Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₆-1, X₁, X₂, X₃, X₄, X₄, X₆)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₂)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₀) :|: 0 < X₀
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, 0, X₂, X₅, X₄, X₅, X₆) :|: X₅ < 8
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₅-8, X₂, 8, X₄, X₅, X₆) :|: 8 ≤ X₅
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: X₃ < 1
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 1 ≤ X₃
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
Preprocessing
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ for location l6
Found invariant X₆ ≤ 1 ∧ X₅+X₆ ≤ 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₀+X₆ ≤ 1 ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₀+X₅ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l7
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂ for location l5
Found invariant X₆ ≤ 1 ∧ X₅+X₆ ≤ 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₀+X₆ ≤ 1 ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₀+X₅ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l8
Found invariant X₆ ≤ X₂ for location l1
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ for location l4
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₆-1, X₁, X₂, X₃, X₄, X₄, X₆) :|: X₆ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₂)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₀) :|: 0 < X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, 0, X₂, X₅, X₄, X₅, X₆) :|: X₅ < 8 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₅-8, X₂, 8, X₄, X₅, X₆) :|: 8 ≤ X₅ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: X₃ < 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1 ∧ X₅+X₆ ≤ 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₀+X₆ ≤ 1 ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₀+X₅ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0
MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₀) :|: 0 < X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₆-1 ]
l5 [X₀ ]
l6 [X₀ ]
l3 [X₀ ]
knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₆-1, X₁, X₂, X₃, X₄, X₄, X₆) :|: X₆ ≤ X₂
MPRF for transition t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ of depth 1:
new bound:
X₂⋅X₄+2⋅X₄ {O(n^2)}
MPRF:
l1 [X₄ ]
l4 [X₅ ]
l5 [X₅-1 ]
l6 [X₅-1 ]
l3 [X₅ ]
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ of depth 1:
new bound:
3⋅X₂+6 {O(n)}
MPRF:
l1 [3 ]
l4 [3⋅X₆-3⋅X₀-1 ]
l5 [3⋅X₆-3⋅X₀ ]
l6 [3⋅X₆-3⋅X₀ ]
l3 [3⋅X₆-3⋅X₀ ]
MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, 0, X₂, X₅, X₄, X₅, X₆) :|: X₅ < 8 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂ of depth 1:
new bound:
X₂⋅X₄+2⋅X₄ {O(n^2)}
MPRF:
l1 [X₄ ]
l4 [X₅ ]
l5 [X₅ ]
l6 [X₁ ]
l3 [X₅ ]
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₅-8, X₂, 8, X₄, X₅, X₆) :|: 8 ≤ X₅ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂ of depth 1:
new bound:
15⋅X₂⋅X₄+30⋅X₄ {O(n^2)}
MPRF:
l1 [15⋅X₄ ]
l4 [8⋅X₄+7⋅X₅-7 ]
l5 [8⋅X₄+7⋅X₅-7 ]
l6 [8⋅X₁+8⋅X₄+1-X₅ ]
l3 [8⋅X₄+7⋅X₅-7 ]
MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₂⋅X₄+2⋅X₄ {O(n^2)}
MPRF:
l1 [X₄ ]
l4 [X₅ ]
l5 [X₅ ]
l6 [X₁+X₃ ]
l3 [X₅ ]
MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₁, X₆) :|: X₃ < 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₂⋅X₄+2⋅X₄ {O(n^2)}
MPRF:
l1 [X₄ ]
l4 [X₅ ]
l5 [X₅ ]
l6 [X₁+1 ]
l3 [X₅ ]
Analysing control-flow refined program
