Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+4, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+2, X₂, X₃)

Preprocessing

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

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

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+4, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+2, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁

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

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

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

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₂+2⋅X₃+4 {O(n)}

TWN-Loops:

entry: t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
results in twn-loop: twn:Inv: [X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁+4,X₂,X₃) :|: X₁ < X₀
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * 4 * n^1
X₂: X₂
X₃: X₃

Termination: true
Formula:

4 < 0
∨ 4 < 0 ∧ 1+X₁ < X₀ ∧ 4 ≤ 0 ∧ 0 ≤ 4
∨ 4 < 0 ∧ 4 ≤ 0 ∧ 0 ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₁ < X₀ ∧ 4 ≤ 0 ∧ 0 ≤ 4 ∧ 4 < 0
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 4 ≤ 0 ∧ 0 ≤ 4
∨ X₁ < X₀ ∧ 4 ≤ 0 ∧ 0 ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁

Stabilization-Threshold for: X₁ < X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+4 {O(n)}

2⋅X₂+2⋅X₃+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 2⋅X₂+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+4 {O(n)}

2⋅X₂+2⋅X₃+4 {O(n)}

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

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

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

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

Analysing control-flow refined program

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___2

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l4___4

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l1___3

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ 3+X₃ ∧ X₀ ≤ X₃ ∧ 4+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ 3+X₀ ∧ X₀ ≤ X₁ for location n_l4___1

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

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

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___2

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l4___4

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l1___3

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ 3+X₃ ∧ X₀ ≤ X₃ ∧ 4+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ 3+X₀ ∧ X₀ ≤ X₁ for location n_l4___1

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

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

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: 2⋅X₂+2⋅X₃+4 {O(n)}
t₃: inf {Infinity}
t₁: 1 {O(1)}
t₄: 2⋅X₂+2⋅X₃+4 {O(n)}
t₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: 2⋅X₂+2⋅X₃+4 {O(n)}
t₃: inf {Infinity}
t₁: 1 {O(1)}
t₄: 2⋅X₂+2⋅X₃+4 {O(n)}
t₅: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₃ {O(n)}
t₂, X₁: 8⋅X₃+9⋅X₂+16 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: 8⋅X₃+9⋅X₂+16 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}