Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(F, F, 10, 0, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, F) :|: X₃+1 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃

Preprocessing

Eliminate variables {F,X₀,X₁,X₄} that do not contribute to the problem

Found invariant X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 10 ≤ X₃ ∧ 20 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂ for location l2

Found invariant X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 0 ≤ X₃ ∧ 10 ≤ X₂+X₃ ∧ X₂ ≤ 10+X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₂, X₃) → l1(10, 0)
t₈: l1(X₂, X₃) → l1(X₂, X₃+1) :|: X₃+1 ≤ X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 0 ≤ X₃ ∧ 10 ≤ X₂+X₃ ∧ X₂ ≤ 10+X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂
t₉: l1(X₂, X₃) → l2(X₂, X₃) :|: X₂ ≤ X₃ ∧ X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 0 ≤ X₃ ∧ 10 ≤ X₂+X₃ ∧ X₂ ≤ 10+X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂

Found invariant X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 10 ≤ X₃ ∧ 20 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂ for location l2

Found invariant X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 0 ≤ X₃ ∧ 10 ≤ X₂+X₃ ∧ X₂ ≤ 10+X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 26 {O(1)}

TWN-Loops:

entry: t₇: l0(X₂, X₃) → l1(10, 0)
results in twn-loop: twn:Inv: [X₃ ≤ 10 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 20 ∧ 0 ≤ X₃ ∧ 10 ≤ X₂+X₃ ∧ X₂ ≤ 10+X₃ ∧ X₂ ≤ 10 ∧ 10 ≤ X₂] , (X₂,X₃) -> (X₂,X₃+1) :|: X₃+1 ≤ X₂
order: [X₂; X₃]
closed-form:
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₃+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₂ ∧ X₂ ≤ X₃+1

Stabilization-Threshold for: X₃+1 ≤ X₂
alphas_abs: X₃+1+X₂
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₇:
X₂: 10 {O(1)}
X₃: 0 {O(1)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 26 {O(1)}

26 {O(1)}

All Bounds

Timebounds

Overall timebound:28 {O(1)}
t₇: 1 {O(1)}
t₈: 26 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 28 {O(1)}
t₇: 1 {O(1)}
t₈: 26 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₂: 10 {O(1)}
t₇, X₃: 0 {O(1)}
t₈, X₂: 10 {O(1)}
t₈, X₃: 10 {O(1)}
t₉, X₂: 10 {O(1)}
t₉, X₃: 10 {O(1)}