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 7 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 7+X₁ ∧ X₁+X₅ ≤ 7 ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 7 ∧ X₃ ≤ 7+X₁ ∧ X₁+X₃ ≤ 7 ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location n_l6___6
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 8 ≤ X₅ ∧ 16 ≤ X₄+X₅ ∧ 15 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 8 ≤ X₁+X₅ ∧ 8+X₁ ≤ X₅ ∧ 8 ≤ X₄ ∧ 15 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 8 ≤ X₁+X₄ ∧ 8+X₁ ≤ X₄ ∧ X₃ ≤ 7 ∧ X₃ ≤ 7+X₁ ∧ 7 ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l6___1
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 8 ≤ X₅ ∧ 16 ≤ X₄+X₅ ∧ 16 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 8 ≤ X₁+X₅ ∧ 8+X₁ ≤ X₅ ∧ 8 ≤ X₄ ∧ 16 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 8 ≤ X₁+X₄ ∧ 8+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 8 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l6___5
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 6 ∧ X₃ ≤ 6+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l6___4
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l3___3
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ for location n_l5___2
Found invariant X₆ ≤ 1 ∧ X₅+X₆ ≤ 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₀+X₆ ≤ 1 ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₀+X₅ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l7
Found invariant X₆ ≤ 1 ∧ X₅+X₆ ≤ 1 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ X₀+X₆ ≤ 1 ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₀+X₅ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l8
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂ for location n_l5___7
Found invariant X₆ ≤ X₂ for location l1
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ for location l4
Found invariant X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 1+X₀ ≤ X₂ for location l3
knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₉₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅, X₀+1) :|: X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ X₅ ≤ X₄ ∧ 0 < X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 1+X₀ ≤ X₂
knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₀₀: n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___5(X₀, X₅-8, X₂, 8, X₄, X₅, X₀+1) :|: 0 < X₄ ∧ 1+X₀ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 8 ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂
knowledge_propagation leads to new time bound X₂+2 {O(n)} for transition t₁₀₁: n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___6(X₀, 0, X₂, X₅, X₄, X₅, X₀+1) :|: 0 < X₄ ∧ 1+X₀ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ < 8 ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₂
MPRF for transition t₉₆: n_l3___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅, X₀+1) :|: X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 0 < X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
16⋅X₂⋅X₄+32⋅X₄+64⋅X₂+136 {O(n^2)}
MPRF:
l3 [8⋅X₆-8⋅X₀ ]
l1 [8 ]
l4 [8 ]
n_l5___2 [8⋅X₁ ]
n_l5___7 [8 ]
n_l3___3 [8⋅X₅+8 ]
n_l6___5 [8⋅X₁+8⋅X₃ ]
n_l6___1 [7⋅X₁+X₅ ]
n_l6___6 [8⋅X₁+X₆+7-X₀ ]
n_l6___4 [8⋅X₁+8 ]
MPRF for transition t₁₁₇: n_l3___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
4⋅X₂⋅X₄+8⋅X₂+8⋅X₄+16 {O(n^2)}
MPRF:
l3 [4⋅X₆-4⋅X₀-4 ]
n_l5___7 [0 ]
l1 [0 ]
l4 [0 ]
n_l5___2 [X₆-X₀ ]
n_l3___3 [1 ]
n_l6___5 [X₅-X₁-7 ]
n_l6___1 [X₃-6 ]
n_l6___6 [1 ]
n_l6___4 [1 ]
MPRF for transition t₉₈: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___5(X₀, X₅-8, X₂, 8, X₄, X₅, X₀+1) :|: X₅ ≤ X₄ ∧ 0 < X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 8 ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₄+4⋅X₄+8⋅X₂+16 {O(n^2)}
