Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1)
t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃+1-X₂, X₂-1, X₂, X₃)
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₁-1, X₀+X₁-1)
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1
t₁₂: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁: l8(X₀, X₁, X₂, X₃) → l6(X₁, X₁, X₂, X₃)
Preprocessing
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ for location l2
Found invariant X₁ ≤ 1 for location l7
Found invariant 2 ≤ X₁ for location l5
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ for location l4
Found invariant X₁ ≤ 1 for location l9
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃+1-X₂, X₂-1, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₁-1, X₀+X₁-1) :|: 2 ≤ X₁
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1
t₁₂: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1
t₁: l8(X₀, X₁, X₂, X₃) → l6(X₁, X₁, X₂, X₃)
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₁+1 ]
l3 [X₂+2 ]
l4 [X₁-1 ]
l1 [X₁+1 ]
l6 [X₁+1 ]
l5 [X₁+1 ]
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁ {O(n)}
MPRF:
l2 [X₃ ]
l3 [X₃ ]
l4 [X₃ ]
l1 [X₃+1 ]
l6 [X₀+X₁ ]
l5 [X₀+X₁ ]
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
3⋅X₁+1 {O(n)}
MPRF:
l2 [2⋅X₃+2-X₂ ]
l3 [2⋅X₃+1-X₂ ]
l4 [2⋅X₁+2⋅X₃-3⋅X₂ ]
l1 [2⋅X₁+2⋅X₃-3⋅X₂ ]
l6 [2⋅X₀+X₁+1 ]
l5 [2⋅X₀+X₁+1 ]
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁ {O(n)}
MPRF:
l2 [X₃+1 ]
l3 [X₃ ]
l4 [X₃ ]
l1 [X₃+1 ]
l6 [X₀+X₁ ]
l5 [X₀+X₁ ]
MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁ {O(n)}
MPRF:
l2 [X₃+1 ]
l3 [X₃+1 ]
l4 [X₁+X₃-X₂-1 ]
l1 [X₁+X₃-X₂ ]
l6 [X₀+X₁ ]
l5 [X₀+X₁ ]
MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
3⋅X₁ {O(n)}
MPRF:
l2 [2⋅X₃+1-X₂ ]
l3 [2⋅X₃-X₂ ]
l4 [2⋅X₃+1-X₂ ]
l1 [2⋅X₃+1-X₂ ]
l6 [2⋅X₀+X₁ ]
l5 [2⋅X₀+X₁ ]
MPRF for transition t₁₁: l4(X₀, X₁, X₂, X₃) → l6(X₃+1-X₂, X₂-1, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁+3 {O(n)}
MPRF:
l2 [2⋅X₁ ]
l3 [2⋅X₂+2 ]
l4 [2⋅X₂+2 ]
l1 [2⋅X₁ ]
l6 [2⋅X₁+3 ]
l5 [2⋅X₁ ]
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₁-1, X₀+X₁-1) :|: 2 ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₂ ]
l3 [X₁-1 ]
l4 [X₁-1 ]
l1 [X₁-1 ]
l6 [X₁+1 ]
l5 [X₁+1 ]
MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₂+1 ]
l3 [X₁ ]
l4 [X₁ ]
l1 [X₂+1 ]
l6 [X₁+1 ]
l5 [X₁ ]
All Bounds
Timebounds
Overall timebound:17⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₅: X₁+1 {O(n)}
t₆: 2⋅X₁ {O(n)}
t₇: 3⋅X₁+1 {O(n)}
t₈: 2⋅X₁ {O(n)}
t₉: 2⋅X₁ {O(n)}
t₁₀: 3⋅X₁ {O(n)}
t₁₁: 2⋅X₁+3 {O(n)}
t₄: X₁+1 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 17⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₅: X₁+1 {O(n)}
t₆: 2⋅X₁ {O(n)}
t₇: 3⋅X₁+1 {O(n)}
t₈: 2⋅X₁ {O(n)}
t₉: 2⋅X₁ {O(n)}
t₁₀: 3⋅X₁ {O(n)}
t₁₁: 2⋅X₁+3 {O(n)}
t₄: X₁+1 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₅, X₀: 14⋅X₁⋅X₁+30⋅X₁ {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁ {O(n)}
t₅, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₆, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁ {O(n)}
t₆, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₇, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₈, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₉, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₁₀, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₁₁, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 3⋅X₁ {O(n)}
t₁₁, X₃: 14⋅X₁⋅X₁+30⋅X₁ {O(n^2)}
t₄, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₂, X₀: 7⋅X₁⋅X₁+15⋅X₁ {O(n^2)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 3⋅X₁+X₂ {O(n)}
t₂, X₃: 14⋅X₁⋅X₁+30⋅X₁+X₃ {O(n^2)}
t₃, X₀: 7⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 3⋅X₁+X₂ {O(n)}
t₃, X₃: 14⋅X₁⋅X₁+30⋅X₁+X₃ {O(n^2)}
t₁₂, X₀: 7⋅X₁⋅X₁+16⋅X₁ {O(n^2)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₂, X₂: 3⋅X₁+X₂ {O(n)}
t₁₂, X₃: 14⋅X₁⋅X₁+30⋅X₁+X₃ {O(n^2)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}