Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₃
t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: E+1 ≤ 0
t₈: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: E+1 ≤ 0 ∧ 1 ≤ E
t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 1 ≤ E
t₁₀: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ 0
t₁₁: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ 0
t₁₂: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃-1) :|: 1 ≤ 0
t₁₃: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃-1) :|: 1 ≤ 0
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃)
t₁₅: l3(X₀, X₁, X₂, X₃) → l5(X₀+1, X₃, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀+1, X₁)
t₂: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁₆: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l5(0, X₀, X₂, X₃)
Preprocessing
Cut unsatisfiable transition t₈: l2→l1
Cut unsatisfiable transition t₁₀: l2→l1
Cut unsatisfiable transition t₁₁: l2→l1
Cut unsatisfiable transition t₁₂: l2→l1
Cut unsatisfiable transition t₁₃: l2→l1
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₀ for location l5
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l8
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: E+1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 1 ≤ E ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₅: l3(X₀, X₁, X₂, X₃) → l5(X₀+1, X₃, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₃: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₆: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃) → l5(0, X₀, X₂, X₃)
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l2 [X₁+1-X₀ ]
l3 [X₃-X₀ ]
l1 [X₁+1-X₀ ]
l5 [X₁+1-X₀ ]
l4 [X₁+1-X₀ ]
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: E+1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l2 [X₃-1 ]
l3 [X₃-1 ]
l1 [X₃-1 ]
l5 [X₁-1 ]
l4 [X₁-1 ]
MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 1 ≤ E ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l2 [X₃-1 ]
l3 [X₃-1 ]
l1 [X₃-1 ]
l5 [X₁-1 ]
l4 [X₁-1 ]
MPRF for transition t₁₅: l3(X₀, X₁, X₂, X₃) → l5(X₀+1, X₃, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l2 [X₁+1-X₀ ]
l3 [X₃+1-X₀ ]
l1 [X₁+1-X₀ ]
l5 [X₁+1-X₀ ]
l4 [X₁+1-X₀ ]
MPRF for transition t₄: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₁-X₀-1 ]
l3 [X₁-X₀-1 ]
l1 [X₁-X₀-1 ]
l5 [X₁-X₀ ]
l4 [X₁-X₀ ]
MPRF for transition t₂: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₃-X₀-1 ]
l3 [X₂-X₀-1 ]
l1 [X₃-X₀-1 ]
l5 [X₁-X₀ ]
l4 [X₁-X₀-1 ]
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
3⋅X₀⋅X₀+X₀ {O(n^2)}
MPRF:
l2 [X₁+X₃-X₂-1 ]
l3 [X₁+X₃-X₂ ]
l5 [2⋅X₁-X₂ ]
l4 [2⋅X₁-X₀ ]
l1 [X₁+X₃-X₂ ]
MPRF for transition t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃) :|: X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀ {O(n^2)}
MPRF:
l2 [X₁-X₂ ]
l3 [X₁-X₂ ]
l5 [X₁-X₃ ]
l4 [X₁ ]
l1 [X₁-X₂ ]
Analysing control-flow refined program
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___6
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___7
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___1
Found invariant 1+X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 4 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___2
Found invariant 0 ≤ X₀ for location l5