MPRF:
l3 [0 ]
l1 [0 ]
l4 [0 ]
n_l5___2 [X₁ ]
n_l5___7 [0 ]
n_l3___3 [X₅ ]
n_l6___5 [X₅-X₃ ]
n_l6___1 [X₅-8 ]
n_l6___6 [0 ]
n_l6___4 [X₁ ]
MPRF for transition t₉₉: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___6(X₀, 0, X₂, X₅, X₄, X₅, X₀+1) :|: X₅ ≤ X₄ ∧ 0 < X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ < 8 ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
3⋅X₂⋅X₄+7⋅X₂+7⋅X₄+14 {O(n^2)}
MPRF:
l3 [X₅ ]
l1 [X₄ ]
l4 [X₄ ]
n_l5___2 [X₁+X₄ ]
n_l5___7 [X₄ ]
n_l3___3 [X₄+X₅ ]
n_l6___5 [X₄+X₅ ]
n_l6___1 [X₄+X₅-8 ]
n_l6___6 [X₄+X₅-X₃ ]
n_l6___4 [X₁+X₄ ]
MPRF for transition t₁₀₂: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___4(X₀, X₁, X₂, X₃-1, X₄, X₅, X₀+1) :|: X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 8 ∧ X₃ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ 7 ∧ X₅ ≤ X₄ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 8 ≤ X₅ ∧ 16 ≤ X₄+X₅ ∧ 15 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 8 ≤ X₁+X₅ ∧ 8+X₁ ≤ X₅ ∧ 8 ≤ X₄ ∧ 15 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 8 ≤ X₁+X₄ ∧ 8+X₁ ≤ X₄ ∧ X₃ ≤ 7 ∧ X₃ ≤ 7+X₁ ∧ 7 ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
3⋅X₂⋅X₄+32⋅X₂⋅X₂+111⋅X₂+7⋅X₄+95 {O(n^2)}
MPRF:
l3 [X₄-1 ]
l1 [X₄-1 ]
l4 [X₄-1 ]
n_l5___2 [X₄+X₅-2 ]
n_l5___7 [X₄-1 ]
n_l3___3 [X₄+X₅-1 ]
n_l6___5 [8⋅X₀+X₄+X₅-8⋅X₆ ]
n_l6___1 [X₁+X₄ ]
n_l6___6 [X₁+X₄-1 ]
n_l6___4 [X₁+X₄-1 ]
MPRF for transition t₁₀₃: n_l6___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l3___3(X₀, X₁, X₂, X₃, X₄, X₁, X₀+1) :|: X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₃ ≤ 8 ∧ X₃ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ 7 ∧ X₅ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₅ ≤ 8+X₁ ∧ X₃ < 1 ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 6 ∧ X₃ ≤ 6+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₄+8⋅X₂⋅X₂+4⋅X₄+41⋅X₂+51 {O(n^2)}
MPRF:
l3 [1 ]
n_l5___7 [X₀+2-X₆ ]
l1 [1 ]
l4 [1 ]
n_l5___2 [X₁+X₆-X₀ ]
n_l3___3 [X₅+1 ]
n_l6___5 [X₅+1 ]
n_l6___1 [X₁+2 ]
n_l6___6 [X₅+2⋅X₆-2⋅X₀-X₃ ]
n_l6___4 [X₁+2 ]
MPRF for transition t₁₀₄: n_l6___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___4(X₀, X₁, X₂, X₃-1, X₄, X₅, X₀+1) :|: X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₃ ≤ 8 ∧ X₃ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 0 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ 7 ∧ X₅ ≤ X₄ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 6 ∧ X₃ ≤ 6+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
19⋅X₂⋅X₄+24⋅X₂⋅X₂+238⋅X₂+45⋅X₄+353 {O(n^2)}
MPRF:
l3 [7⋅X₀+7⋅X₄+8-7⋅X₂ ]
n_l5___7 [7⋅X₅+8⋅X₆-X₀-7⋅X₂ ]
l1 [7⋅X₄+7⋅X₆+1-7⋅X₂ ]
l4 [7⋅X₄+7⋅X₆-7⋅X₂-6 ]
n_l5___2 [6⋅X₁+7⋅X₄-6 ]
n_l3___3 [7⋅X₄+6⋅X₅-6 ]
n_l6___5 [6⋅X₀+7⋅X₄+6⋅X₅-6⋅X₆ ]
n_l6___1 [X₃+7⋅X₄+6⋅X₅-20 ]
n_l6___6 [X₁+7⋅X₄+6⋅X₅-6 ]
n_l6___4 [X₁+X₃+7⋅X₄+5⋅X₅-11 ]
MPRF for transition t₁₀₅: n_l6___5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₀+1) :|: X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 8 ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ 8 ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 8+X₁ ≤ X₅ ∧ X₅ ≤ 8+X₁ ∧ 0 ≤ X₁ ∧ 8+X₁ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ X₄ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 8+X₁ ∧ 8 ≤ X₅ ∧ 16 ≤ X₄+X₅ ∧ 16 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 8 ≤ X₁+X₅ ∧ 8+X₁ ≤ X₅ ∧ 8 ≤ X₄ ∧ 16 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 8 ≤ X₁+X₄ ∧ 8+X₁ ≤ X₄ ∧ X₃ ≤ 8 ∧ X₃ ≤ 8+X₁ ∧ 8 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₄+4⋅X₄+X₂+2 {O(n^2)}
MPRF:
l3 [0 ]
l1 [0 ]
l4 [0 ]
