Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁₂: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆
t₁₈: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆)
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < X₅
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l6

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l15

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l17

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l7

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l5

Found invariant X₁ ≤ X₅ for location l8

Found invariant X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location l16

Found invariant X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁₂: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₈: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < X₅ ∧ X₁ ≤ X₅
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l16 [X₂+1-X₅ ]
l6 [X₂-X₅ ]
l7 [X₂+1-X₀ ]
l5 [X₂+1-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂+1-X₅ ]

MPRF for transition t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l16 [X₂+1-X₅ ]
l6 [X₂+1-X₅ ]
l7 [X₂+1-X₅ ]
l5 [X₂+2-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂+1-X₅ ]

MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l16 [X₂+1-X₅ ]
l6 [X₂+1-X₅ ]
l7 [X₂-X₅ ]
l5 [X₂+1-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂+1-X₅ ]

MPRF for transition t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l16 [X₂+1-X₅ ]
l6 [X₂+1-X₅ ]
l7 [X₂+2-X₀ ]
l5 [X₂+1-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂+1-X₅ ]

MPRF for transition t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l16 [X₂-X₅ ]
l6 [X₂-X₅ ]
l7 [X₂-X₅ ]
l5 [X₂+1-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂-X₅ ]

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l6

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l15

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l17

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l7

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l5

Found invariant X₁ ≤ X₅ for location l8

Found invariant X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location l16

Found invariant X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₁₂ 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

TWN-Loops:

entry: t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅
results in twn-loop: twn:Inv: [X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂] , (X₀,X₁,X₂,X₃,X₄,X₅,X₆) -> (X₀,X₁,X₂,X₃,X₄,X₅,X₆+1) :|: X₆ ≤ X₄
order: [X₁; X₂; X₃; X₄; X₅; X₆]
closed-form:
X₁: X₁
X₂: X₂
X₃: X₃
X₄: X₄
X₅: X₅
X₆: X₆ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₆ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₆ ≤ X₄ ∧ X₄ ≤ X₆

Stabilization-Threshold for: X₆ ≤ X₄
alphas_abs: X₆+X₄
M: 0
N: 1
Bound: 2⋅X₄+2⋅X₆+2 {O(n)}

relevant size-bounds w.r.t. t₁₀:
X₄: X₄ {O(n)}
X₆: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀: X₁+X₂+1 {O(n)}
Results in: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₄ 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

relevant size-bounds w.r.t. t₁₀:
X₄: X₄ {O(n)}
X₆: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀: X₁+X₂+1 {O(n)}
Results in: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}

Analysing control-flow refined program

Found invariant X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l14___2

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l6

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l15

Found invariant X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l16___3

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l17

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l7

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l5

Found invariant X₁ ≤ X₅ for location l8

Found invariant X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l16___1

Found invariant X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l14

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₁₂₇: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l16___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂

knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₁₂₉: n_l16___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂

MPRF for transition t₁₂₆: n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l16___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₅ ≤ X₂ ∧ 1+X₃ ≤ X₆ ∧ X₆ ≤ 1+X₄ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:

new bound:

2⋅X₁⋅X₄+2⋅X₂⋅X₄+3⋅X₁⋅X₃+3⋅X₂⋅X₃+3⋅X₁+3⋅X₂+3⋅X₄+4⋅X₃+4 {O(n^2)}

MPRF:

n_l16___3 [X₄+1-X₆ ]
l7 [X₄+1-X₃ ]
l5 [X₄+1-X₃ ]
l8 [X₄+1-X₃ ]
l14 [X₄+1-X₆ ]
l6 [X₄+1-X₃ ]
n_l16___1 [2⋅X₄+1-X₃-X₆ ]
n_l14___2 [2⋅X₄+2-X₃-X₆ ]

MPRF for transition t₁₃₃: n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l7 [X₂+1-X₀ ]
l5 [X₂+1-X₀ ]
l8 [X₂+1-X₅ ]
l14 [X₂+1-X₅ ]
l6 [X₂-X₅ ]
n_l16___1 [X₂+1-X₅ ]
n_l16___3 [X₂+1-X₅ ]
n_l14___2 [X₂+1-X₅ ]

MPRF for transition t₁₂₈: n_l16___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:

new bound:

2⋅X₁⋅X₃+2⋅X₂⋅X₃+X₁⋅X₄+X₂⋅X₄+2⋅X₃+3⋅X₁+3⋅X₂+X₄+4 {O(n^2)}

MPRF:

n_l16___3 [1 ]
l7 [1 ]
l5 [1 ]
l8 [1 ]
l14 [1 ]
l6 [1 ]
n_l16___1 [X₄+2-X₆ ]
n_l14___2 [X₄+2-X₆ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₁⋅X₄+4⋅X₂⋅X₄+8⋅X₁⋅X₃+8⋅X₂⋅X₃+13⋅X₁+13⋅X₂+4⋅X₄+8⋅X₃+25 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₂: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₈: 1 {O(1)}
t₁₄: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁⋅X₄+4⋅X₂⋅X₄+8⋅X₁⋅X₃+8⋅X₂⋅X₃+13⋅X₁+13⋅X₂+4⋅X₄+8⋅X₃+25 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₂: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₈: 1 {O(1)}
t₁₄: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₅: 1 {O(1)}

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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₁ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₂, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₂, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+6⋅X₃+4 {O(n^2)}
t₁₃, X₀: 2⋅X₀+2⋅X₂+4⋅X₁+2 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₃, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₈, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₈, X₁: 2⋅X₁ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₈, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₈, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+X₆+4 {O(n^2)}
t₁₄, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₄, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+6⋅X₃+4 {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
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)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₁₇, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₅, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₆, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₀, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₀, X₆: 2⋅X₃ {O(n)}
t₁₁, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₁, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+X₆+4 {O(n^2)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}