Initial Problem

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

Preprocessing

Eliminate variables {D,X₀,X₂} that do not contribute to the problem

Found invariant X₁ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₀: l0(X₁) → l1(X₁)
t₁₁: l1(X₁) → l1(X₁-1) :|: 1 ≤ X₁
t₁₂: l1(X₁) → l2(X₁) :|: X₁ ≤ 0
t₁₃: l2(X₁) → l2(X₁) :|: X₁ ≤ 0

Found invariant X₁ ≤ 0 for location l2

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 2⋅X₁+4 {O(n)}

TWN-Loops:

entry: t₁₀: l0(X₁) → l1(X₁)
results in twn-loop: twn: (X₁) -> (X₁-1) :|: 1 ≤ X₁
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₁₀:
X₁: X₁ {O(n)}
Runtime-bound of t₁₀: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}

2⋅X₁+4 {O(n)}

Found invariant X₁ ≤ 0 for location l2

Analysing control-flow refined program

Found invariant X₁ ≤ 0 for location l2

Found invariant X₁ ≤ 0 for location l2

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Sizebounds

t₁₀, X₁: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}