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 t₇₈: n_l4___3→n_l1___1

Cut unsatisfiable transition t₉₄: n_l4___5→l2

Cut unsatisfiable transition t₉₅: 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 t₇₆: 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 t₈₁: 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 t₇₃: 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 t₇₉: 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:

X₀+2 {O(n)}

MPRF:

n_l4___3 [X₀+1-X₂ ]
n_l1___2 [X₀-X₂ ]

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₁+4⋅X₀+10 {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
t₈₂: 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
t₇₃: 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
t₇₄: 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
t₇₅: 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
t₇₆: 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
t₇₇: 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
t₉₃: 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
t₇₉: 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
t₈₀: 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
t₈₁: 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:2⋅X₁+4⋅X₀+19 {O(n)}
t₀: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₇₃: X₀+1 {O(n)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: X₀+X₁+3 {O(n)}
t₇₇: 1 {O(1)}
t₇₉: X₀+2 {O(n)}
t₉₃: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: X₀+X₁+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₁+4⋅X₀+19 {O(n)}
t₀: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₇₃: X₀+1 {O(n)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: X₀+X₁+3 {O(n)}
t₇₇: 1 {O(1)}
t₇₉: X₀+2 {O(n)}
t₉₃: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: 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)}
t₈₂, X₀: X₀ {O(n)}
t₈₂, X₁: X₁ {O(n)}
t₈₂, X₂: X₀+1 {O(n)}
t₇₃, X₀: X₀ {O(n)}
t₇₃, X₁: X₁ {O(n)}
t₇₃, X₂: X₀+2 {O(n)}
t₇₄, X₀: X₀ {O(n)}
t₇₄, X₁: X₁ {O(n)}
t₇₄, X₂: 1 {O(1)}
t₇₅, X₀: X₀ {O(n)}
t₇₅, X₁: X₁ {O(n)}
t₇₅, X₂: 0 {O(1)}
t₇₆, X₀: X₀ {O(n)}
t₇₆, X₁: X₁ {O(n)}
t₇₆, X₂: 2⋅X₀+X₁+5 {O(n)}
t₇₇, X₀: X₀ {O(n)}
t₇₇, X₁: X₁ {O(n)}
t₇₇, X₂: X₀+2 {O(n)}
t₇₉, X₀: X₀ {O(n)}
t₇₉, X₁: X₁ {O(n)}
t₇₉, X₂: X₀+2 {O(n)}
t₉₃, X₀: 2⋅X₀ {O(n)}
t₉₃, X₁: 2⋅X₁ {O(n)}
t₉₃, X₂: X₀+3 {O(n)}
t₈₀, X₀: X₀ {O(n)}
t₈₀, X₁: X₁ {O(n)}
t₈₀, X₂: 0 {O(1)}
t₈₁, X₀: X₀ {O(n)}
t₈₁, X₁: X₁ {O(n)}
t₈₁, X₂: 2⋅X₀+X₁+5 {O(n)}