Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₀-2, X₂, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁+1, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₁
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁-2, X₂, X₃, X₄, X₅)
Preprocessing
Eliminate variables {X₂,X₃,X₅} that do not contribute to the problem
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6
Found invariant 4 ≤ X₄ ∧ 6 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 8 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location l7
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 1 for location l8
Found invariant X₀ ≤ X₄ for location l1
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 1 for location l4
Found invariant 2 ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₀: l0(X₀, X₁, X₄) → l2(X₀, X₁, X₄)
t₂₁: l1(X₀, X₁, X₄) → l3(X₀, X₁, X₄) :|: 1 < X₀ ∧ X₀ ≤ X₄
t₂₂: l1(X₀, X₁, X₄) → l4(X₀, X₁, X₄) :|: X₀ ≤ 1 ∧ X₀ ≤ X₄
t₂₃: l2(X₀, X₁, X₄) → l1(X₄, X₁, X₄)
t₂₄: l3(X₀, X₁, X₄) → l6(X₀, X₀-2, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2 ≤ X₀
t₂₅: l4(X₀, X₁, X₄) → l8(X₀, X₁, X₄) :|: X₀ ≤ X₄ ∧ X₀ ≤ 1
t₂₆: l5(X₀, X₁, X₄) → l1(X₁+1, X₁, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₈: l6(X₀, X₁, X₄) → l5(X₀, X₁, X₄) :|: X₁ ≤ 1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₇: l6(X₀, X₁, X₄) → l7(X₀, X₁, X₄) :|: 1 < X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₉: l7(X₀, X₁, X₄) → l6(X₀, X₁-2, X₄) :|: 4 ≤ X₄ ∧ 6 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 8 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀
MPRF for transition t₂₁: l1(X₀, X₁, X₄) → l3(X₀, X₁, X₄) :|: 1 < X₀ ∧ X₀ ≤ X₄ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₀-2 ]
l1 [X₀-1 ]
l5 [X₁ ]
l7 [X₁ ]
l6 [X₁ ]
MPRF for transition t₂₄: l3(X₀, X₁, X₄) → l6(X₀, X₀-2, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₀-1 ]
l1 [X₀-1 ]
l5 [X₀-2 ]
l7 [X₀-2 ]
l6 [X₀-2 ]
MPRF for transition t₂₆: l5(X₀, X₁, X₄) → l1(X₁+1, X₁, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l5 [X₁+2 ]
l7 [X₀ ]
l6 [X₀ ]
MPRF for transition t₂₇: l6(X₀, X₁, X₄) → l7(X₀, X₁, X₄) :|: 1 < X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₄+1 {O(n)}
MPRF:
l3 [X₀+X₄-1 ]
l1 [X₀+X₄-1 ]
l5 [X₁+X₄ ]
l7 [X₁+X₄-2 ]
l6 [X₁+X₄ ]
MPRF for transition t₂₈: l6(X₀, X₁, X₄) → l5(X₀, X₁, X₄) :|: X₁ ≤ 1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l5 [X₀-1 ]
l7 [X₀ ]
l6 [X₀ ]
MPRF for transition t₂₉: l7(X₀, X₁, X₄) → l6(X₀, X₁-2, X₄) :|: 4 ≤ X₄ ∧ 6 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 8 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ of depth 1:
new bound:
X₄+2 {O(n)}
MPRF:
l3 [X₀-2 ]
l1 [X₀-2 ]
l5 [X₁-1 ]
l7 [X₁-1 ]
l6 [X₁-1 ]
All Bounds
Timebounds
Overall timebound:7⋅X₄+9 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: X₄+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₄+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₄ {O(n)}
t₂₇: 2⋅X₄+1 {O(n)}
t₂₈: X₄ {O(n)}
t₂₉: X₄+2 {O(n)}
Costbounds
Overall costbound: 7⋅X₄+9 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: X₄+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₄+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₄ {O(n)}
t₂₇: 2⋅X₄+1 {O(n)}
t₂₈: X₄ {O(n)}
t₂₉: X₄+2 {O(n)}
Sizebounds
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₀: X₄+2 {O(n)}
t₂₁, X₁: X₁+1 {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₂, X₀: X₄+2 {O(n)}
t₂₂, X₁: X₁+1 {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₃, X₀: X₄ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: X₄+2 {O(n)}
t₂₄, X₁: X₄+2 {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₅, X₀: X₄+2 {O(n)}
t₂₅, X₁: X₁+1 {O(n)}
t₂₅, X₄: 2⋅X₄ {O(n)}
t₂₆, X₀: 2 {O(1)}
t₂₆, X₁: 1 {O(1)}
t₂₆, X₄: X₄ {O(n)}
t₂₇, X₀: X₄+2 {O(n)}
t₂₇, X₁: X₄+2 {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₈, X₀: 2⋅X₄+4 {O(n)}
t₂₈, X₁: 1 {O(1)}
t₂₈, X₄: X₄ {O(n)}
t₂₉, X₀: X₄+2 {O(n)}
t₂₉, X₁: X₄+2 {O(n)}
t₂₉, X₄: X₄ {O(n)}