Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁+(X₂)³, X₂+1) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂) :|: 0 < X₁

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁+(X₂)³, X₂+1) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂) :|: 0 < X₁ ∧ X₀ ≤ 0

Found invariant X₀ ≤ 0 for location l2

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₀+4 {O(n)}

TWN-Loops:

entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁+(X₂)³,X₂+1) :|: 0 < X₀
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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

relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}

2⋅X₀+4 {O(n)}

Found invariant X₀ ≤ 0 for location l2

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

Found invariant X₀ ≤ 0 for location l2

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₂: 2⋅X₀+X₂+4 {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₂: 2⋅X₀+2⋅X₂+4 {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₂: 2⋅X₀+2⋅X₂+4 {O(n)}