Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(0, X₁, X₂, X₃, X₄, X₃)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 0, X₂, X₃, X₄, X₅) :|: X₅ < X₂
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁, X₂, X₃, X₄, 0)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₅
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+1, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l5

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l8

Found invariant 0 ≤ X₀ for location l1

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₄ ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ 0 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(0, X₁, X₂, X₃, X₄, X₃)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 0, X₂, X₃, X₄, X₅) :|: X₅ < X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ 0 ≤ X₀
t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁, X₂, X₃, X₄, 0) :|: 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₅ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₄ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀-1 ]
l1 [X₄-X₀ ]
l5 [X₄-X₀-1 ]
l7 [X₄-X₀-1 ]
l6 [X₄-X₀-1 ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 0, X₂, X₃, X₄, X₅) :|: X₅ < X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
l5 [X₄-X₀-1 ]
l7 [X₄-X₀-1 ]
l6 [X₄-X₀-1 ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
l5 [X₄-X₀-1 ]
l7 [X₄-X₀ ]
l6 [X₄-X₀ ]

MPRF for transition t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁, X₂, X₃, X₄, 0) :|: 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
l5 [X₄-X₀ ]
l7 [X₄-X₀ ]
l6 [X₄-X₀ ]

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
l5 [X₄-X₀-1 ]
l7 [X₄-X₀ ]
l6 [X₄-X₀ ]

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l5

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l8

Found invariant 0 ≤ X₀ for location l1

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₆ 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

TWN-Loops:

entry: t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 0, X₂, X₃, X₄, X₅) :|: X₅ < X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀,X₁+1,X₂,X₃,X₄,X₅) :|: X₁ < X₅
order: [X₀; X₁; X₂; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ X₁ < X₅ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₅
alphas_abs: X₅
M: 0
N: 1
Bound: 2⋅X₅+2 {O(n)}

relevant size-bounds w.r.t. t₄:
X₅: X₃ {O(n)}
Runtime-bound of t₄: X₄ {O(n)}
Results in: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

relevant size-bounds w.r.t. t₄:
X₅: X₃ {O(n)}
Runtime-bound of t₄: X₄ {O(n)}
Results in: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

Analysing control-flow refined program

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___2

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l7___3

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l5

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l8

Found invariant 0 ≤ X₀ for location l1

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant 1+X₅ ≤ X₂ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 5 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l7___1

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₄ {O(n)} for transition t₈₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ < X₅ ∧ 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₄ {O(n)} for transition t₉₀: n_l7___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___2(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ X₁ < X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₈₇: n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₅ ∧ 1+X₅ ≤ X₂ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ < X₅ ∧ 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃⋅X₄+2⋅X₄ {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
l6 [0 ]
n_l7___3 [0 ]
l5 [0 ]
n_l7___1 [X₅-X₁ ]
n_l6___2 [X₅+1-X₁ ]

MPRF for transition t₉₄: n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
l6 [X₄-X₀ ]
l5 [X₄-X₀-1 ]
n_l7___1 [X₄-X₀ ]
n_l7___3 [X₄-X₀ ]
n_l6___2 [X₄-X₀ ]

MPRF for transition t₈₉: n_l7___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___2(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ X₁ < X₅ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₄ ∧ 1+X₅ ≤ X₂ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 5 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₄+X₃⋅X₄+X₂+X₄ {O(n^2)}

MPRF:

l3 [X₂ ]
l1 [X₂ ]
l6 [X₂ ]
n_l7___3 [X₂ ]
l5 [X₂ ]
n_l7___1 [X₂+X₅-X₁ ]
n_l6___2 [X₂+X₅-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₃⋅X₄+13⋅X₄+4 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₁₀: 1 {O(1)}
t₉: X₄ {O(n)}
t₆: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}
t₇: X₄ {O(n)}
t₈: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}

Costbounds

Overall costbound: 4⋅X₃⋅X₄+13⋅X₄+4 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₁₀: 1 {O(1)}
t₉: X₄ {O(n)}
t₆: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}
t₇: X₄ {O(n)}
t₈: 2⋅X₃⋅X₄+4⋅X₄ {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)}
t₀, X₅: X₅ {O(n)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: 2⋅X₃⋅X₄+4⋅X₄+X₁ {O(n^2)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₃ {O(n)}
t₃, X₀: X₄ {O(n)}
t₃, X₁: 2⋅X₃⋅X₄+2⋅X₁+4⋅X₄ {O(n^2)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₃ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 0 {O(1)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₃ {O(n)}
t₅, X₀: X₄ {O(n)}
t₅, X₁: 2⋅X₃⋅X₄+4⋅X₄+X₁ {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₃ {O(n)}
t₁₀, X₀: X₄ {O(n)}
t₁₀, X₁: 2⋅X₃⋅X₄+2⋅X₁+4⋅X₄ {O(n^2)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₀, X₄: 2⋅X₄ {O(n)}
t₁₀, X₅: X₃ {O(n)}
t₉, X₀: X₄ {O(n)}
t₉, X₁: 2⋅X₃⋅X₄+4⋅X₄+X₁ {O(n^2)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: 0 {O(1)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₃ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₁: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: 2⋅X₃ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₁: 2⋅X₃⋅X₄+4⋅X₄ {O(n^2)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₃ {O(n)}