Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, (X₀)²+X₃) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂-1, X₃) :|: 1 ≤ X₁+X₂

Preprocessing

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁₀: l1(X₀, X₁, X₂) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂) :|: 1 ≤ X₀
t₁₁: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₂: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂-1) :|: 1 ≤ X₁+X₂

MPRF for transition t₁₀: l1(X₀, X₁, X₂) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]

MPRF for transition t₁₂: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂-1) :|: 1 ≤ X₁+X₂ of depth 1:

new bound:

39⋅X₂+61⋅X₁ {O(n)}

• l2: [X₁+X₂]

All Bounds

Timebounds

Overall timebound:39⋅X₂+61⋅X₁+X₀+2 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 39⋅X₂+61⋅X₁ {O(n)}

Costbounds

Overall costbound: 39⋅X₂+61⋅X₁+X₀+2 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 39⋅X₂+61⋅X₁ {O(n)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 14⋅X₂+22⋅X₁ {O(n)}
t₁₀, X₂: 24⋅X₂+38⋅X₁ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: 14⋅X₂+23⋅X₁ {O(n)}
t₁₁, X₂: 25⋅X₂+38⋅X₁ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 53⋅X₂+84⋅X₁ {O(n)}
t₁₂, X₂: 64⋅X₂+99⋅X₁ {O(n)}