n_l5___2 [X₁-1 ]
n_l5___7 [0 ]
n_l3___3 [X₅ ]
n_l6___5 [X₁+1 ]
n_l6___1 [X₁ ]
n_l6___6 [0 ]
n_l6___4 [X₁ ]
MPRF for transition t₁₀₆: n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l6___4(X₀, X₁, X₂, X₃-1, X₄, X₅, X₀+1) :|: X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 8 ∧ X₃ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₅ ≤ X₄ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₅ ≤ 8+X₁ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ X₄ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₃ ≤ 8 ∧ X₅ ≤ 8+X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₂ ∧ X₀+1 ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ X₆ ≤ X₂ ∧ X₆ ≤ 1+X₀ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ 7 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 7+X₁ ∧ X₁+X₅ ≤ 7 ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ 7 ∧ X₃ ≤ 7+X₁ ∧ X₁+X₃ ≤ 7 ∧ 1 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₄+4⋅X₄+X₂+2 {O(n^2)}
MPRF:
l3 [X₆-X₀-1 ]
n_l5___7 [X₀+X₄+1-X₅-X₆ ]
l1 [0 ]
l4 [0 ]
n_l5___2 [X₁ ]
n_l3___3 [X₅ ]
n_l6___5 [X₅ ]
n_l6___1 [X₁ ]
n_l6___6 [1 ]
n_l6___4 [X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:19⋅X₂⋅X₄+38⋅X₄+5⋅X₂+13 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂+2 {O(n)}
t₁: 1 {O(1)}
t₃: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₄: 3⋅X₂+6 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₂+1 {O(n)}
t₅: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₆: 15⋅X₂⋅X₄+30⋅X₄ {O(n^2)}
t₇: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₈: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 19⋅X₂⋅X₄+38⋅X₄+5⋅X₂+13 {O(n^2)}
t₀: 1 {O(1)}
t₂: X₂+2 {O(n)}
t₁: 1 {O(1)}
t₃: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₄: 3⋅X₂+6 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₂+1 {O(n)}
t₅: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₆: 15⋅X₂⋅X₄+30⋅X₄ {O(n^2)}
t₇: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₈: X₂⋅X₄+2⋅X₄ {O(n^2)}
t₁₁: 1 {O(1)}
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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₂, X₀: 2⋅X₂+2 {O(n)}
t₂, X₁: 2⋅X₄+X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: 2⋅X₄ {O(n)}
t₂, X₆: 3⋅X₂+2 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₂ {O(n)}
t₃, X₀: 2⋅X₂+2 {O(n)}
t₃, X₁: 4⋅X₄+X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: 2⋅X₄ {O(n)}
t₃, X₆: 3⋅X₂+2 {O(n)}
t₄, X₀: 2⋅X₂+2 {O(n)}
t₄, X₁: 2⋅X₄+X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: 4⋅X₄ {O(n)}
t₄, X₆: 6⋅X₂+4 {O(n)}
t₉, X₀: 2⋅X₂+2 {O(n)}
t₉, X₁: 2⋅X₄+X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: 4⋅X₄ {O(n)}
t₉, X₆: 6⋅X₂+4 {O(n)}
t₁₀, X₀: 2⋅X₂+2 {O(n)}
t₁₀, X₁: 2⋅X₄+X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 4⋅X₄ {O(n)}
t₁₀, X₆: 2⋅X₂+2 {O(n)}
t₅, X₀: 2⋅X₂+2 {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 7 {O(1)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: 7 {O(1)}
t₅, X₆: 3⋅X₂+2 {O(n)}
t₆, X₀: 2⋅X₂+2 {O(n)}
t₆, X₁: 2⋅X₄ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 8 {O(1)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: 2⋅X₄ {O(n)}
t₆, X₆: 3⋅X₂+2 {O(n)}
t₇, X₀: 2⋅X₂+2 {O(n)}
t₇, X₁: 2⋅X₄ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: 7 {O(1)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: 2⋅X₄+7 {O(n)}
t₇, X₆: 3⋅X₂+2 {O(n)}
t₈, X₀: 2⋅X₂+2 {O(n)}
t₈, X₁: 2⋅X₄ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: 2⋅X₄ {O(n)}
t₈, X₆: 3⋅X₂+2 {O(n)}
t₁₁, X₀: 2⋅X₂+2 {O(n)}
t₁₁, X₁: 2⋅X₄+X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: 4⋅X₄ {O(n)}
t₁₁, X₆: 6⋅X₂+4 {O(n)}