Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0
t₂: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ 0 ∧ 1 ≤ X₁
t₃: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ 0 ∧ X₁+1 ≤ 0
t₄: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₅: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀+1 ≤ 0 ∧ 2 ≤ X₀+X₁
t₆: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₇: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀+1 ≤ 0 ∧ 2 ≤ X₀+X₁
t₈: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁
t₉: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁+1 ≤ 0
t₁₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
t₁₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁+1 ≤ 0
t₁₂: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁+X₀+1 ≤ 0
t₁₃: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0
t₁₄: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ X₁+2 ≤ 0 ∧ 1 ≤ X₀ ∧ X₁+X₀+1 ≤ 0
t₁₅: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ X₁+2 ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0
t₁₆: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁
t₁₇: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁+1 ≤ 0
t₁₈: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ X₀+2 ≤ 0 ∧ 1 ≤ X₁
t₁₉: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ X₀+2 ≤ 0 ∧ X₁+1 ≤ 0

Preprocessing

Cut unsatisfiable transition t₅: l1→l1

Cut unsatisfiable transition t₇: l1→l1

Cut unsatisfiable transition t₈: l1→l1

Cut unsatisfiable transition t₁₀: l1→l1

Cut unsatisfiable transition t₁₂: l1→l1

Cut unsatisfiable transition t₁₄: l1→l1

Cut unsatisfiable transition t₁₇: l1→l1

Cut unsatisfiable transition t₁₉: l1→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0
t₂: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ 0 ∧ 1 ≤ X₁
t₃: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ 0 ∧ X₁+1 ≤ 0
t₄: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₆: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₉: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁+1 ≤ 0
t₁₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁+1 ≤ 0
t₁₃: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0
t₁₅: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ X₁+2 ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0
t₁₆: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁
t₁₈: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ X₀+2 ≤ 0 ∧ 1 ≤ X₁

MPRF for transition t₄: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

3⋅X₁ {O(n)}

MPRF:

l1 [X₁ ]

MPRF for transition t₆: l1(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁ {O(n)}

MPRF:

l1 [X₀+X₁ ]

MPRF for transition t₉: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁+1 ≤ 0 of depth 1:

new bound:

3⋅X₀ {O(n)}

MPRF:

l1 [X₀ ]

MPRF for transition t₁₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁+1 ≤ 0 of depth 1:

new bound:

2⋅X₀+2⋅X₁ {O(n)}

MPRF:

l1 [X₀-X₁ ]

MPRF for transition t₁₃: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0 of depth 1:

new bound:

2⋅X₀+2⋅X₁ {O(n)}

MPRF:

l1 [-X₀-X₁ ]

MPRF for transition t₁₅: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₀ ≤ X₁ ∧ X₁+2 ≤ 0 ∧ X₀+1 ≤ 0 ∧ X₁+X₀+1 ≤ 0 of depth 1:

new bound:

3⋅X₁ {O(n)}

MPRF:

l1 [-X₁ ]

MPRF for transition t₁₆: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁ {O(n)}

MPRF:

l1 [X₁-X₀ ]

MPRF for transition t₁₈: l1(X₀, X₁) → l1(X₀+1, X₁) :|: 0 ≤ X₁+X₀ ∧ X₀+1 ≤ X₁ ∧ X₀+2 ≤ 0 ∧ 1 ≤ X₁ of depth 1:

new bound:

3⋅X₀ {O(n)}

MPRF:

l1 [-X₀ ]

All Bounds

Timebounds

Overall timebound:14⋅X₀+14⋅X₁+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 3⋅X₁ {O(n)}
t₆: 2⋅X₀+2⋅X₁ {O(n)}
t₉: 3⋅X₀ {O(n)}
t₁₁: 2⋅X₀+2⋅X₁ {O(n)}
t₁₃: 2⋅X₀+2⋅X₁ {O(n)}
t₁₅: 3⋅X₁ {O(n)}
t₁₆: 2⋅X₀+2⋅X₁ {O(n)}
t₁₈: 3⋅X₀ {O(n)}

Costbounds

Overall costbound: 14⋅X₀+14⋅X₁+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 3⋅X₁ {O(n)}
t₆: 2⋅X₀+2⋅X₁ {O(n)}
t₉: 3⋅X₀ {O(n)}
t₁₁: 2⋅X₀+2⋅X₁ {O(n)}
t₁₃: 2⋅X₀+2⋅X₁ {O(n)}
t₁₅: 3⋅X₁ {O(n)}
t₁₆: 2⋅X₀+2⋅X₁ {O(n)}
t₁₈: 3⋅X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: 2⋅X₁+4⋅X₀ {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₉, X₀: 2⋅X₀ {O(n)}
t₉, X₁: 2⋅X₀+4⋅X₁ {O(n)}
t₁₁, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₁₅, X₀: 2⋅X₁+4⋅X₀ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₈, X₀: 2⋅X₀ {O(n)}
t₁₈, X₁: 2⋅X₀+4⋅X₁ {O(n)}