Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0, nondef.1, nondef.3
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1+X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₄, X₄) :|: X₄+1 ≤ X₂
t₁₆: l10(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₂₁: l11(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₁: l12(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, 1) :|: 2 < X₂
t₂: l12(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 2
t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁₂: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ 0
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₃
t₂₀: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1)
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, nondef.1, X₂, X₃, X₄)
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₉: l7(X₀, X₁, X₂, X₃, X₄) → l5(nondef.0, X₁, X₂, X₃, X₄)
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)
t₁₇: l9(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, nondef.3-1, X₄) :|: X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ nondef.3 ≤ 0 ∧ 0 ≤ nondef.3
t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, nondef.3-1, X₄) :|: 0 < 1+X₃ ∧ 0 ≤ nondef.3 ∧ 2⋅nondef.3 ≤ 1+X₃ ∧ X₃ < 2⋅nondef.3+1
t₁₉: l9(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, nondef.3-1, X₄) :|: X₃+1 < 0 ∧ nondef.3 ≤ 0 ∧ 1+X₃ ≤ 2⋅nondef.3 ∧ 2⋅nondef.3 < X₃+3

Preprocessing

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l2

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l6

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l7

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l5

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l8

Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₂ for location l1

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l10

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l4

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l3

Cut unsatisfiable transition t₁₇: l9→l3

Cut unsatisfiable transition t₁₉: l9→l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0, nondef.1, nondef.3
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1+X₄ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₄, X₄) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₂
t₁₆: l10(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂₁: l11(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₁: l12(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, 1) :|: 2 < X₂
t₂: l12(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 2
t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₁₂: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₂₀: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, nondef.1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₉: l7(X₀, X₁, X₂, X₃, X₄) → l5(nondef.0, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀
t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, nondef.3-1, X₄) :|: 0 < 1+X₃ ∧ 0 ≤ nondef.3 ∧ 2⋅nondef.3 ≤ 1+X₃ ∧ X₃ < 2⋅nondef.3+1 ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₄, X₄) :|: X₄+1 ≤ X₂ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₂ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF:

l4 [X₂-X₄ ]
l1 [X₂+1-X₄ ]
l2 [X₂-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
l5 [X₂-X₄ ]
l8 [X₂-X₄ ]
l10 [X₂-X₄ ]
l9 [X₂-X₄ ]
l3 [X₂-X₄ ]

MPRF for transition t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l4 [X₂-X₄-1 ]
l1 [X₂-X₄ ]
l2 [X₂-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
l5 [X₂-X₄ ]
l8 [X₂-X₄ ]
l10 [X₂-X₄ ]
l9 [X₂-X₄ ]
l3 [X₂-X₄ ]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l4 [X₂-X₄-1 ]
l1 [X₂-X₄ ]
l2 [X₂-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
l5 [X₂-X₄ ]
l8 [X₂-X₄ ]
l10 [X₂-X₄ ]
l9 [X₂-X₄ ]
l3 [X₂-X₄ ]

MPRF for transition t₂₀: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l4 [X₂-X₄ ]
l1 [X₂-X₄ ]
l2 [X₂-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
l5 [X₂-X₄ ]
l8 [X₂-X₄ ]
l10 [X₂-X₄ ]
l9 [X₂-X₄ ]
l3 [X₂-X₄ ]

MPRF for transition t₁₆: l10(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}

MPRF:

l1 [2⋅X₄ ]
l4 [2⋅X₃-1 ]
l2 [2⋅X₃ ]
l6 [2⋅X₃ ]
l7 [2⋅X₃ ]
l5 [2⋅X₃ ]
l8 [2⋅X₃ ]
l10 [2⋅X₃-1 ]
l9 [2⋅X₃-2 ]
l3 [2⋅X₃ ]

MPRF for transition t₁₂: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}

MPRF:

l1 [2⋅X₄+3 ]
l4 [2⋅X₃ ]
l2 [2⋅X₃+3 ]
l6 [2⋅X₃+3 ]
l7 [2⋅X₃+3 ]
l5 [2⋅X₃+3 ]
l8 [2⋅X₃+1 ]
l10 [2⋅X₃+1 ]
l9 [2⋅X₃+1 ]
l3 [2⋅X₃+3 ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+7⋅X₂+8 {O(n^2)}

