Initial Problem

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

Preprocessing

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location l3

Problem after Preprocessing

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

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₃+4 {O(n)}

TWN-Loops:

entry: t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
results in twn-loop: twn: (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂+X₃,X₃-1) :|: 1 ≤ X₃
order: [X₃]
closed-form:
X₃: X₃ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1

Stabilization-Threshold for: 1 ≤ X₃
alphas_abs: X₃
M: 0
N: 1
Bound: 2⋅X₃+2 {O(n)}

relevant size-bounds w.r.t. t₀:
X₃: X₃ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₃+4 {O(n)}

2⋅X₃+4 {O(n)}

Analysing control-flow refined program

Found invariant X₃ ≤ 0 for location l2

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

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

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l2___1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l3___2

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₃+4 {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}
t₄: inf {Infinity}
t₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₃+4 {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}
t₄: inf {Infinity}
t₅: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 4⋅X₃⋅X₃+10⋅X₃+X₂ {O(n^2)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 4⋅X₃⋅X₃+10⋅X₃+2⋅X₂ {O(n^2)}
t₂, X₃: 2⋅X₃ {O(n)}
t₃, X₀: 8⋅X₃⋅X₃+20⋅X₃+4⋅X₂ {O(n^2)}
t₃, X₁: 8⋅X₃⋅X₃+20⋅X₃+4⋅X₂ {O(n^2)}
t₃, X₂: 4⋅X₃⋅X₃+10⋅X₃+2⋅X₂ {O(n^2)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₂: 4⋅X₃⋅X₃+10⋅X₃+2⋅X₂ {O(n^2)}
t₄, X₃: 2⋅X₃ {O(n)}
t₅, X₂: 4⋅X₃⋅X₃+10⋅X₃+2⋅X₂ {O(n^2)}
t₅, X₃: 2⋅X₃ {O(n)}