Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₄: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
t₅: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0

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
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0

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

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

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

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

MPRF for transition t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₁ ]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₀, X₀: 2⋅X₀ {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₃, X₀: 5⋅X₀ {O(n)}
t₃, X₁: 5⋅X₁ {O(n)}