MPRF:

l1 [2⋅X₄+1 ]
l4 [X₃ ]
l2 [X₃ ]
l6 [X₃ ]
l7 [X₃ ]
l5 [X₃ ]
l8 [X₃ ]
l10 [X₃ ]
l9 [X₃ ]
l3 [2⋅X₃+1 ]

MPRF for transition t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, nondef.1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

MPRF:

l1 [2⋅X₂ ]
l4 [2⋅X₃ ]
l2 [2⋅X₃ ]
l6 [2⋅X₃+2 ]
l7 [2⋅X₃+2 ]
l5 [2⋅X₃+2 ]
l8 [2⋅X₃ ]
l10 [2⋅X₃ ]
l9 [2⋅X₃ ]
l3 [2⋅X₃+2 ]

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}

MPRF:

l1 [2⋅X₄ ]
l4 [-1 ]
l2 [X₃-2 ]
l6 [X₃ ]
l7 [X₃-2 ]
l5 [X₃-2 ]
l8 [X₃-2 ]
l10 [X₃-2 ]
l9 [X₃-2 ]
l3 [2⋅X₃-1 ]

MPRF for transition t₉: l7(X₀, X₁, X₂, X₃, X₄) → l5(nondef.0, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}

MPRF:

l1 [2⋅X₄ ]
l4 [2⋅X₃-3 ]
l2 [2⋅X₃-3 ]
l6 [2⋅X₃-1 ]
l7 [2⋅X₃-1 ]
l5 [2⋅X₃-3 ]
l8 [2⋅X₃-3 ]
l10 [2⋅X₃-3 ]
l9 [2⋅X₃-3 ]
l3 [2⋅X₃-1 ]

MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}

MPRF:

l1 [2⋅X₄ ]
l4 [X₃ ]
l2 [X₃ ]
l6 [X₃ ]
l7 [X₃ ]
l5 [X₃ ]
l8 [X₃ ]
l10 [X₃-1 ]
l9 [X₃-1 ]
l3 [2⋅X₃ ]

MPRF for transition t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, nondef.3-1, X₄) :|: 0 < 1+X₃ ∧ 0 ≤ nondef.3 ∧ 2⋅nondef.3 ≤ 1+X₃ ∧ X₃ < 2⋅nondef.3+1 ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+9⋅X₂+11 {O(n^2)}

MPRF:

l1 [X₂+X₄+4 ]
l4 [2⋅X₃ ]
l2 [2⋅X₃+1 ]
l6 [2⋅X₃+1 ]
l7 [2⋅X₃+1 ]
l5 [2⋅X₃+1 ]
l8 [2⋅X₃+1 ]
l10 [X₃+2 ]
l9 [X₃+2 ]
l3 [2⋅X₃+1 ]

Analysing control-flow refined program

Cut unsatisfiable transition t₆: l3→l4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l7___14

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___11

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___3

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l9___9

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l10___2

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l5___5

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l9___1

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l2___12

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l7___6

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___8

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l5___13

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l6___7

Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₂ for location l1

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l10___10

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location l3

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l2___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ for location n_l6___15

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₅₆: l3(X₀, X₁, X₂, X₃, X₄) → n_l6___15(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 < X₃ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 0 < X₃ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₆₀: n_l6___15(X₀, X₁, X₂, X₃, X₄) → n_l7___14(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₆₂: n_l7___14(X₀, X₁, X₂, X₃, X₄) → n_l5___13(NoDet0, X₁, X₂, Arg3_P, Arg4_P) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ Arg3_P ∧ 3 ≤ X₂ ∧ Arg3_P ≤ Arg4_P ∧ 1+Arg4_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₅₈: n_l5___13(X₀, X₁, X₂, X₃, X₄) → n_l2___12(X₀, NoDet0, X₂, Arg3_P, Arg4_P) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ Arg3_P ∧ 3 ≤ X₂ ∧ Arg3_P ≤ Arg4_P ∧ 1+Arg4_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₅₄: n_l2___12(X₀, X₁, X₂, X₃, X₄) → n_l8___11(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₁ < X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₇₉: n_l2___12(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₆₄: n_l8___11(X₀, X₁, X₂, X₃, X₄) → n_l10___10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ X₁ < X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₅₂: n_l10___10(X₀, X₁, X₂, X₃, X₄) → n_l9___9(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀

knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₆₇: n_l9___9(X₀, X₁, X₂, X₃, X₄) → n_l3___8(X₀, Arg1_P, Arg2_P, Arg3_P, Arg4_P) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ Arg2_P ∧ 1+Arg4_P ≤ Arg2_P ∧ X₃ ≤ Arg4_P ∧ X₃ < 3+2⋅Arg3_P ∧ 1+2⋅Arg3_P ≤ X₃ ∧ 1+Arg1_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀

MPRF for transition t₁₅₃: n_l10___2(X₀, X₁, X₂, X₃, X₄) → n_l9___1(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+10⋅X₂+12 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
n_l9___9 [0 ]
l4 [0 ]
n_l2___12 [0 ]
n_l2___4 [X₃ ]
n_l6___15 [0 ]
n_l6___7 [X₃ ]
n_l7___14 [0 ]
n_l5___13 [0 ]
n_l7___6 [X₃ ]
n_l5___5 [X₃ ]
n_l8___11 [0 ]
n_l10___10 [0 ]
n_l8___3 [X₃ ]
n_l10___2 [X₃ ]
n_l9___1 [X₃-1 ]
n_l3___8 [2⋅X₃ ]

MPRF for transition t₁₅₅: n_l2___4(X₀, X₁, X₂, X₃, X₄) → n_l8___3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₁ < X₀ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

3⋅X₂⋅X₂+13⋅X₂+12 {O(n^2)}

MPRF:

l3 [X₂ ]
l1 [X₂ ]
n_l9___9 [X₂ ]
l4 [X₂ ]
n_l2___12 [X₂ ]
n_l2___4 [X₂+X₃+1 ]
n_l6___15 [X₂ ]
n_l6___7 [X₂+2⋅X₃ ]
n_l7___14 [X₂ ]
n_l5___13 [X₂ ]
n_l7___6 [X₂+2⋅X₃ ]
n_l5___5 [X₂+X₃+1 ]
n_l8___11 [X₂ ]
n_l10___10 [X₂ ]
n_l8___3 [X₂+X₃-1 ]
n_l10___2 [X₂+X₃-1 ]
n_l9___1 [X₂+X₃-1 ]
n_l3___8 [X₂+2⋅X₃ ]

MPRF for transition t₁₈₀: n_l2___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₄ ]
l1 [X₂-X₄ ]
l4 [X₂-X₄-1 ]
n_l2___12 [X₂-X₃ ]
n_l2___4 [X₂-X₄ ]
n_l6___15 [X₂-X₃ ]
n_l6___7 [X₂-X₄ ]
n_l7___14 [X₂-X₄ ]
n_l5___13 [X₂-X₃ ]
n_l7___6 [X₂-X₄ ]
n_l5___5 [X₂-X₄ ]
n_l8___11 [X₂-X₃ ]
n_l10___10 [X₂-X₄ ]
n_l8___3 [X₂-X₄ ]
n_l10___2 [X₂-X₄ ]
n_l9___1 [X₂-X₄ ]
n_l9___9 [X₂-X₄ ]
n_l3___8 [X₂-X₄ ]

MPRF for transition t₁₅₇: n_l3___8(X₀, X₁, X₂, X₃, X₄) → n_l6___7(X₀, X₁, X₂, X₃, X₄) :|: 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 0 < X₃ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+12⋅X₂+16 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
n_l9___9 [0 ]
l4 [0 ]
n_l2___12 [0 ]
n_l2___4 [2⋅X₃ ]
n_l6___15 [0 ]
n_l6___7 [2⋅X₃ ]
n_l7___14 [0 ]
n_l5___13 [0 ]
n_l7___6 [2⋅X₃ ]
n_l5___5 [2⋅X₃ ]
n_l8___11 [0 ]
n_l10___10 [0 ]
n_l8___3 [2⋅X₃ ]
n_l10___2 [2⋅X₃ ]
n_l9___1 [2⋅X₃ ]
n_l3___8 [2⋅X₃+2 ]

