Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₁

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₁

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀+X₂ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₂ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₂ {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 2⋅X₁+X₀ {O(n)}
t₀, X₂: 2⋅X₂+X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅X₁+X₀ {O(n)}
t₁, X₂: 2⋅X₂+X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}