Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, X₁, 0, 0, 0) :|: X₁ ≤ 0
t₂: l0(X₀, X₁, X₂, X₃, X₄) → l2(1, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 0, 0, 0) :|: 101 ≤ X₀
t₀: l2(X₀, X₁, X₂, X₃, X₄) → l2(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 100 ∧ 1 ≤ X₁

Preprocessing

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀ for location l2

Found invariant X₀ ≤ 101 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀, X₁) → l1(0, X₁) :|: X₁ ≤ 0
t₈: l0(X₀, X₁) → l2(1, X₁) :|: 1 ≤ X₁
t₁₁: l2(X₀, X₁) → l1(X₀, X₁) :|: 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀
t₁₀: l2(X₀, X₁) → l2(1+X₀, X₁) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀ for location l2

Found invariant X₀ ≤ 101 ∧ 0 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 205 {O(1)}

TWN-Loops:

entry: t₈: l0(X₀, X₁) → l2(1, X₁) :|: 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 1 ≤ X₀] , (X₀,X₁) -> (1+X₀,X₁) :|: X₀ ≤ 100 ∧ 1 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 100 ∧ 100 ≤ X₀
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 100 ∧ 100 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 100
alphas_abs: 100
M: 0
N: 1
Bound: 202 {O(1)}

relevant size-bounds w.r.t. t₈:
Runtime-bound of t₈: 1 {O(1)}
Results in: 205 {O(1)}

205 {O(1)}

All Bounds

Timebounds

Overall timebound:208 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 205 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 208 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 205 {O(1)}
t₁₁: 1 {O(1)}

Sizebounds

t₈, X₀: 1 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 0 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 101 {O(1)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 101 {O(1)}
t₁₁, X₁: X₁ {O(n)}