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l8
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3
Found invariant 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___4
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀₃: l1(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₁₃: n_l2___7(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂+1, X₃) :|: 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₁₄: n_l2___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃-1) :|: 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₁₅: n_l2___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃-1) :|: 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
MPRF for transition t₁₀₀: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
12⋅X₀⋅X₀+9⋅X₀ {O(n^2)}
MPRF:
n_l2___7 [3⋅X₁-X₃ ]
l1 [2⋅X₃ ]
l5 [2⋅X₁ ]
l4 [2⋅X₁ ]
l3 [2⋅X₃ ]
n_l2___1 [3⋅X₁-X₂ ]
n_l1___5 [3⋅X₁-X₂ ]
n_l2___2 [3⋅X₃+2-X₂ ]
n_l1___3 [3⋅X₃+3-X₂ ]
n_l2___4 [3⋅X₁-X₂ ]
n_l1___6 [3⋅X₁-X₂ ]
MPRF for transition t₁₂₅: n_l1___3(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₁-X₂ ]
l5 [X₁-X₀-1 ]
l4 [X₁-X₀-1 ]
l3 [X₂-X₀-2 ]
n_l2___1 [X₁-X₀-1 ]
n_l2___2 [X₁-X₀-1 ]
n_l1___3 [X₁-X₀-1 ]
n_l2___4 [X₁-X₂ ]
n_l1___5 [X₁-X₀-1 ]
n_l2___7 [X₃-X₀-1 ]
n_l1___6 [X₁-X₀-1 ]
MPRF for transition t₁₀₁: n_l1___5(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 2+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
MPRF:
l1 [0 ]
l5 [0 ]
l4 [0 ]
l3 [0 ]
n_l2___1 [X₃-X₂ ]
n_l1___5 [X₃+1-X₂ ]
n_l2___2 [0 ]
n_l1___3 [0 ]
n_l2___4 [0 ]
n_l2___7 [0 ]
n_l1___6 [0 ]
MPRF for transition t₁₂₆: n_l1___5(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₁-X₀-1 ]
l5 [X₁-X₀-1 ]
l4 [X₁-X₀-1 ]
l3 [X₃-X₀-2 ]
n_l2___1 [X₁-X₀-1 ]
n_l2___2 [X₃-X₀ ]
n_l1___3 [X₃-X₀ ]
n_l2___4 [X₁-X₂ ]
n_l1___5 [X₁-X₀-1 ]
n_l2___7 [X₁-X₂ ]
n_l1___6 [X₁-X₀-1 ]
MPRF for transition t₁₀₂: n_l1___6(X₀, X₁, X₂, X₃) → n_l2___4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₃ ]
l5 [X₁ ]
l4 [X₁ ]
l3 [X₃ ]
n_l2___1 [X₃ ]
n_l2___2 [X₃ ]
n_l1___3 [X₃ ]
n_l2___4 [X₃ ]
n_l1___5 [X₃ ]
n_l2___7 [X₁ ]
n_l1___6 [X₃+1 ]
MPRF for transition t₁₂₇: n_l1___6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₃-1 ]
l5 [X₁-1 ]
l4 [X₁-1 ]
l3 [X₂-1 ]
n_l2___1 [X₃-1 ]
n_l2___2 [X₁-1 ]
n_l1___3 [X₁-1 ]
n_l2___4 [2⋅X₀+X₁+1-2⋅X₂ ]
n_l1___5 [X₁-1 ]
n_l2___7 [X₁-1 ]
n_l1___6 [X₁-1 ]
MPRF for transition t₁₀₄: n_l2___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂, X₃-1) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₁-2 ]
l5 [X₁-2 ]
l4 [X₁-2 ]
l3 [X₂-2 ]
n_l2___1 [X₃-2 ]
n_l2___2 [X₁-3 ]
n_l1___3 [X₁-3 ]
n_l2___4 [2⋅X₀+X₁-2⋅X₂ ]
n_l1___5 [X₃-2 ]
n_l2___7 [2⋅X₀+X₃-2⋅X₂ ]
n_l1___6 [X₁-2 ]
MPRF for transition t₁₀₅: n_l2___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂, X₃-1) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₁-2 ]
l5 [X₁-2 ]
l4 [X₁-2 ]
l3 [X₂-2 ]
n_l2___1 [X₃-2 ]
n_l2___2 [X₁-3 ]
n_l1___3 [X₁-3 ]
n_l2___4 [X₁-2 ]
n_l1___5 [X₃-2 ]
n_l2___7 [2⋅X₀+X₃-2⋅X₂ ]
n_l1___6 [X₁-2 ]
MPRF for transition t₁₀₆: n_l2___1(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂+1, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
MPRF:
l1 [0 ]
l5 [0 ]
l4 [0 ]
l3 [0 ]
n_l2___1 [X₁-X₂ ]
n_l1___5 [X₁-X₂ ]
n_l2___2 [0 ]
n_l1___3 [0 ]
n_l2___4 [0 ]
n_l2___7 [0 ]
