Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₂, X₂, X₃, X₄) :|: X₁ ≤ 0 ∧ 0 < X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ 0
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unsatisfiable transition t₅: l3→l1

Cut unsatisfiable transition t₆: l3→l1

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

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

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₈: l0(X₀, X₁, X₂, X₄) → l2(X₀, X₁, X₂, X₄)
t₁₉: l1(X₀, X₁, X₂, X₄) → l3(X₀, X₁, X₂, X₄) :|: 0 < X₀ ∧ X₀ ≤ X₂
t₂₀: l1(X₀, X₁, X₂, X₄) → l4(X₀, X₁, X₂, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₂
t₂₁: l2(X₀, X₁, X₂, X₄) → l1(X₂, X₄, X₂, X₄)
t₂₂: l3(X₀, X₁, X₂, X₄) → l1(X₀, X₁-1, X₂, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₂₃: l3(X₀, X₁, X₂, X₄) → l1(X₀-1, X₂, X₂, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₂₄: l4(X₀, X₁, X₂, X₄) → l5(X₀, X₁, X₂, X₄) :|: X₀ ≤ X₂ ∧ X₀ ≤ 0

MPRF for transition t₂₃: l3(X₀, X₁, X₂, X₄) → l1(X₀-1, X₂, X₂, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]

Found invariant 1 ≤ 0 for location l5

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

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

Found invariant X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₉ 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}

TWN-Loops:

entry: t₂₃: l3(X₀, X₁, X₂, X₄) → l1(X₀-1, X₂, X₂, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₄) -> (X₀,X₁-1,X₂,X₄) :|: 0 < X₀ ∧ 0 < X₁ ∧ 0 < X₁
entry: t₂₁: l2(X₀, X₁, X₂, X₄) → l1(X₂, X₄, X₂, X₄)
results in twn-loop: twn:Inv: [X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₄) -> (X₀,X₁-1,X₂,X₄) :|: 0 < X₀ ∧ 0 < X₁ ∧ 0 < X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂

Termination: true
Formula:

1 < 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀

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

relevant size-bounds w.r.t. t₂₃:
X₁: X₂ {O(n)}
Runtime-bound of t₂₃: X₂ {O(n)}
Results in: 2⋅X₂⋅X₂+5⋅X₂ {O(n^2)}

order: [X₀; X₁; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂
X₄: X₄

Termination: true
Formula:

1 < 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀

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

relevant size-bounds w.r.t. t₂₁:
X₁: X₄ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 2⋅X₄+5 {O(n)}

2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₂ 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}

relevant size-bounds w.r.t. t₂₃:
X₁: X₂ {O(n)}
Runtime-bound of t₂₃: X₂ {O(n)}
Results in: 2⋅X₂⋅X₂+5⋅X₂ {O(n^2)}

relevant size-bounds w.r.t. t₂₁:
X₁: X₄ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 2⋅X₄+5 {O(n)}

2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₈₆: n_l1___2→l4

Cut unsatisfiable transition t₈₈: n_l1___6→l4

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

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

Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

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

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___7

MPRF for transition t₇₀: n_l1___2(X₀, X₁, X₂, X₄) → n_l3___1(X₀, X₁, X₂, X₄) :|: X₀ ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

n_l3___1 [X₀-1 ]
n_l3___3 [X₀ ]
n_l1___2 [X₀ ]
n_l1___5 [X₀ ]
n_l3___4 [X₀-1 ]
n_l1___6 [X₀-1 ]

MPRF for transition t₇₁: n_l1___5(X₀, X₁, X₂, X₄) → n_l3___3(X₀, X₁, X₂, X₄) :|: X₀ ≤ X₂ ∧ 0 < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

n_l3___1 [X₀ ]
n_l3___3 [X₀ ]
n_l1___2 [X₀ ]
n_l1___5 [X₀+1 ]
n_l3___4 [X₀ ]
n_l1___6 [X₀ ]

MPRF for transition t₇₄: n_l3___1(X₀, X₁, X₂, X₄) → n_l1___6(X₀, X₁-1, X₂, X₄) :|: X₀ ≤ X₂ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

n_l3___1 [X₀ ]
n_l3___3 [X₀ ]
n_l1___2 [X₀ ]
n_l1___5 [X₀ ]
n_l3___4 [X₀-1 ]
n_l1___6 [X₀-1 ]

