Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₃: f1(X₀, X₁, X₂, X₃, X₄) → f300(1000, X₁, X₂, X₃, X₄)
t₁: f300(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, 0, 0) :|: X₀ ≤ 100 ∧ X₁ ≤ 9
t₂: f300(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, 0, 0) :|: 10 ≤ X₁
t₀: f300(X₀, X₁, X₂, X₃, X₄) → f300(X₀-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 9 ∧ 101 ≤ X₀

Preprocessing

Eliminate variables [X₂; X₃; X₄] that do not contribute to the problem

Found invariant X₀ ≤ 1000 ∧ 100 ≤ X₀ for location f300

Found invariant X₀ ≤ 1000 for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₉: f1(X₀, X₁) → f300(1000, X₁)
t₁₀: f300(X₀, X₁) → f2(X₀, X₁) :|: X₀ ≤ 100 ∧ X₁ ≤ 9 ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₁: f300(X₀, X₁) → f2(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀
t₁₂: f300(X₀, X₁) → f300(X₀-1, X₁) :|: X₁ ≤ 9 ∧ 101 ≤ X₀ ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀

MPRF for transition t₁₂: f300(X₀, X₁) → f300(X₀-1, X₁) :|: X₁ ≤ 9 ∧ 101 ≤ X₀ ∧ X₀ ≤ 1000 ∧ 100 ≤ X₀ of depth 1:

new bound:

1000 {O(1)}

MPRF:

• f300: [X₀]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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