Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(1, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, 1, X₂) :|: X₀ ≤ 5
t₁₀: l1(X₀, X₁, X₂) → l3(1, X₁, X₂) :|: 6 ≤ X₀
t₉: l2(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 6 ≤ X₁
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₁ ≤ 5
t₃: l3(X₀, X₁, X₂) → l4(X₀, 1, X₂) :|: X₀ ≤ 5
t₈: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 6 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l3(X₀+1, X₁, X₂) :|: 6 ≤ X₁
t₄: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: X₁ ≤ 5
t₆: l6(X₀, X₁, X₂) → l4(X₀, X₁+1, X₂) :|: 6 ≤ X₂
t₅: l6(X₀, X₁, X₂) → l6(X₀, X₁, X₂+1) :|: X₂ ≤ 5
Preprocessing
Found invariant X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 ∧ 1 ≤ X₀ for location l2
Found invariant X₂ ≤ 6 ∧ X₂ ≤ 5+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ 5+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 5 ∧ X₁ ≤ 4+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 6 ≤ X₀ for location l5
Found invariant X₀ ≤ 6 ∧ 1 ≤ X₀ for location l1
Found invariant X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(1, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, 1, X₂) :|: X₀ ≤ 5 ∧ X₀ ≤ 6 ∧ 1 ≤ X₀
t₁₀: l1(X₀, X₁, X₂) → l3(1, X₁, X₂) :|: 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 6 ≤ X₁ ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 ∧ 1 ≤ X₀
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₁ ≤ 5 ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 ∧ 1 ≤ X₀
t₃: l3(X₀, X₁, X₂) → l4(X₀, 1, X₂) :|: X₀ ≤ 5 ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 6 ≤ X₀ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l3(X₀+1, X₁, X₂) :|: 6 ≤ X₁ ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: X₁ ≤ 5 ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l6(X₀, X₁, X₂) → l4(X₀, X₁+1, X₂) :|: 6 ≤ X₂ ∧ X₂ ≤ 6 ∧ X₂ ≤ 5+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ 5+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 5 ∧ X₁ ≤ 4+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l6(X₀, X₁, X₂) → l6(X₀, X₁, X₂+1) :|: X₂ ≤ 5 ∧ X₂ ≤ 6 ∧ X₂ ≤ 5+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ 5+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 5 ∧ X₁ ≤ 4+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₁: l1(X₀, X₁, X₂) → l2(X₀, 1, X₂) :|: X₀ ≤ 5 ∧ X₀ ≤ 6 ∧ 1 ≤ X₀ of depth 1:
new bound:
8 {O(1)}
MPRF:
l2 [6-X₀ ]
l1 [7-X₀ ]
MPRF for transition t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₁ ≤ 5 ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 ∧ 1 ≤ X₀ of depth 1:
new bound:
36 {O(1)}
MPRF:
l2 [32-5⋅X₀-X₁ ]
l1 [31-5⋅X₀ ]
MPRF for transition t₉: l2(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 6 ≤ X₁ ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 5 ∧ 1 ≤ X₀ of depth 1:
new bound:
7 {O(1)}
MPRF:
l2 [6-X₀ ]
l1 [6-X₀ ]
MPRF for transition t₃: l3(X₀, X₁, X₂) → l4(X₀, 1, X₂) :|: X₀ ≤ 5 ∧ 1 ≤ X₀ of depth 1:
new bound:
7 {O(1)}
MPRF:
l3 [6-X₀ ]
l6 [5-X₀ ]
l4 [5-X₀ ]
MPRF for transition t₄: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: X₁ ≤ 5 ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
49 {O(1)}
MPRF:
l3 [-X₁ ]
l6 [5-X₁ ]
l4 [6-X₁ ]
MPRF for transition t₇: l4(X₀, X₁, X₂) → l3(X₀+1, X₁, X₂) :|: 6 ≤ X₁ ∧ X₁ ≤ 6 ∧ X₁ ≤ 5+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
7 {O(1)}
MPRF:
l3 [4-2⋅X₀ ]
l6 [1 ]
l4 [1 ]
MPRF for transition t₅: l6(X₀, X₁, X₂) → l6(X₀, X₁, X₂+1) :|: X₂ ≤ 5 ∧ X₂ ≤ 6 ∧ X₂ ≤ 5+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ 5+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 5 ∧ X₁ ≤ 4+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
252 {O(1)}
MPRF:
l3 [-5⋅X₁ ]
l6 [32-5⋅X₁-X₂ ]
l4 [31-5⋅X₁ ]
MPRF for transition t₆: l6(X₀, X₁, X₂) → l4(X₀, X₁+1, X₂) :|: 6 ≤ X₂ ∧ X₂ ≤ 6 ∧ X₂ ≤ 5+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ 5+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 4+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 5 ∧ X₁ ≤ 4+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
49 {O(1)}
MPRF:
l3 [-X₁ ]
l6 [6-X₁ ]
l4 [6-X₁ ]
All Bounds
Timebounds
Overall timebound:418 {O(1)}
t₀: 1 {O(1)}
t₁: 8 {O(1)}
t₁₀: 1 {O(1)}
t₂: 36 {O(1)}
t₉: 7 {O(1)}
t₃: 7 {O(1)}
t₈: 1 {O(1)}
t₄: 49 {O(1)}
t₇: 7 {O(1)}
t₅: 252 {O(1)}
t₆: 49 {O(1)}
Costbounds
Overall costbound: 418 {O(1)}
t₀: 1 {O(1)}
t₁: 8 {O(1)}
t₁₀: 1 {O(1)}
t₂: 36 {O(1)}
t₉: 7 {O(1)}
t₃: 7 {O(1)}
t₈: 1 {O(1)}
t₄: 49 {O(1)}
t₇: 7 {O(1)}
t₅: 252 {O(1)}
t₆: 49 {O(1)}
Sizebounds
t₀, X₀: 1 {O(1)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 5 {O(1)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁₀, X₀: 1 {O(1)}
t₁₀, X₁: 6 {O(1)}
t₁₀, X₂: X₂ {O(n)}
t₂, X₀: 5 {O(1)}
t₂, X₁: 6 {O(1)}
t₂, X₂: X₂ {O(n)}
t₉, X₀: 6 {O(1)}
t₉, X₁: 6 {O(1)}
t₉, X₂: X₂ {O(n)}
t₃, X₀: 5 {O(1)}
t₃, X₁: 1 {O(1)}
t₃, X₂: X₂+6 {O(n)}
t₈, X₀: 6 {O(1)}
t₈, X₁: 6 {O(1)}
t₈, X₂: 6 {O(1)}
t₄, X₀: 5 {O(1)}
t₄, X₁: 5 {O(1)}
t₄, X₂: 1 {O(1)}
t₇, X₀: 6 {O(1)}
t₇, X₁: 6 {O(1)}
t₇, X₂: 6 {O(1)}
t₅, X₀: 5 {O(1)}
t₅, X₁: 5 {O(1)}
t₅, X₂: 6 {O(1)}
t₆, X₀: 5 {O(1)}
t₆, X₁: 6 {O(1)}
t₆, X₂: 6 {O(1)}