Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₂, 0, X₄) :|: 0 < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₄, X₁, 1, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₃, X₃, X₄) :|: X₁ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁-1, X₂, 1, X₄)
Preprocessing
Found invariant X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location l6
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₀ ≤ X₄ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ for location l1
Found invariant X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location l4
Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₂, 0, X₄) :|: 0 < X₂ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₄, X₁, 1, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₃, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁-1, X₂, 1, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
l1 [X₀ ]
l5 [X₁-1 ]
l3 [X₁ ]
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁-1, X₂, 1, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
l1 [X₀ ]
l5 [X₁ ]
l3 [X₁ ]
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₂, 0, X₄) :|: 0 < X₂ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₄+2 {O(n)}
MPRF:
l5 [X₂ ]
l3 [X₂+X₃ ]
l1 [X₂+1 ]
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₃, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
2⋅X₄+1 {O(n)}
MPRF:
l5 [X₃+1 ]
l3 [X₃+1 ]
l1 [X₂ ]
All Bounds
Timebounds
Overall timebound:6⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+2 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: 2⋅X₄+1 {O(n)}
t₇: 1 {O(1)}
t₆: X₄ {O(n)}
Costbounds
Overall costbound: 6⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₄+2 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: 2⋅X₄+1 {O(n)}
t₇: 1 {O(1)}
t₆: X₄ {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₄ {O(n)}
t₂, X₁: X₄ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: 0 {O(1)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₄ {O(n)}
t₃, X₁: 2⋅X₄ {O(n)}
t₃, X₂: 0 {O(1)}
t₃, X₃: 1 {O(1)}
t₃, X₄: X₄ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 1 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₄, X₀: 2⋅X₄ {O(n)}
t₄, X₁: X₄ {O(n)}
t₄, X₂: 1 {O(1)}
t₄, X₃: 1 {O(1)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₄ {O(n)}
t₅, X₁: 2⋅X₄ {O(n)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 1 {O(1)}
t₅, X₄: X₄ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₁: 2⋅X₄ {O(n)}
t₇, X₂: 0 {O(1)}
t₇, X₃: 1 {O(1)}
t₇, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₄ {O(n)}
t₆, X₁: X₄ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: 1 {O(1)}
t₆, X₄: X₄ {O(n)}