MPRF for transition t₇₅: n_l3___3(X₀, X₁, X₂, X₄) → n_l1___2(X₀, X₁-1, X₂, X₄) :|: 1+X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

n_l3___1 [X₀-1 ]
n_l3___3 [X₀ ]
n_l1___2 [X₀-1 ]
n_l1___5 [X₀ ]
n_l3___4 [X₀-1 ]
n_l1___6 [X₀-1 ]

MPRF for transition t₇₆: n_l3___4(X₀, X₁, X₂, X₄) → n_l1___5(X₀-1, X₂, X₂, X₄) :|: X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

MPRF:

n_l3___1 [X₀+X₂-X₁ ]
n_l3___3 [X₀+1 ]
n_l1___2 [X₀+X₂-X₁ ]
n_l1___5 [X₀+1 ]
n_l3___4 [X₀+1 ]
n_l1___6 [X₀+1 ]

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₂ ≤ X₁ ∧ 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 ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

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

Found invariant 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 n_l1___5

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

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

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___7

Found invariant X₄ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6

Found invariant X₄ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₄ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₄ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

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

Found invariant X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant X₄ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₇₂ 12⋅X₂⋅X₂+2⋅X₄+20⋅X₂+14 {O(n^2)}

TWN-Loops:

entry: t₇₉: n_l3___7(X₀, X₁, X₂, X₄) → n_l1___6(X₀, X₁-1, X₂, X₄) :|: 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₄) -> (X₀,X₁-1,X₂,X₄) :|: X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂
entry: t₇₄: n_l3___1(X₀, X₁, X₂, X₄) → n_l1___6(X₀, X₁-1, X₂, X₄) :|: X₀ ≤ X₂ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₄) -> (X₀,X₁-1,X₂,X₄) :|: X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂
order: [X₀; X₁; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂
X₄: X₄

Termination: true
Formula:

X₀ < X₂ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 < X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 < X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀

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

relevant size-bounds w.r.t. t₇₉:
X₁: X₄ {O(n)}
Runtime-bound of t₇₉: 1 {O(1)}
Results in: 2⋅X₄+7 {O(n)}

order: [X₀; X₁; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂
X₄: X₄

Termination: true
Formula:

X₀ < X₂ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 < X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 < X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀

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

relevant size-bounds w.r.t. t₇₄:
X₁: 3⋅X₂ {O(n)}
Runtime-bound of t₇₄: 2⋅X₂+1 {O(n)}
Results in: 12⋅X₂⋅X₂+20⋅X₂+7 {O(n^2)}

12⋅X₂⋅X₂+2⋅X₄+20⋅X₂+14 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₇₇ 12⋅X₂⋅X₂+2⋅X₄+20⋅X₂+14 {O(n^2)}

relevant size-bounds w.r.t. t₇₉:
X₁: X₄ {O(n)}
Runtime-bound of t₇₉: 1 {O(1)}
Results in: 2⋅X₄+7 {O(n)}

relevant size-bounds w.r.t. t₇₄:
X₁: 3⋅X₂ {O(n)}
Runtime-bound of t₇₄: 2⋅X₂+1 {O(n)}
Results in: 12⋅X₂⋅X₂+20⋅X₂+7 {O(n^2)}

12⋅X₂⋅X₂+2⋅X₄+20⋅X₂+14 {O(n^2)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₂⋅X₂+11⋅X₂+4⋅X₄+14 {O(n^2)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}
t₂₃: X₂ {O(n)}
t₂₄: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₂⋅X₂+11⋅X₂+4⋅X₄+14 {O(n^2)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 2⋅X₂⋅X₂+2⋅X₄+5⋅X₂+5 {O(n^2)}
t₂₃: X₂ {O(n)}
t₂₄: 1 {O(1)}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: X₂ {O(n)}
t₁₉, X₁: X₂+X₄ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₂₀, X₀: 2⋅X₂ {O(n)}
t₂₀, X₁: X₂+X₄ {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: X₄ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₂, X₀: X₂ {O(n)}
t₂₂, X₁: X₂+X₄ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₀: X₂ {O(n)}
t₂₃, X₁: X₂ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: 2⋅X₂ {O(n)}
t₂₄, X₁: X₂+X₄ {O(n)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}