Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₁, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, 1, X₀+1, X₃, X₄)
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₂-2, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₁
t₅: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₂
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁+1, X₂, X₃, X₄)
Preprocessing
Eliminate variables {X₄} that do not contribute to the problem
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l8
Found invariant X₀ ≤ X₃ for location l1
Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂₁: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃
t₂₂: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₀ ≤ X₃
t₂₃: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₂₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, 1, X₀+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀
t₂₅: l4(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ 1+X₀ ≤ 0
t₂₆: l5(X₀, X₁, X₂, X₃) → l1(X₂-2, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₈: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₉: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁+1, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₂₁: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀+1 ]
l5 [X₁+X₂-X₀-3 ]
l7 [X₂-1 ]
l6 [X₂-1 ]
MPRF for transition t₂₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, 1, X₀+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+4 {O(n)}
MPRF:
l3 [X₀+4 ]
l1 [X₀+4 ]
l5 [X₁+X₂-X₀ ]
l7 [X₀+3 ]
l6 [X₀+3 ]
MPRF for transition t₂₆: l5(X₀, X₁, X₂, X₃) → l1(X₂-2, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l5 [X₀+1 ]
l7 [X₂ ]
l6 [X₂ ]
MPRF for transition t₂₈: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l5 [X₀ ]
l7 [X₂ ]
l6 [X₀+1 ]
MPRF for transition t₂₇: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+4⋅X₃+4 {O(n^2)}
MPRF:
l3 [X₀+2 ]
l5 [X₂ ]
l1 [X₀+2 ]
l7 [X₂-X₁ ]
l6 [X₂+1-X₁ ]
MPRF for transition t₂₉: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁+1, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
3⋅X₃⋅X₃+11⋅X₃+8 {O(n^2)}
MPRF:
l3 [X₀+1 ]
l5 [2⋅X₂-X₀-2 ]
l1 [X₀+1 ]
l7 [X₂+1-X₁ ]
l6 [X₂+1-X₁ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₂₈: l6→l5
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___2
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l7___3
Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l8
Found invariant X₀ ≤ X₃ for location l1
Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l7___1
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₃+4 {O(n)} for transition t₆₇: l6(X₀, X₁, X₂, X₃) → n_l7___3(X₀, X₁, X₀+1, X₃) :|: X₂ ≤ 1+X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₃+4 {O(n)} for transition t₆₉: n_l7___3(X₀, X₁, X₂, X₃) → n_l6___2(X₀, X₁+1, X₀+1, X₃) :|: X₂ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₆₆: n_l6___2(X₀, X₁, X₂, X₃) → n_l7___1(X₀, X₁, X₀+1, X₃) :|: X₂ ≤ 1+X₃ ∧ 1 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+10⋅X₃+24 {O(n^2)}
MPRF:
l3 [0 ]
l1 [0 ]
l6 [0 ]
n_l7___3 [0 ]
l5 [2⋅X₂-X₀-X₁ ]
n_l7___1 [X₀+2-X₁ ]
n_l6___2 [X₀+3-X₁ ]
MPRF for transition t₇₃: n_l6___2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l6 [X₀+1 ]
l5 [X₀ ]
n_l7___1 [X₀+1 ]
n_l7___3 [X₀+X₁ ]
n_l6___2 [X₀+1 ]
MPRF for transition t₆₈: n_l7___1(X₀, X₁, X₂, X₃) → n_l6___2(X₀, X₁+1, X₀+1, X₃) :|: X₀ ≤ X₃ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₃⋅X₃+13⋅X₃+17 {O(n^2)}
MPRF:
l3 [X₃-1 ]
l1 [X₃-1 ]
l6 [X₃-1 ]
n_l7___3 [X₃-1 ]
l5 [X₂+X₃-X₁ ]
n_l7___1 [X₂+X₃-X₁ ]
n_l6___2 [X₂+X₃-X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₃⋅X₃+19⋅X₃+23 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: X₃+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₃+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₃+1 {O(n)}
t₂₇: X₃⋅X₃+4⋅X₃+4 {O(n^2)}
t₂₈: X₃+1 {O(n)}
t₂₉: 3⋅X₃⋅X₃+11⋅X₃+8 {O(n^2)}
Costbounds
Overall costbound: 4⋅X₃⋅X₃+19⋅X₃+23 {O(n^2)}
t₂₀: 1 {O(1)}
t₂₁: X₃+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₃+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₃+1 {O(n)}
t₂₇: X₃⋅X₃+4⋅X₃+4 {O(n^2)}
t₂₈: X₃+1 {O(n)}
t₂₉: 3⋅X₃⋅X₃+11⋅X₃+8 {O(n^2)}
Sizebounds
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: X₃+1 {O(n)}
t₂₁, X₁: 3⋅X₃⋅X₃+11⋅X₃+X₁+9 {O(n^2)}
t₂₁, X₂: X₂+X₃+2 {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 2⋅X₃+1 {O(n)}
t₂₂, X₁: 3⋅X₃⋅X₃+11⋅X₃+X₁+9 {O(n^2)}
t₂₂, X₂: X₂+X₃+2 {O(n)}
t₂₂, X₃: 2⋅X₃ {O(n)}
t₂₃, X₀: X₃ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: X₃+1 {O(n)}
t₂₄, X₁: 1 {O(1)}
t₂₄, X₂: X₃+2 {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: 2⋅X₃+1 {O(n)}
t₂₅, X₁: 3⋅X₃⋅X₃+11⋅X₃+X₁+9 {O(n^2)}
t₂₅, X₂: X₂+X₃+2 {O(n)}
t₂₅, X₃: 2⋅X₃ {O(n)}
t₂₆, X₀: X₃+1 {O(n)}
t₂₆, X₁: 3⋅X₃⋅X₃+11⋅X₃+9 {O(n^2)}
t₂₆, X₂: X₃+2 {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: X₃+1 {O(n)}
t₂₇, X₁: 3⋅X₃⋅X₃+11⋅X₃+9 {O(n^2)}
t₂₇, X₂: X₃+2 {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₈, X₀: X₃+1 {O(n)}
t₂₈, X₁: 3⋅X₃⋅X₃+11⋅X₃+9 {O(n^2)}
t₂₈, X₂: X₃+2 {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₉, X₀: X₃+1 {O(n)}
t₂₉, X₁: 3⋅X₃⋅X₃+11⋅X₃+9 {O(n^2)}
t₂₉, X₂: X₃+2 {O(n)}
t₂₉, X₃: X₃ {O(n)}