Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(0, 0, H, X₃, X₄, X₅, X₆)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, X₁, 0, 0, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₂+1 ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: 1 ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀+1, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ H+1 ≤ 0
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀+1, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ 1 ≤ H
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₀, 0, 0) :|: X₀ ≤ 9
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+1, X₀+1, H, X₃, X₄, X₅, X₆) :|: X₀ ≤ 9
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀
Preprocessing
Eliminate variables {X₁,X₃,X₄,X₅,X₆} that do not contribute to the problem
Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l2
Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l4
Found invariant 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₂
Temp_Vars: H
Locations: l0, l1, l2, l3, l4
Transitions:
t₂₁: l0(X₀, X₂) → l1(0, H)
t₂₄: l1(X₀, X₂) → l2(0, 0) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₂: l1(X₀, X₂) → l3(X₀, X₂) :|: X₂+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₃: l1(X₀, X₂) → l3(X₀, X₂) :|: 1 ≤ X₂ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₆: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 9 ∧ H+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₇: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₂) → l4(X₀, X₂) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₈: l2(X₀, X₂) → l4(X₀, X₂) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₉: l3(X₀, X₂) → l1(X₀+1, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₃₀: l3(X₀, X₂) → l2(0, X₂) :|: 10 ≤ X₀ ∧ 0 ≤ X₀
MPRF for transition t₂₂: l1(X₀, X₂) → l3(X₀, X₂) :|: X₂+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:
new bound:
11 {O(1)}
MPRF:
l3 [10-X₀ ]
l1 [11-X₀ ]
MPRF for transition t₂₃: l1(X₀, X₂) → l3(X₀, X₂) :|: 1 ≤ X₂ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:
new bound:
11 {O(1)}
MPRF:
l3 [10-X₀ ]
l1 [11-X₀ ]
MPRF for transition t₂₉: l3(X₀, X₂) → l1(X₀+1, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF:
l3 [10-X₀ ]
l1 [10-X₀ ]
MPRF for transition t₂₆: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 9 ∧ H+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:
new bound:
20 {O(1)}
MPRF:
l2 [10-X₀ ]
MPRF for transition t₂₇: l2(X₀, X₂) → l2(X₀+1, X₂) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:
new bound:
20 {O(1)}
MPRF:
l2 [10-X₀ ]
All Bounds
Timebounds
Overall timebound:77 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 11 {O(1)}
t₂₃: 11 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 20 {O(1)}
t₂₇: 20 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 10 {O(1)}
t₃₀: 1 {O(1)}
Costbounds
Overall costbound: 77 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 11 {O(1)}
t₂₃: 11 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 20 {O(1)}
t₂₇: 20 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 10 {O(1)}
t₃₀: 1 {O(1)}
Sizebounds
t₂₁, X₀: 0 {O(1)}
t₂₂, X₀: 10 {O(1)}
t₂₃, X₀: 10 {O(1)}
t₂₄, X₀: 0 {O(1)}
t₂₄, X₂: 0 {O(1)}
t₂₅, X₀: 10 {O(1)}
t₂₆, X₀: 10 {O(1)}
t₂₇, X₀: 10 {O(1)}
t₂₈, X₀: 9 {O(1)}
t₂₉, X₀: 10 {O(1)}
t₃₀, X₀: 0 {O(1)}