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(1000, X₁, X₂, X₃, X₄)
t₀: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 101 ≤ X₀ ∧ X₁ ≤ 9
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, 0, 0, 0) :|: X₀ ≤ 100 ∧ X₁ ≤ 9
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, 0, 0, 0) :|: 10 ≤ X₁

Preprocessing

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

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location l2

Found invariant X₀ ≤ 1000 ∧ 100 ≤ 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(1000, X₁)
t₁₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 101 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 100 ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀

MPRF for transition t₁₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 101 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀ of depth 1:

new bound:

1000 {O(1)}

All Bounds

Timebounds

Overall timebound:1003 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1000 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 1003 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1000 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Sizebounds

t₉, X₀: 1000 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 999 {O(1)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 100 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 1000 {O(1)}
t₁₂, X₁: X₁ {O(n)}