Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₁: l1→l1

Cut unsatisfiable transition t₂: l1→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀+1 ≤ X₁ ∧ X₀ ≤ X₁

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

new bound:

X₀+X₁ {O(n)}

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

new bound:

X₀+X₁+1 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2 {O(n)}
t₀: X₀+X₁ {O(n)}
t₃: X₀+X₁+1 {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2 {O(n)}
t₀: X₀+X₁ {O(n)}
t₃: X₀+X₁+1 {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 2⋅X₁+X₀ {O(n)}
t₃, X₀: 2⋅X₀+X₁+1 {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}