Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆
Temp_Vars: R, S
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l1(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, 0, X₁₅, X₁₆)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l2(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₀ ≤ 9
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l3(X₀, X₁, 0, X₃, 0, 0, 0, 0, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, 1000) :|: 10 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l1(X₀+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l2(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, S, S, X₁₆) :|: X₁ ≤ 9
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₂ ≤ 9
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₄, X₅, X₆, X₇, 1500, S, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₂
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, X₃+1, X₄+S, X₅+1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9 ∧ R+1 ≤ 0
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆+S, X₇+1, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9
Preprocessing
Eliminate variables {S,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆} that do not contribute to the problem
Found invariant X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l4
Found invariant 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: R
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₂₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₂₄: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃) :|: 10 ≤ X₀ ∧ 0 ≤ X₀
t₂₆: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₂₈: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 10 ≤ X₂ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₃₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 10 ≤ X₃ ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₂₉: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ R+1 ≤ 0 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₃₀: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF:
l2 [9-X₀ ]
l1 [10-X₀ ]
MPRF for transition t₂₅: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
100 {O(1)}
MPRF:
l2 [10-X₁ ]
l1 [-X₁ ]
MPRF for transition t₂₆: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF:
l2 [1 ]
l1 [0 ]
MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF:
l4 [9-X₂ ]
l3 [10-X₂ ]
MPRF for transition t₂₉: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ R+1 ≤ 0 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:
new bound:
110 {O(1)}
MPRF:
l4 [X₀+1-X₃ ]
l3 [X₀-X₃ ]
MPRF for transition t₃₀: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:
new bound:
110 {O(1)}
MPRF:
l4 [X₀+1-X₃ ]
l3 [X₀-X₃ ]
MPRF for transition t₃₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 10 ≤ X₃ ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:
new bound:
100 {O(1)}
MPRF:
l4 [X₀ ]
l3 [X₀+1-2⋅X₂ ]
All Bounds
Timebounds
Overall timebound:453 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 10 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 100 {O(1)}
t₂₆: 10 {O(1)}
t₂₇: 10 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 110 {O(1)}
t₃₀: 110 {O(1)}
t₃₁: 100 {O(1)}
Costbounds
Overall costbound: 453 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 10 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 100 {O(1)}
t₂₆: 10 {O(1)}
t₂₇: 10 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 110 {O(1)}
t₃₀: 110 {O(1)}
t₃₁: 100 {O(1)}
Sizebounds
t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: 9 {O(1)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: 10 {O(1)}
t₂₄, X₁: 10 {O(1)}
t₂₄, X₂: 0 {O(1)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: 9 {O(1)}
t₂₅, X₁: 10 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: 10 {O(1)}
t₂₆, X₁: 10 {O(1)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: 10 {O(1)}
t₂₇, X₁: 10 {O(1)}
t₂₇, X₂: 9 {O(1)}
t₂₇, X₃: 0 {O(1)}
t₂₈, X₀: 10 {O(1)}
t₂₈, X₁: 10 {O(1)}
t₂₈, X₂: 38 {O(1)}
t₂₈, X₃: 10 {O(1)}
t₂₉, X₀: 10 {O(1)}
t₂₉, X₁: 10 {O(1)}
t₂₉, X₂: 18 {O(1)}
t₂₉, X₃: 10 {O(1)}
t₃₀, X₀: 10 {O(1)}
t₃₀, X₁: 10 {O(1)}
t₃₀, X₂: 18 {O(1)}
t₃₀, X₃: 10 {O(1)}
t₃₁, X₀: 10 {O(1)}
t₃₁, X₁: 10 {O(1)}
t₃₁, X₂: 38 {O(1)}
t₃₁, X₃: 10 {O(1)}