n_l1___6 [0 ]
MPRF for transition t₁₀₇: n_l2___2(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 4 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₁ ]
l5 [X₁ ]
l4 [X₁ ]
l3 [X₂ ]
n_l2___1 [X₁ ]
n_l2___2 [X₃ ]
n_l1___3 [X₃ ]
n_l2___4 [X₃ ]
n_l1___5 [X₁ ]
n_l2___7 [X₃ ]
n_l1___6 [X₃ ]
MPRF for transition t₁₀₈: n_l2___2(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 4 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₁ ]
l5 [X₁ ]
l4 [X₁ ]
l3 [X₂ ]
n_l2___1 [X₁ ]
n_l2___2 [X₃ ]
n_l1___3 [X₃ ]
n_l2___4 [X₃ ]
n_l1___5 [X₁ ]
n_l2___7 [X₃ ]
n_l1___6 [X₃ ]
MPRF for transition t₁₀₉: n_l2___2(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 4 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀+7⋅X₀ {O(n^2)}
MPRF:
n_l2___7 [-X₂ ]
l1 [0 ]
l5 [0 ]
l4 [0 ]
l3 [0 ]
n_l2___1 [X₁-X₂ ]
n_l1___5 [X₁-X₂ ]
n_l2___2 [X₁-X₂ ]
n_l1___3 [X₁-X₂ ]
n_l2___4 [X₁-X₂ ]
n_l1___6 [X₁-X₂ ]
MPRF for transition t₁₁₀: n_l2___4(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₁-2 ]
l5 [X₁-2 ]
l4 [X₁-2 ]
l3 [X₂-2 ]
n_l2___1 [X₃-2 ]
n_l2___2 [X₁-3 ]
n_l1___3 [X₁-3 ]
n_l2___4 [X₁-2 ]
n_l1___5 [X₁-2 ]
n_l2___7 [2⋅X₀+X₃-2⋅X₂ ]
n_l1___6 [X₁-2 ]
MPRF for transition t₁₁₁: n_l2___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₃ ]
l5 [X₁ ]
l4 [X₁ ]
l3 [X₂ ]
n_l2___1 [X₃ ]
n_l2___2 [X₃ ]
n_l1___3 [X₃ ]
n_l2___4 [X₃ ]
n_l1___5 [X₁ ]
n_l2___7 [X₁ ]
n_l1___6 [X₃ ]
MPRF for transition t₁₁₂: n_l2___4(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₃ ]
l5 [X₁ ]
l4 [X₁ ]
l3 [X₂ ]
n_l2___1 [X₃ ]
n_l2___2 [X₃ ]
n_l1___3 [X₃ ]
n_l2___4 [X₃ ]
n_l1___5 [X₁ ]
n_l2___7 [X₁ ]
n_l1___6 [X₃ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₀: 1 {O(1)}
t₅: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₆: X₀+1 {O(n)}
t₇: X₀+1 {O(n)}
t₉: X₀+1 {O(n)}
t₁₄: X₀⋅X₀ {O(n^2)}
t₁₅: X₀+1 {O(n)}
t₄: X₀ {O(n)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀⋅X₀+7⋅X₀+8 {O(n^2)}
t₀: 1 {O(1)}
t₅: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₆: X₀+1 {O(n)}
t₇: X₀+1 {O(n)}
t₉: X₀+1 {O(n)}
t₁₄: X₀⋅X₀ {O(n^2)}
t₁₅: X₀+1 {O(n)}
t₄: X₀ {O(n)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₁₆: 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: X₀+1 {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: X₀⋅X₀+X₀+2 {O(n^2)}
t₅, X₃: X₀ {O(n)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: 3⋅X₀⋅X₀+4⋅X₀+8 {O(n^2)}
t₆, X₃: 4⋅X₀ {O(n)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: X₀ {O(n)}
t₇, X₂: X₀⋅X₀+X₀+2 {O(n^2)}
t₇, X₃: X₀ {O(n)}
t₉, X₀: X₀+1 {O(n)}
t₉, X₁: X₀ {O(n)}
t₉, X₂: X₀⋅X₀+X₀+2 {O(n^2)}
t₉, X₃: X₀ {O(n)}
t₁₄, X₀: X₀+1 {O(n)}
t₁₄, X₁: X₀ {O(n)}
t₁₄, X₂: X₀⋅X₀+X₀+2 {O(n^2)}
t₁₄, X₃: X₀ {O(n)}
t₁₅, X₀: X₀+1 {O(n)}
t₁₅, X₁: X₀ {O(n)}
t₁₅, X₂: 3⋅X₀⋅X₀+4⋅X₀+8 {O(n^2)}
t₁₅, X₃: 4⋅X₀ {O(n)}
t₄, X₀: X₀+1 {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀+2 {O(n)}
t₄, X₃: X₀ {O(n)}
t₂, X₀: X₀+1 {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: 3⋅X₀⋅X₀+4⋅X₀+X₂+8 {O(n^2)}
t₂, X₃: 4⋅X₀+X₃ {O(n)}
t₃, X₀: X₀+1 {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: 3⋅X₀⋅X₀+4⋅X₀+X₂+8 {O(n^2)}
t₃, X₃: 4⋅X₀+X₃ {O(n)}
t₁₆, X₀: X₀+1 {O(n)}
t₁₆, X₁: 2⋅X₀ {O(n)}
t₁₆, X₂: 3⋅X₀⋅X₀+4⋅X₀+X₂+8 {O(n^2)}
t₁₆, X₃: 4⋅X₀+X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}