MPRF for transition t₁₇₈: n_l3___8(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₃ ]
l1 [X₂-X₄ ]
l4 [X₂-X₄-1 ]
n_l2___12 [X₂-X₃ ]
n_l2___4 [X₂-X₄ ]
n_l6___15 [X₂-X₄ ]
n_l6___7 [X₂-X₄ ]
n_l7___14 [X₂-X₃ ]
n_l5___13 [X₂-X₄ ]
n_l7___6 [X₂-X₄ ]
n_l5___5 [X₂-X₄ ]
n_l8___11 [X₂-X₄ ]
n_l10___10 [X₂-X₃ ]
n_l8___3 [X₂-X₄ ]
n_l10___2 [X₂-X₄ ]
n_l9___1 [X₂-X₄ ]
n_l9___9 [X₂-X₄ ]
n_l3___8 [X₂-X₄ ]

MPRF for transition t₁₅₉: n_l5___5(X₀, X₁, X₂, X₃, X₄) → n_l2___4(X₀, NoDet0, X₂, Arg3_P, Arg4_P) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ Arg3_P ∧ 3 ≤ X₂ ∧ Arg3_P ≤ Arg4_P ∧ 1+Arg4_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ of depth 1:

new bound:

2⋅X₂⋅X₂+11⋅X₂+14 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
n_l9___9 [0 ]
l4 [0 ]
n_l2___12 [0 ]
n_l2___4 [X₃ ]
n_l6___15 [0 ]
n_l6___7 [X₃+2 ]
n_l7___14 [0 ]
n_l5___13 [0 ]
n_l7___6 [X₃+2 ]
n_l5___5 [X₃+2 ]
n_l8___11 [0 ]
n_l10___10 [0 ]
n_l8___3 [X₃ ]
n_l10___2 [X₃ ]
n_l9___1 [X₃ ]
n_l3___8 [2⋅X₃+1 ]

MPRF for transition t₁₆₁: n_l6___7(X₀, X₁, X₂, X₃, X₄) → n_l7___6(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 0 < X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+10⋅X₂+12 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
n_l9___9 [0 ]
l4 [0 ]
n_l2___12 [0 ]
n_l2___4 [X₃-1 ]
n_l6___15 [0 ]
n_l6___7 [X₃ ]
n_l7___14 [0 ]
n_l5___13 [0 ]
n_l7___6 [X₃-1 ]
n_l5___5 [X₃-1 ]
n_l8___11 [0 ]
n_l10___10 [0 ]
n_l8___3 [X₃-1 ]
n_l10___2 [X₃-1 ]
n_l9___1 [X₃-1 ]
n_l3___8 [2⋅X₃ ]

MPRF for transition t₁₆₃: n_l7___6(X₀, X₁, X₂, X₃, X₄) → n_l5___5(NoDet0, X₁, X₂, Arg3_P, Arg4_P) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ Arg3_P ∧ 3 ≤ X₂ ∧ Arg3_P ≤ Arg4_P ∧ 1+Arg4_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+12⋅X₂+16 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
n_l9___9 [0 ]
l4 [0 ]
n_l2___12 [0 ]
n_l2___4 [2⋅X₃ ]
n_l6___15 [0 ]
n_l6___7 [2⋅X₃+2 ]
n_l7___14 [0 ]
n_l5___13 [0 ]
n_l7___6 [2⋅X₃+2 ]
n_l5___5 [2⋅X₃ ]
n_l8___11 [0 ]
n_l10___10 [0 ]
n_l8___3 [2⋅X₃ ]
n_l10___2 [2⋅X₃ ]
n_l9___1 [2⋅X₃ ]
n_l3___8 [2⋅X₃+2 ]

MPRF for transition t₁₆₅: n_l8___3(X₀, X₁, X₂, X₃, X₄) → n_l10___2(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₂ ∧ X₁ < X₀ ∧ 1+X₄ ≤ X₂ ∧ 3 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

