Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₂: l1→l1

Problem after Preprocessing

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

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₂+1 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: X₂+1 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₁, X₂: 2⋅X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}