Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Analysing control-flow refined program

Found invariant 1+X₀ ≤ 0 for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

Found invariant 1+X₀ ≤ 0 for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₄₄ 4⋅X₀+6 {O(n)}

TWN-Loops:

entry: t₄₇: l1(X₀) → n_l1___1(X₀-1) :|: 1 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀] , (X₀) -> (X₀-1) :|: 0 ≤ X₀ ∧ 1 ≤ X₀
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₄₇:
X₀: X₀ {O(n)}
Runtime-bound of t₄₇: 1 {O(1)}
Results in: 4⋅X₀+6 {O(n)}

4⋅X₀+6 {O(n)}

Found invariant 1+X₀ ≤ 0 for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}