Initial Problem

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

Preprocessing

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l6

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l7

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

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

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

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

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

MPRF for transition t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l3 [X₀-X₁-1 ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]

MPRF for transition t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l3 [X₀-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l5

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l5

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1

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

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀⋅X₀+X₀+1 {O(n^2)}

MPRF:

l3 [X₂+1 ]
l4 [X₂ ]
l5 [X₂ ]
l1 [X₂+1 ]

MPRF for transition t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀⋅X₀+X₀+1 {O(n^2)}

MPRF:

l3 [X₂+1 ]
l4 [X₂+1 ]
l5 [X₂ ]
l1 [X₂+1 ]

MPRF for transition t₇: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀⋅X₀ {O(n^2)}

MPRF:

l3 [X₂ ]
l4 [X₂ ]
l5 [X₂ ]
l1 [X₂ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀₃: n_l4___5→l6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l6

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___3

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

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l7

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₉₀: n_l1___3(X₀, X₁, X₂) → n_l4___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l4___2 [X₂ ]
n_l5___1 [X₂ ]
n_l1___3 [X₂+1 ]

MPRF for transition t₉₃: n_l4___2(X₀, X₁, X₂) → n_l5___1(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l4___2 [X₂+1 ]
n_l5___1 [X₂ ]
n_l1___3 [X₂+1 ]

MPRF for transition t₉₅: n_l5___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

n_l4___2 [X₂ ]
n_l5___1 [X₂ ]
n_l1___3 [X₂ ]

CFR: Improvement to new bound with the following program:

new bound:

5⋅X₀+2 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l6, l7, n_l1___3, n_l4___2, n_l4___5, n_l4___6, n_l5___1, n_l5___4
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₁: l1(X₀, X₁, X₂) → n_l4___5(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₂: l1(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₀, 0, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₉₀: n_l1___3(X₀, X₁, X₂) → n_l4___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀₂: n_l4___2(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉₃: n_l4___2(X₀, X₁, X₂) → n_l5___1(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉₄: n_l4___5(X₀, X₁, X₂) → n_l5___4(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀₄: n_l4___6(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₉₅: n_l5___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₉₆: n_l5___4(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:5⋅X₀+11 {O(n)}
t₀: 1 {O(1)}
t₂: X₀ {O(n)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₀ {O(n)}
t₈: 1 {O(1)}
t₉₀: X₀+1 {O(n)}
t₉₃: X₀+1 {O(n)}
t₁₀₂: 1 {O(1)}
t₉₄: 1 {O(1)}
t₁₀₄: 1 {O(1)}
t₉₅: X₀ {O(n)}
t₉₆: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₀+11 {O(n)}
t₀: 1 {O(1)}
t₂: X₀ {O(n)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₀ {O(n)}
t₈: 1 {O(1)}
t₉₀: X₀+1 {O(n)}
t₉₃: X₀+1 {O(n)}
t₁₀₂: 1 {O(1)}
t₉₄: 1 {O(1)}
t₁₀₄: 1 {O(1)}
t₉₅: X₀ {O(n)}
t₉₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₀ {O(n)}
t₉₁, X₀: X₀ {O(n)}
t₉₁, X₁: X₀ {O(n)}
t₉₁, X₂: X₀ {O(n)}
t₉₂, X₀: X₀ {O(n)}
t₉₂, X₁: 0 {O(1)}
t₉₂, X₂: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: 0 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: 0 {O(1)}
t₉₀, X₀: X₀ {O(n)}
t₉₀, X₁: X₀ {O(n)}
t₉₀, X₂: X₀ {O(n)}
t₉₃, X₀: X₀ {O(n)}
t₉₃, X₁: X₀ {O(n)}
t₉₃, X₂: X₀ {O(n)}
t₁₀₂, X₀: X₀ {O(n)}
t₁₀₂, X₁: X₀ {O(n)}
t₁₀₂, X₂: 0 {O(1)}
t₉₄, X₀: X₀ {O(n)}
t₉₄, X₁: X₀ {O(n)}
t₉₄, X₂: X₀ {O(n)}
t₁₀₄, X₀: X₀ {O(n)}
t₁₀₄, X₁: 0 {O(1)}
t₁₀₄, X₂: 0 {O(1)}
t₉₅, X₀: X₀ {O(n)}
t₉₅, X₁: X₀ {O(n)}
t₉₅, X₂: X₀ {O(n)}
t₉₆, X₀: X₀ {O(n)}
t₉₆, X₁: X₀ {O(n)}
t₉₆, X₂: X₀ {O(n)}