___1

Cut unsatisfiable transition t₂₂₄: n_l4___5→l2

Cut unsatisfiable transition t₂₂₅: n_l4___7→l2

Cut unreachable locations [n_l1___1] from the program graph

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___6

Found invariant X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___8

Found invariant X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___5

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

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___7

MPRF for transition t₂₀₆: n_l1___6(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+X₁+3 {O(n)}

MPRF:

n_l4___7 [X₁+1-X₂ ]
n_l1___6 [X₁+1-X₂ ]

MPRF for transition t₂₁₁: n_l4___7(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+X₁+4 {O(n)}

MPRF:

n_l4___7 [X₁+2-X₂ ]
n_l1___6 [X₁+1-X₂ ]

MPRF for transition t₂₀₃: n_l1___2(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l4___3 [X₀-X₂ ]
n_l1___2 [X₀-X₂ ]

MPRF for transition t₂₀₉: n_l4___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l4___3 [X₁-X₂ ]
n_l1___2 [X₁-X₂-1 ]

CFR: Improvement to new bound with the following program:

new bound:

3⋅X₀+3⋅X₁+9 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2, l3, l4, l5, n_l1___2, n_l1___4, n_l1___6, n_l1___8, n_l4___3, n_l4___5, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂₁₂: l4(X₀, X₁, X₂) → n_l1___8(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₃: n_l1___2(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₂₀₄: n_l1___4(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₅: n_l1___6(X₀, X₁, X₂) → n_l4___5(X₀, X₁, 0) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₆: n_l1___6(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₇: n_l1___8(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₂₃: n_l4___3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₉: n_l4___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₁₀: n_l4___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₁₁: n_l4___7(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:3⋅X₀+3⋅X₁+18 {O(n)}
t₀: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂₁₂: 1 {O(1)}
t₂₀₃: X₀+1 {O(n)}
t₂₀₄: 1 {O(1)}
t₂₀₅: 1 {O(1)}
t₂₀₆: X₀+X₁+3 {O(n)}
t₂₀₇: 1 {O(1)}
t₂₀₉: X₁+1 {O(n)}
t₂₂₃: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₁: X₀+X₁+4 {O(n)}

Costbounds

Overall costbound: 3⋅X₀+3⋅X₁+18 {O(n)}
t₀: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂₁₂: 1 {O(1)}
t₂₀₃: X₀+1 {O(n)}
t₂₀₄: 1 {O(1)}
t₂₀₅: 1 {O(1)}
t₂₀₆: X₀+X₁+3 {O(n)}
t₂₀₇: 1 {O(1)}
t₂₀₉: X₁+1 {O(n)}
t₂₂₃: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₁: X₀+X₁+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₀+3 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀+1 {O(n)}
t₂₁₂, X₀: X₀ {O(n)}
t₂₁₂, X₁: X₁ {O(n)}
t₂₁₂, X₂: X₀+1 {O(n)}
t₂₀₃, X₀: X₀ {O(n)}
t₂₀₃, X₁: X₁ {O(n)}
t₂₀₃, X₂: X₀+2 {O(n)}
t₂₀₄, X₀: X₀ {O(n)}
t₂₀₄, X₁: X₁ {O(n)}
t₂₀₄, X₂: 1 {O(1)}
t₂₀₅, X₀: X₀ {O(n)}
t₂₀₅, X₁: X₁ {O(n)}
t₂₀₅, X₂: 0 {O(1)}
t₂₀₆, X₀: X₀ {O(n)}
t₂₀₆, X₁: X₁ {O(n)}
t₂₀₆, X₂: 2⋅X₀+X₁+5 {O(n)}
t₂₀₇, X₀: X₀ {O(n)}
t₂₀₇, X₁: X₁ {O(n)}
t₂₀₇, X₂: X₀+2 {O(n)}
t₂₀₉, X₀: X₀ {O(n)}
t₂₀₉, X₁: X₁ {O(n)}
t₂₀₉, X₂: X₀+2 {O(n)}
t₂₂₃, X₀: 2⋅X₀ {O(n)}
t₂₂₃, X₁: 2⋅X₁ {O(n)}
t₂₂₃, X₂: X₀+3 {O(n)}
t₂₁₀, X₀: X₀ {O(n)}
t₂₁₀, X₁: X₁ {O(n)}
t₂₁₀, X₂: 0 {O(1)}
t₂₁₁, X₀: X₀ {O(n)}
t₂₁₁, X₁: X₁ {O(n)}
t₂₁₁, X₂: 2⋅X₀+X₁+5 {O(n)}