Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(0, C)
t₁: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 49
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 50 ≤ X₀

Preprocessing

Eliminate variables {C,X₁} that do not contribute to the problem

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location l2

Found invariant X₀ ≤ 50 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀) → l1(0)
t₈: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 49 ∧ X₀ ≤ 50 ∧ 0 ≤ X₀
t₉: l1(X₀) → l2(X₀) :|: 50 ≤ X₀ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location l2

Found invariant X₀ ≤ 50 ∧ 0 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 102 {O(1)}

TWN-Loops:

entry: t₇: l0(X₀) → l1(0)
results in twn-loop: twn:Inv: [X₀ ≤ 50 ∧ 0 ≤ X₀] , (X₀) -> (X₀+1) :|: X₀ ≤ 49
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 49 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 49 ∧ 49 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 49
alphas_abs: 49
M: 0
N: 1
Bound: 100 {O(1)}

relevant size-bounds w.r.t. t₇:
Runtime-bound of t₇: 1 {O(1)}
Results in: 102 {O(1)}

102 {O(1)}

All Bounds

Timebounds

Overall timebound:104 {O(1)}
t₇: 1 {O(1)}
t₈: 102 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 104 {O(1)}
t₇: 1 {O(1)}
t₈: 102 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₀: 0 {O(1)}
t₈, X₀: 50 {O(1)}
t₉, X₀: 50 {O(1)}