Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂
t₁₀: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₂ ≤ X₁
t₁₁: l7(X₀, X₁, X₂, X₃) → l5(X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ < X₂
t₁₂: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁

Preprocessing

Cut unsatisfiable transition t₁₀: l7→l5

Cut unsatisfiable transition t₁₁: l7→l5

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(0, 0, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₂: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₁₂: l7(X₀, X₁, X₂, X₃) → l5(X₀+1, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l7 [X₃-X₀ ]
l5 [X₃-X₀ ]

MPRF for transition t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+X₃ {O(n^2)}

MPRF:

l7 [X₃-X₁-1 ]
l5 [X₃-X₁ ]

MPRF for transition t₉: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁+1, X₂, X₃) :|: X₁ < X₂ ∧ X₁ < X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₂ {O(n^2)}

MPRF:

l7 [X₂-X₁ ]
l5 [X₂-X₁ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l5→l6

Cut unsatisfiable transition t₉₇: n_l5___1→l6

Cut unsatisfiable transition t₉₉: n_l5___5→l6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l5___5

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l7___6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l7___2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l7___4

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___3

MPRF for transition t₈₃: n_l5___1(X₀, X₁, X₂, X₃) → n_l7___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

n_l7___2 [X₃-X₀ ]
n_l5___1 [X₃-X₀ ]
n_l5___3 [X₃-X₀ ]
n_l7___4 [X₃-X₀-1 ]
n_l5___5 [X₃-X₀-1 ]

MPRF for transition t₈₄: n_l5___3(X₀, X₁, X₂, X₃) → n_l7___2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

n_l7___2 [X₃-X₀ ]
n_l5___1 [X₃-X₀ ]
n_l5___3 [X₃+1-X₀ ]
n_l7___4 [X₃-X₀ ]
n_l5___5 [X₃-X₀ ]

MPRF for transition t₈₇: n_l7___2(X₀, X₁, X₂, X₃) → n_l5___1(X₀, X₁+1, X₂, X₃) :|: X₀ < X₃ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ < X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

n_l7___2 [X₃+1-X₀ ]
n_l5___1 [X₃-X₀ ]
n_l5___3 [X₃+1-X₀ ]
n_l7___4 [X₃-X₀ ]
n_l5___5 [X₃-X₀ ]

MPRF for transition t₈₈: n_l7___4(X₀, X₁, X₂, X₃) → n_l5___3(X₀+1, 0, X₁, X₃) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

n_l7___2 [X₃-X₀ ]
n_l5___1 [X₃-X₀ ]
n_l5___3 [X₃-X₀ ]
n_l7___4 [X₃-X₀ ]
n_l5___5 [X₃-X₀ ]

MPRF for transition t₈₅: n_l5___5(X₀, X₁, X₂, X₃) → n_l7___4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+X₂+2 {O(n^2)}

MPRF:

n_l5___3 [X₃ ]
n_l7___2 [X₂ ]
n_l5___1 [X₂ ]
n_l7___4 [X₂-X₁ ]
n_l5___5 [X₂+1-X₁ ]

MPRF for transition t₈₉: n_l7___4(X₀, X₁, X₂, X₃) → n_l5___5(X₀, X₁+1, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ < X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+X₂+2 {O(n^2)}

MPRF:

n_l5___3 [X₃ ]
n_l7___2 [X₃ ]
n_l5___1 [X₂+1 ]
n_l7___4 [X₂+1-X₁ ]
n_l5___5 [X₂+1-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:X₂⋅X₃+X₃⋅X₃+2⋅X₃+X₂+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃⋅X₃+X₃ {O(n^2)}
t₈: 1 {O(1)}
t₁₃: 1 {O(1)}
t₉: X₂⋅X₃+X₂ {O(n^2)}
t₁₂: X₃ {O(n)}

Costbounds

Overall costbound: X₂⋅X₃+X₃⋅X₃+2⋅X₃+X₂+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃⋅X₃+X₃ {O(n^2)}
t₈: 1 {O(1)}
t₁₃: 1 {O(1)}
t₉: X₂⋅X₃+X₂ {O(n^2)}
t₁₂: X₃ {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: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₁: 0 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: X₂⋅X₃+X₂ {O(n^2)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₃ {O(n)}
t₈, X₁: 0 {O(1)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₀+X₃ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: 3⋅X₂ {O(n)}
t₁₃, X₃: 3⋅X₃ {O(n)}
t₉, X₀: X₃ {O(n)}
t₉, X₁: X₂⋅X₃+X₂ {O(n^2)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₂, X₀: X₃ {O(n)}
t₁₂, X₁: 0 {O(1)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}