Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 ≤ X₂
t₃: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
t₄: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁

Preprocessing

Cut unsatisfiable transition t₂: l1→l1

Cut unsatisfiable transition t₄: l1→l1

Cut unsatisfiable transition t₅: l1→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁

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

new bound:

X₀+X₁ {O(n)}

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

new bound:

X₀+X₁ {O(n)}

MPRF for transition t₃: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+X₂ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+3⋅X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₁ {O(n)}
t₃: X₁+X₂ {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+3⋅X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₁ {O(n)}
t₃: X₁+X₂ {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₃, X₀: 4⋅X₁+7⋅X₀ {O(n)}
t₃, X₁: 3⋅X₁ {O(n)}
t₃, X₂: 4⋅X₂+X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}