Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(0, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 99
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₀-2, X₂, X₀-2, X₄, X₅, X₆) :|: X₀+1 ≤ 0 ∧ 100 ≤ X₀
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₀-2, X₄, X₅, X₆) :|: 100 ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆) :|: H+1 ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆)
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₁, X₁, X₄, X₁, H) :|: I+1 ≤ 0
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₁, X₁, X₄, X₁, H)
t₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₁, X₄, X₁, H)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆) :|: H+1 ≤ 0
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆)
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₂, X₂, X₅, X₆)

Preprocessing

Cut unsatisfiable transition t₁₃: l1→l2

Cut unreachable locations [l2; l3] from the program graph

Eliminate variables {X₁,X₂,X₃,X₄,X₅,X₆} that do not contribute to the problem

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

Found invariant X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l4
Transitions:
t₃₂: l0(X₀) → l1(0)
t₃₃: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 99 ∧ X₀ ≤ 100 ∧ 0 ≤ X₀
t₃₄: l1(X₀) → l4(X₀) :|: 100 ≤ X₀ ∧ X₀ ≤ 100 ∧ 0 ≤ X₀

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

Found invariant X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₃₃ 202 {O(1)}

TWN-Loops:

entry: t₃₂: l0(X₀) → l1(0)
results in twn-loop: twn:Inv: [X₀ ≤ 100 ∧ 0 ≤ X₀] , (X₀) -> (X₀+1) :|: X₀ ≤ 99
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 99 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 99 ∧ 99 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 99
alphas_abs: 99
M: 0
N: 1
Bound: 200 {O(1)}

relevant size-bounds w.r.t. t₃₂:
Runtime-bound of t₃₂: 1 {O(1)}
Results in: 202 {O(1)}

202 {O(1)}

All Bounds

Timebounds

Overall timebound:204 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 202 {O(1)}
t₃₄: 1 {O(1)}

Costbounds

Overall costbound: 204 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 202 {O(1)}
t₃₄: 1 {O(1)}

Sizebounds

t₃₂, X₀: 0 {O(1)}
t₃₃, X₀: 100 {O(1)}
t₃₄, X₀: 100 {O(1)}