Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀
t₂: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀

Preprocessing

Found invariant 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀
t₂: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant 0 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₀+208 {O(n)}

TWN-Loops:

entry: t₁: l0(X₀) → l1(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀] , (X₀) -> (X₀-1) :|: 1 ≤ X₀
entry: t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀] , (X₀) -> (X₀-1) :|: 1 ≤ X₀
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₁:
X₀: 100 {O(1)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 204 {O(1)}

order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

Stabilization-Threshold for: 1 ≤ 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+208 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+210 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀+208 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+210 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀+208 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: 100 {O(1)}
t₂, X₀: X₀+100 {O(n)}