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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ < X₃
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 1
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: 1 < X₀

Preprocessing

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4

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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < 1 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: 1 < X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l1→l2

Cut unsatisfiable transition t₆: l1→l2

Cut unsatisfiable transition t₁₀₈: n_l1___4→l2

Cut unsatisfiable transition t₁₀₉: n_l1___5→l2

Cut unsatisfiable transition t₁₀₇: n_l1___6→l2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___2

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___5

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l4___7

MPRF for transition t₈₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 < X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

n_l4___1 [X₁ ]
n_l1___4 [X₁+1 ]

MPRF for transition t₈₇: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l4___1 [X₁ ]
n_l1___4 [X₁ ]

MPRF for transition t₈₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l4___2 [X₁-1 ]
n_l1___5 [X₁ ]

MPRF for transition t₈₈: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₀ < 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l4___2 [X₁ ]
n_l1___5 [X₁ ]

MPRF for transition t₈₅: n_l1___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

n_l4___3 [X₃-X₁ ]
n_l1___6 [X₃+1-X₁ ]

MPRF for transition t₈₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ < X₃ ∧ 2 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

n_l4___3 [X₃-X₁ ]
n_l1___6 [X₃-X₁ ]

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₃+6⋅X₂+4 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___4, n_l1___5, n_l1___6, n_l4___1, n_l4___2, n_l4___3, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₈₆: l1(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₂, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₁₀₅: n_l1___4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈₃: n_l1___4(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 < X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀₆: n_l1___5(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈₄: n_l1___5(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₁₀: n_l1___6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₈₅: n_l1___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ X₁ < X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₈₇: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈₈: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₀ < 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ < X₃ ∧ 2 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₉₀: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___4(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉₁: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁-1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ < 1 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉₂: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(1, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁

All Bounds

Timebounds

Overall timebound:2⋅X₃+6⋅X₂+16 {O(n)}
t₀: 1 {O(1)}
t₈₆: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₈₃: X₂+1 {O(n)}
t₁₀₅: 1 {O(1)}
t₈₄: X₂ {O(n)}
t₁₀₆: 1 {O(1)}
t₈₅: X₂+X₃+2 {O(n)}
t₁₁₀: 1 {O(1)}
t₈₇: X₂ {O(n)}
t₈₈: X₂ {O(n)}
t₈₉: X₂+X₃+1 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+6⋅X₂+16 {O(n)}
t₀: 1 {O(1)}
t₈₆: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₈₃: X₂+1 {O(n)}
t₁₀₅: 1 {O(1)}
t₈₄: X₂ {O(n)}
t₁₀₆: 1 {O(1)}
t₈₅: X₂+X₃+2 {O(n)}
t₁₁₀: 1 {O(1)}
t₈₇: X₂ {O(n)}
t₈₈: X₂ {O(n)}
t₈₉: X₂+X₃+1 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₈₆, X₀: X₀ {O(n)}
t₈₆, X₁: X₂ {O(n)}
t₈₆, X₂: X₂ {O(n)}
t₈₆, X₃: X₃ {O(n)}
t₁₀, X₀: 6⋅X₀+1 {O(n)}
t₁₀, X₁: 2⋅X₁+3⋅X₂+X₃+3 {O(n)}
t₁₀, X₂: 8⋅X₂ {O(n)}
t₁₀, X₃: 8⋅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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₈₃, X₀: X₀ {O(n)}
t₈₃, X₁: X₂ {O(n)}
t₈₃, X₂: X₂ {O(n)}
t₈₃, X₃: X₃ {O(n)}
t₁₀₅, X₀: 2⋅X₀ {O(n)}
t₁₀₅, X₁: 0 {O(1)}
t₁₀₅, X₂: 2⋅X₂ {O(n)}
t₁₀₅, X₃: 2⋅X₃ {O(n)}
t₈₄, X₀: X₀ {O(n)}
t₈₄, X₁: X₂ {O(n)}
t₈₄, X₂: X₂ {O(n)}
t₈₄, X₃: X₃ {O(n)}
t₁₀₆, X₀: 2⋅X₀ {O(n)}
t₁₀₆, X₁: 0 {O(1)}
t₁₀₆, X₂: 2⋅X₂ {O(n)}
t₁₀₆, X₃: 2⋅X₃ {O(n)}
t₈₅, X₀: 1 {O(1)}
t₈₅, X₁: 2⋅X₂+X₃+2 {O(n)}
t₈₅, X₂: X₂ {O(n)}
t₈₅, X₃: X₃ {O(n)}
t₁₁₀, X₀: 1 {O(1)}
t₁₁₀, X₁: 3⋅X₂+X₃+3 {O(n)}
t₁₁₀, X₂: 2⋅X₂ {O(n)}
t₁₁₀, X₃: 2⋅X₃ {O(n)}
t₈₇, X₀: X₀ {O(n)}
t₈₇, X₁: X₂ {O(n)}
t₈₇, X₂: X₂ {O(n)}
t₈₇, X₃: X₃ {O(n)}
t₈₈, X₀: X₀ {O(n)}
t₈₈, X₁: X₂ {O(n)}
t₈₈, X₂: X₂ {O(n)}
t₈₈, X₃: X₃ {O(n)}
t₈₉, X₀: 1 {O(1)}
t₈₉, X₁: 2⋅X₂+X₃+2 {O(n)}
t₈₉, X₂: X₂ {O(n)}
t₈₉, X₃: X₃ {O(n)}
t₉₀, X₀: X₀ {O(n)}
t₉₀, X₁: X₂ {O(n)}
t₉₀, X₂: X₂ {O(n)}
t₉₀, X₃: X₃ {O(n)}
t₉₁, X₀: X₀ {O(n)}
t₉₁, X₁: X₂ {O(n)}
t₉₁, X₂: X₂ {O(n)}
t₉₁, X₃: X₃ {O(n)}
t₉₂, X₀: 1 {O(1)}
t₉₂, X₁: X₂+1 {O(n)}
t₉₂, X₂: X₂ {O(n)}
t₉₂, X₃: X₃ {O(n)}