Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₅: l3→l1

Cut unsatisfiable transition t₆: l3→l1

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

Found invariant X₂ ≤ X₁ for location l1

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

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₁, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁

MPRF for transition t₇: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₂ ]
l1 [X₂ ]

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 X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l4

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}

TWN-Loops:

entry: t₇: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁] , (X₀,X₁,X₂,X₃) -> (X₀-1,X₁,X₂,X₃) :|: 0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀
entry: t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₁, X₃)
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁] , (X₀,X₁,X₂,X₃) -> (X₀-1,X₁,X₂,X₃) :|: 0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

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

Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₇:
X₀: X₁ {O(n)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 2⋅X₁⋅X₁+5⋅X₁ {O(n^2)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}

2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}

relevant size-bounds w.r.t. t₇:
X₀: X₁ {O(n)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 2⋅X₁⋅X₁+5⋅X₁ {O(n^2)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}

2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+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 X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___6

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

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

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

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

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

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1

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

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

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l3___7

MPRF for transition t₇₀: n_l1___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

4⋅X₁+2 {O(n)}

MPRF:

n_l3___1 [2⋅X₂-2 ]
n_l3___3 [2⋅X₂ ]
n_l1___2 [2⋅X₂ ]
n_l1___5 [2⋅X₂ ]
n_l3___4 [2⋅X₂-2 ]
n_l1___6 [2⋅X₂-2 ]

MPRF for transition t₇₁: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___3 [X₂ ]
n_l1___2 [X₂ ]
n_l1___5 [X₂+1 ]
n_l3___4 [X₂ ]
n_l1___6 [X₂ ]

MPRF for transition t₇₄: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___3 [X₂ ]
n_l1___2 [X₂ ]
n_l1___5 [X₂ ]
n_l3___4 [X₂-1 ]
n_l1___6 [X₂-1 ]

MPRF for transition t₇₅: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀-1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

n_l3___1 [X₂-1 ]
n_l3___3 [X₂ ]
n_l1___2 [X₂-1 ]
n_l1___5 [X₂ ]
n_l3___4 [X₂-1 ]
n_l1___6 [X₂-1 ]

MPRF for transition t₇₆: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___5(X₁, X₁, X₂-1, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___3 [X₂ ]
n_l1___2 [X₂ ]
n_l1___5 [X₂ ]
n_l3___4 [X₂ ]
n_l1___6 [X₂ ]

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___6

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___4

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

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

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

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

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ X₁ ≤ 1 for location l4

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

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l3___7

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___6

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___4

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___3

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___5

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l4

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₇₂ 12⋅X₁⋅X₁+2⋅X₃+20⋅X₁+14 {O(n^2)}

TWN-Loops:

entry: t₇₉: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀-1,X₁,X₂,X₃) :|: X₂ ≤ X₁ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂
entry: t₇₄: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀-1,X₁,X₂,X₃) :|: X₂ ≤ X₁ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₇₉:
X₀: X₃ {O(n)}
Runtime-bound of t₇₉: 1 {O(1)}
Results in: 2⋅X₃+7 {O(n)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

relevant size-bounds w.r.t. t₇₄:
X₀: 3⋅X₁ {O(n)}
Runtime-bound of t₇₄: 2⋅X₁+1 {O(n)}
Results in: 12⋅X₁⋅X₁+20⋅X₁+7 {O(n^2)}

12⋅X₁⋅X₁+2⋅X₃+20⋅X₁+14 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₇₇ 12⋅X₁⋅X₁+2⋅X₃+20⋅X₁+14 {O(n^2)}

relevant size-bounds w.r.t. t₇₉:
X₀: X₃ {O(n)}
Runtime-bound of t₇₉: 1 {O(1)}
Results in: 2⋅X₃+7 {O(n)}

relevant size-bounds w.r.t. t₇₄:
X₀: 3⋅X₁ {O(n)}
Runtime-bound of t₇₄: 2⋅X₁+1 {O(n)}
Results in: 12⋅X₁⋅X₁+20⋅X₁+7 {O(n^2)}

12⋅X₁⋅X₁+2⋅X₃+20⋅X₁+14 {O(n^2)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₁⋅X₁+11⋅X₁+4⋅X₃+14 {O(n^2)}
t₀: 1 {O(1)}
t₂: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁⋅X₁+11⋅X₁+4⋅X₃+14 {O(n^2)}
t₀: 1 {O(1)}
t₂: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₁+X₃ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₁+X₃ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₁ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₁ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: X₁+X₃ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: X₃ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₁+X₃ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₁ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}