Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
t₃: f1(X₀, X₁, X₂) → f2(X₀, X₁, X₂)
t₀: f2(X₀, X₁, X₂) → f2(1+X₀, 1+X₁, X₂) :|: X₀ ≤ 1
t₁: f2(X₀, X₁, X₂) → f2(1+X₀, 1+X₁, X₂) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₂: f2(X₀, X₁, X₂) → f300(X₀, X₁, D) :|: 2 ≤ X₀ ∧ 3 ≤ X₁

Preprocessing

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

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f300

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₁₀: f1(X₀, X₁) → f2(X₀, X₁)
t₁₁: f2(X₀, X₁) → f2(1+X₀, 1+X₁) :|: X₀ ≤ 1
t₁₂: f2(X₀, X₁) → f2(1+X₀, 1+X₁) :|: X₁ ≤ 2 ∧ 2 ≤ X₀
t₁₃: f2(X₀, X₁) → f300(X₀, X₁) :|: 2 ≤ X₀ ∧ 3 ≤ X₁

MPRF for transition t₁₁: f2(X₀, X₁) → f2(1+X₀, 1+X₁) :|: X₀ ≤ 1 of depth 1:

new bound:

X₀+2 {O(n)}

• f2: [2-X₀]

MPRF for transition t₁₂: f2(X₀, X₁) → f2(1+X₀, 1+X₁) :|: X₁ ≤ 2 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁+3 {O(n)}

• f2: [3-X₁]

All Bounds

Timebounds

Overall timebound:X₀+X₁+7 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀+2 {O(n)}
t₁₂: X₁+3 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+7 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀+2 {O(n)}
t₁₂: X₁+3 {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₀+2 {O(n)}
t₁₁, X₁: X₀+X₁+2 {O(n)}
t₁₂, X₀: 3⋅X₀+X₁+5 {O(n)}
t₁₂, X₁: 3⋅X₁+X₀+5 {O(n)}
t₁₃, X₀: 6⋅X₀+X₁+7 {O(n)}
t₁₃, X₁: 2⋅X₀+5⋅X₁+7 {O(n)}