Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
t₄: f2(X₀, X₁, X₂) → f300(X₀, X₁, X₂)
t₁: f300(X₀, X₁, X₂) → f1(X₀, X₁, D) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀+X₁ ≤ 0
t₂: f300(X₀, X₁, X₂) → f1(X₀, X₁, D) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₃: f300(X₀, X₁, X₂) → f1(X₀, X₁, D) :|: X₁ ≤ 0
t₀: f300(X₀, X₁, X₂) → f300(X₀-1, X₀-2, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁

Preprocessing

Cut unsatisfiable transition [t₁: f300→f1]

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

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₁₂: f2(X₀, X₁) → f300(X₀, X₁)
t₁₃: f300(X₀, X₁) → f1(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₄: f300(X₀, X₁) → f1(X₀, X₁) :|: X₁ ≤ 0
t₁₅: f300(X₀, X₁) → f300(X₀-1, X₀-2) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁

MPRF for transition t₁₅: f300(X₀, X₁) → f300(X₀-1, X₀-2) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

• f300: [X₀]

All Bounds

Timebounds

Overall timebound:X₀+3 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₀ {O(n)}

Costbounds

Overall costbound: X₀+3 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₀ {O(n)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 2⋅X₀ {O(n)}
t₁₄, X₁: 2⋅X₀+X₁ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: 2⋅X₀ {O(n)}