Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f0, f5, f7
Transitions:
t₀: f0(X₀, X₁, X₂) → f5(X₀, 0, X₂) :|: 128 ≤ X₀
t₁: f0(X₀, X₁, X₂) → f7(X₀, 0, D) :|: X₀ ≤ 127
t₃: f7(X₀, X₁, X₂) → f5(X₀, X₁, X₂) :|: 36 ≤ X₁
t₂: f7(X₀, X₁, X₂) → f7(X₀, 1+X₁, 1+X₂) :|: X₁ ≤ 35

Preprocessing

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

Found invariant X₁ ≤ 36 ∧ 0 ≤ X₁ for location f5

Found invariant X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127 for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f5, f7
Transitions:
t₇: f0(X₀, X₁) → f5(X₀, 0) :|: 128 ≤ X₀
t₈: f0(X₀, X₁) → f7(X₀, 0) :|: X₀ ≤ 127
t₉: f7(X₀, X₁) → f5(X₀, X₁) :|: 36 ≤ X₁ ∧ X₀+X₁ ≤ 163 ∧ X₀ ≤ 127 ∧ X₀ ≤ 127+X₁ ∧ X₁ ≤ 36 ∧ 0 ≤ X₁
t₁₀: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: X₁ ≤ 35 ∧ X₀+X₁ ≤ 163 ∧ X₀ ≤ 127 ∧ X₀ ≤ 127+X₁ ∧ X₁ ≤ 36 ∧ 0 ≤ X₁

MPRF for transition t₁₀: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: X₁ ≤ 35 ∧ X₀+X₁ ≤ 163 ∧ X₀ ≤ 127 ∧ X₀ ≤ 127+X₁ ∧ X₁ ≤ 36 ∧ 0 ≤ X₁ of depth 1:

new bound:

37 {O(1)}

MPRF:

• f7: [37-X₁]

All Bounds

Timebounds

Overall timebound:40 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 37 {O(1)}

Costbounds

Overall costbound: 40 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 37 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: 0 {O(1)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 36 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 36 {O(1)}