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) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 1, X₀+1, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂-2, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₂
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+1, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₃,X₅} that do not contribute to the problem

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

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

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₄ for location l1

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₀: l0(X₀, X₁, X₂, X₄) → l2(X₀, X₁, X₂, X₄)
t₂₁: l1(X₀, X₁, X₂, X₄) → l3(X₀, X₁, X₂, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ X₄
t₂₂: l1(X₀, X₁, X₂, X₄) → l4(X₀, X₁, X₂, X₄) :|: X₀ < 0 ∧ X₀ ≤ X₄
t₂₃: l2(X₀, X₁, X₂, X₄) → l1(X₄, X₁, X₂, X₄)
t₂₄: l3(X₀, X₁, X₂, X₄) → l6(X₀, 1, X₀+1, X₄) :|: 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₀
t₂₅: l4(X₀, X₁, X₂, X₄) → l8(X₀, X₁, X₂, X₄) :|: X₀ ≤ X₄ ∧ 1+X₀ ≤ 0
t₂₆: l5(X₀, X₁, X₂, X₄) → l1(X₂-2, X₁, X₂, X₄) :|: 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₈: l6(X₀, X₁, X₂, X₄) → l5(X₀, X₁, X₂, X₄) :|: X₂ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l6(X₀, X₁, X₂, X₄) → l7(X₀, X₁, X₂, X₄) :|: X₁ < X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₉: l7(X₀, X₁, X₂, X₄) → l6(X₀, X₁+1, X₂, X₄) :|: 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₁: l1(X₀, X₁, X₂, X₄) → l3(X₀, X₁, X₂, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀+1 ]
l5 [X₂-1 ]
l7 [X₀ ]
l6 [X₀ ]

MPRF for transition t₂₄: l3(X₀, X₁, X₂, X₄) → l6(X₀, 1, X₀+1, X₄) :|: 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l5 [X₁-1 ]
l7 [X₀ ]
l6 [X₀ ]

MPRF for transition t₂₆: l5(X₀, X₁, X₂, X₄) → l1(X₂-2, X₁, X₂, X₄) :|: 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l5 [X₁ ]
l7 [X₂ ]
l6 [X₂ ]

MPRF for transition t₂₈: l6(X₀, X₁, X₂, X₄) → l5(X₀, X₁, X₂, X₄) :|: X₂ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l5 [X₀ ]
l7 [X₂ ]
l6 [X₀+1 ]

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

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

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₄ for location l1

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l4

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

Time-Bound by TWN-Loops:

TWN-Loops: t₂₇ 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

TWN-Loops:

entry: t₂₄: l3(X₀, X₁, X₂, X₄) → l6(X₀, 1, X₀+1, X₄) :|: 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₄) -> (X₀,X₁+1,X₂,X₄) :|: X₁ < X₂
order: [X₀; X₁; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₄: X₄

Termination: true
Formula:

1 < 0
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₁: 1 {O(1)}
X₂: X₄+2 {O(n)}
Runtime-bound of t₂₄: X₄+1 {O(n)}
Results in: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₉ 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

relevant size-bounds w.r.t. t₂₄:
X₁: 1 {O(1)}
X₂: X₄+2 {O(n)}
Runtime-bound of t₂₄: X₄+1 {O(n)}
Results in: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

Analysing control-flow refined program

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___2

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

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

Found invariant 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₄ for location l1

Found invariant X₀ ≤ X₄ ∧ 1+X₀ ≤ 0 for location l4

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

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

knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₈₀: l6(X₀, X₁, X₂, X₄) → n_l7___3(X₀, X₁, X₀+1, X₄) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₄ ∧ X₁ < 1+X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₈₂: n_l7___3(X₀, X₁, X₂, X₄) → n_l6___2(X₀, X₁+1, X₀+1, X₄) :|: X₀ ≤ X₄ ∧ 0 < X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₇₉: n_l6___2(X₀, X₁, X₂, X₄) → n_l7___1(X₀, X₁, X₀+1, X₄) :|: X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ ≤ X₄ ∧ X₁ < 1+X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄⋅X₄+6⋅X₄+5 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
l6 [0 ]
n_l7___3 [0 ]
l5 [0 ]
n_l7___1 [X₀+1-X₁ ]
n_l6___2 [X₀+2-X₁ ]

MPRF for transition t₈₆: n_l6___2(X₀, X₁, X₂, X₄) → l5(X₀, X₁, X₂, X₄) :|: X₂ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l6 [X₀+X₁ ]
l5 [X₀ ]
n_l7___1 [X₀+1 ]
n_l7___3 [X₀+X₁ ]
n_l6___2 [X₀+1 ]

MPRF for transition t₈₁: n_l7___1(X₀, X₁, X₂, X₄) → n_l6___2(X₀, X₁+1, X₀+1, X₄) :|: X₀ ≤ X₄ ∧ X₁ < 1+X₀ ∧ 2 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₄⋅X₄+5⋅X₄+4 {O(n^2)}

MPRF:

l3 [0 ]
l1 [0 ]
l6 [0 ]
n_l7___3 [0 ]
l5 [0 ]
n_l7___1 [X₀+1-X₁ ]
n_l6___2 [X₂-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₄⋅X₄+28⋅X₄+28 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: X₄+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₄+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₄+1 {O(n)}
t₂₇: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}
t₂₈: X₄+1 {O(n)}
t₂₉: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

Costbounds

Overall costbound: 4⋅X₄⋅X₄+28⋅X₄+28 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: X₄+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₄+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₄+1 {O(n)}
t₂₇: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}
t₂₈: X₄+1 {O(n)}
t₂₉: 2⋅X₄⋅X₄+12⋅X₄+10 {O(n^2)}

Sizebounds

t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₀: X₄+1 {O(n)}
t₂₁, X₁: 2⋅X₄⋅X₄+12⋅X₄+X₁+12 {O(n^2)}
t₂₁, X₂: 2⋅X₄+X₂+4 {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₂, X₀: 2⋅X₄+1 {O(n)}
t₂₂, X₁: 2⋅X₄⋅X₄+12⋅X₄+X₁+12 {O(n^2)}
t₂₂, X₂: 2⋅X₄+X₂+4 {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₃, X₀: X₄ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: X₄+1 {O(n)}
t₂₄, X₁: 1 {O(1)}
t₂₄, X₂: X₄+2 {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₅, X₀: 2⋅X₄+1 {O(n)}
t₂₅, X₁: 2⋅X₄⋅X₄+12⋅X₄+X₁+12 {O(n^2)}
t₂₅, X₂: 2⋅X₄+X₂+4 {O(n)}
t₂₅, X₄: 2⋅X₄ {O(n)}
t₂₆, X₀: X₄+1 {O(n)}
t₂₆, X₁: 2⋅X₄⋅X₄+12⋅X₄+12 {O(n^2)}
t₂₆, X₂: 2⋅X₄+4 {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₇, X₀: X₄+1 {O(n)}
t₂₇, X₁: 2⋅X₄⋅X₄+12⋅X₄+11 {O(n^2)}
t₂₇, X₂: X₄+2 {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₈, X₀: X₄+1 {O(n)}
t₂₈, X₁: 2⋅X₄⋅X₄+12⋅X₄+12 {O(n^2)}
t₂₈, X₂: 2⋅X₄+4 {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₉, X₀: X₄+1 {O(n)}
t₂₉, X₁: 2⋅X₄⋅X₄+12⋅X₄+11 {O(n^2)}
t₂₉, X₂: X₄+2 {O(n)}
t₂₉, X₄: X₄ {O(n)}