Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₁
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 0
t₀: l1(X₀, X₁, X₂) → l1(X₀-X₁, 1+X₁, X₂) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀ ≤ 0

Preprocessing

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

Found invariant 1 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁
t₈: l0(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₉: l1(X₀, X₁) → l1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁

MPRF for transition t₉: l1(X₀, X₁) → l1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+3 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: X₀+3 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₉, X₁: X₀+X₁ {O(n)}
t₁₀, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₁+X₀ {O(n)}