Initial Problem

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

Preprocessing

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

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

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

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

MPRF for transition t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l2 [X₂-X₁ ]
l3 [X₂-X₁ ]
l4 [X₂-X₁-1 ]
l1 [X₂-X₁ ]

MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l1(0, X₁+1, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l2 [X₂-X₁ ]
l3 [X₂-X₁ ]
l4 [X₂-X₁ ]
l1 [X₂-X₁ ]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₃ {O(n^2)}

MPRF:

l2 [X₃-X₀ ]
l4 [X₃-X₀ ]
l3 [X₃-X₀-1 ]
l1 [X₃-X₀ ]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₃ {O(n^2)}

MPRF:

l2 [X₃-X₀ ]
l4 [X₃-X₀ ]
l3 [X₃-X₀ ]
l1 [X₃-X₀ ]

knowledge_propagation leads to new time bound X₂⋅X₃+X₂+X₃+1 {O(n^2)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₉₁: n_l1___10→l5

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___6

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___4

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l2___5

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___10

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___3

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l2___2

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+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_l3___12

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

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___9

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___8

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 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_l2___13

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 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_l4___11

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___7

MPRF for transition t₇₀: n_l1___6(X₀, X₁, X₂, X₃) → n_l2___5(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l2___5 [X₂-X₁ ]
n_l2___9 [X₂-X₁ ]
n_l3___4 [X₂-X₁ ]
n_l3___8 [X₂-X₁ ]
n_l1___10 [X₂-X₁ ]
n_l4___7 [X₂-X₁ ]
n_l1___6 [X₂+1-X₁ ]

MPRF for transition t₇₄: n_l2___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l2___5 [X₂+1-X₁ ]
n_l2___9 [X₂-X₁ ]
n_l3___4 [X₂-X₁ ]
n_l3___8 [X₂-X₁ ]
n_l1___10 [X₂-X₁ ]
n_l4___7 [X₂-X₁ ]
n_l1___6 [X₂+1-X₁ ]

MPRF for transition t₇₆: n_l2___9(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l2___5 [X₂-X₁ ]
n_l2___9 [X₂-X₁ ]
n_l3___4 [X₂-X₁ ]
n_l3___8 [X₂-X₁ ]
n_l1___10 [X₂-X₁ ]
n_l4___7 [X₂-X₁-1 ]
n_l1___6 [X₂-X₁ ]

MPRF for transition t₇₈: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___10(X₀+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

n_l2___5 [X₂-X₁ ]
n_l2___9 [X₂-X₁-1 ]
n_l3___4 [X₂-X₁ ]
n_l3___8 [X₂-X₁-1 ]
n_l1___10 [X₂-X₁-1 ]
n_l4___7 [X₂-X₁-1 ]
n_l1___6 [X₂-X₁ ]

MPRF for transition t₈₂: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(0, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

n_l2___5 [X₂-X₁ ]
n_l2___9 [X₂-X₁ ]
n_l3___4 [X₂-X₁ ]
n_l3___8 [X₂-X₁ ]
n_l1___10 [X₂-X₁ ]
n_l4___7 [X₂-X₁ ]
n_l1___6 [X₂-X₁ ]

MPRF for transition t₆₇: n_l1___10(X₀, X₁, X₂, X₃) → n_l2___9(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₃+2 {O(n^2)}

MPRF:

n_l1___6 [X₃ ]
n_l2___5 [X₃ ]
n_l2___9 [X₃-X₀ ]
n_l4___7 [X₃-X₀ ]
n_l3___4 [X₃ ]
n_l3___8 [X₃-X₀ ]
n_l1___10 [X₃+1-X₀ ]

MPRF for transition t₇₅: n_l2___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₃+2 {O(n^2)}

MPRF:

n_l1___6 [X₃ ]
n_l2___5 [X₃ ]
n_l2___9 [X₃+1-X₀ ]
n_l4___7 [X₃-X₀ ]
n_l3___4 [X₃ ]
n_l3___8 [X₃-X₀ ]
n_l1___10 [X₃+1-X₀ ]

MPRF for transition t₇₉: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___10(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₃+X₃+1 {O(n^2)}

MPRF:

n_l1___6 [X₃ ]
n_l2___5 [X₃ ]
n_l2___9 [X₃-X₀ ]
n_l4___7 [X₃-X₀ ]
n_l3___4 [X₃ ]
n_l3___8 [X₃-X₀ ]
n_l1___10 [X₃-X₀ ]

MPRF for transition t₆₉: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF:

n_l2___2 [X₂-X₁ ]
n_l4___1 [X₂-X₁ ]
n_l1___3 [X₂+1-X₁ ]

MPRF for transition t₇₃: n_l2___2(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

n_l2___2 [X₂-X₁ ]
n_l4___1 [X₂-X₁-1 ]
n_l1___3 [X₂-X₁ ]

MPRF for transition t₈₀: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___3(0, X₁+1, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

n_l2___2 [X₂-X₁ ]
n_l4___1 [X₂-X₁ ]
n_l1___3 [X₂-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:3⋅X₂⋅X₃+3⋅X₂+3⋅X₃+5 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂⋅X₃+X₂+X₃+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: X₂⋅X₃+X₃ {O(n^2)}
t₅: X₂ {O(n)}
t₆: X₂⋅X₃+X₃ {O(n^2)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₂⋅X₃+3⋅X₂+3⋅X₃+5 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂⋅X₃+X₂+X₃+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: X₂⋅X₃+X₃ {O(n^2)}
t₅: X₂ {O(n)}
t₆: X₂⋅X₃+X₃ {O(n^2)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₂⋅X₃+X₃ {O(n^2)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: X₂⋅X₃+X₃ {O(n^2)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₂⋅X₃+X₃ {O(n^2)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₂⋅X₃+X₃ {O(n^2)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: 0 {O(1)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: 0 {O(1)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}