3⋅X₂⋅X₂+16⋅X₂+21 {O(n^2)}

MPRF:

l3 [X₂-3 ]
l1 [X₂-3 ]
n_l9___9 [X₂-3 ]
l4 [X₂-3 ]
n_l2___12 [X₂-3 ]
n_l2___4 [X₂+X₃-3 ]
n_l6___15 [X₂-3 ]
n_l6___7 [X₂+X₃-3 ]
n_l7___14 [X₂-3 ]
n_l5___13 [X₂-3 ]
n_l7___6 [X₂+X₃-3 ]
n_l5___5 [X₂+X₃-3 ]
n_l8___11 [X₂-3 ]
n_l10___10 [X₂-3 ]
n_l8___3 [X₂+X₃-3 ]
n_l10___2 [X₂+X₃-4 ]
n_l9___1 [X₂+X₃-4 ]
n_l3___8 [X₂+2⋅X₃-3 ]

MPRF for transition t₁₆₆: n_l9___1(X₀, X₁, X₂, X₃, X₄) → n_l3___8(X₀, Arg1_P, Arg2_P, Arg3_P, Arg4_P) :|: 1 ≤ X₃ ∧ 3 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ Arg2_P ∧ 1+Arg4_P ≤ Arg2_P ∧ X₃ ≤ Arg4_P ∧ X₃ < 3+2⋅Arg3_P ∧ 1+2⋅Arg3_P ≤ X₃ ∧ 1+Arg1_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

3⋅X₂⋅X₂+13⋅X₂+12 {O(n^2)}

MPRF:

l3 [X₂ ]
l1 [X₂ ]
n_l9___9 [X₂ ]
l4 [X₂ ]
n_l2___12 [X₂ ]
n_l2___4 [X₂+2⋅X₃ ]
n_l6___15 [X₂ ]
n_l6___7 [X₂+2⋅X₃ ]
n_l7___14 [X₂ ]
n_l5___13 [X₂ ]
n_l7___6 [X₂+2⋅X₃ ]
n_l5___5 [X₂+2⋅X₃ ]
n_l8___11 [X₂ ]
n_l10___10 [X₂ ]
n_l8___3 [X₂+2⋅X₃ ]
n_l10___2 [X₂+X₃+1 ]
n_l9___1 [X₂+X₃+1 ]
n_l3___8 [X₂+2⋅X₃ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:16⋅X₂⋅X₂+57⋅X₂+65 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₂+2 {O(n)}
t₄: 1 {O(1)}
t₁₆: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₂₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₂: 2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₁₃: X₂+1 {O(n)}
t₅: 2⋅X₂⋅X₂+7⋅X₂+8 {O(n^2)}
t₆: X₂+1 {O(n)}
t₂₀: X₂+1 {O(n)}
t₁₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₇: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₉: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₄: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₈: 2⋅X₂⋅X₂+9⋅X₂+11 {O(n^2)}

Costbounds

Overall costbound: 16⋅X₂⋅X₂+57⋅X₂+65 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₂+2 {O(n)}
t₄: 1 {O(1)}
t₁₆: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₂₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₂: 2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₁₃: X₂+1 {O(n)}
t₅: 2⋅X₂⋅X₂+7⋅X₂+8 {O(n^2)}
t₆: X₂+1 {O(n)}
t₂₀: X₂+1 {O(n)}
t₁₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₇: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₉: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₄: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₈: 2⋅X₂⋅X₂+9⋅X₂+11 {O(n^2)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₂+3 {O(n)}
t₃, X₄: X₂+2 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂+3 {O(n)}
t₄, X₄: X₂+2 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₂+3 {O(n)}
t₁₆, X₄: X₂+2 {O(n)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₁, X₃: X₂+X₃+3 {O(n)}
t₂₁, X₄: X₂+X₄+2 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: 1 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂+3 {O(n)}
t₁₂, X₄: X₂+2 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂+3 {O(n)}
t₁₃, X₄: X₂+2 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₂+3 {O(n)}
t₅, X₄: X₂+2 {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 0 {O(1)}
t₆, X₄: X₂+2 {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₂+3 {O(n)}
t₂₀, X₄: X₂+2 {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂+3 {O(n)}
t₁₁, X₄: X₂+2 {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂+3 {O(n)}
t₇, X₄: X₂+2 {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂+3 {O(n)}
t₉, X₄: X₂+2 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂+3 {O(n)}
t₁₄, X₄: X₂+2 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₂+3 {O(n)}
t₁₈, X₄: X₂+2 {O(n)}