Initial Problem
Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f2
Transitions:
t₀: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
t₂: f0(X₀, X₁) → f2(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: f0(X₀, X₁) → f2(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₄: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀
t₅: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1+X₀ ≤ 0 ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀
t₆: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0
t₇: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1+X₀ ≤ 0 ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0
t₈: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀
t₉: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₀
t₁₀: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ X₀ ≤ 0
t₁₂: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1 ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₃: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₄: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1 ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ X₀ ≤ X₁
t₁₅: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ X₀ ≤ X₁
t₁₆: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
t₁₇: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
t₁₈: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ 0 ∧ 0 ≤ X₀+X₁
t₁₉: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 ∧ 0 ≤ X₀+X₁
Preprocessing
Cut unsatisfiable transition [t₅: f2→f2; t₇: f2→f2; t₈: f2→f2; t₁₀: f2→f2; t₁₂: f2→f2; t₁₄: f2→f2; t₁₇: f2→f2; t₁₉: f2→f2]
Problem after Preprocessing
Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f2
Transitions:
t₀: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
t₂: f0(X₀, X₁) → f2(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: f0(X₀, X₁) → f2(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₄: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀
t₆: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0
t₉: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₀
t₁₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ X₀ ≤ 0
t₁₃: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₅: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ X₀ ≤ X₁
t₁₆: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
t₁₈: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ 0 ∧ 0 ≤ X₀+X₁
MPRF for transition t₄: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ of depth 1:
new bound:
3⋅X₁ {O(n)}
MPRF:
• f2: [X₁]
MPRF for transition t₆: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 of depth 1:
new bound:
2⋅X₀+2⋅X₁ {O(n)}
MPRF:
• f2: [X₀+X₁]
MPRF for transition t₉: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₀ {O(n)}
MPRF:
• f2: [X₀]
MPRF for transition t₁₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: X₀+X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ X₀ ≤ 0 of depth 1:
new bound:
2⋅X₀+2⋅X₁ {O(n)}
MPRF:
• f2: [X₀-X₁]
MPRF for transition t₁₃: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₀+2⋅X₁ {O(n)}
MPRF:
• f2: [-X₀-X₁]
MPRF for transition t₁₅: f2(X₀, X₁) → f2(X₀, 1+X₁) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ X₀ ≤ X₁ of depth 1:
new bound:
3⋅X₁ {O(n)}
MPRF:
• f2: [-X₁]
MPRF for transition t₁₆: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ of depth 1:
new bound:
2⋅X₀+2⋅X₁ {O(n)}
MPRF:
• f2: [X₁-X₀]
MPRF for transition t₁₈: f2(X₀, X₁) → f2(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ 0 ∧ 0 ≤ X₀+X₁ of depth 1:
new bound:
3⋅X₀ {O(n)}
MPRF:
• f2: [-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)}