Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃)
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1)
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, 0) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
Preprocessing
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, 0) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁-X₃ ]
l1 [X₁-X₃ ]
l4 [X₁-X₃ ]
l2 [X₁-X₃ ]
MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁-X₃ ]
l1 [X₁-X₃ ]
l4 [X₁-X₃ ]
l2 [X₁-X₃-1 ]
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₁+X₀+X₁ {O(n^2)}
MPRF:
l2 [X₀+1 ]
l3 [X₀-X₂ ]
l4 [X₀-X₂ ]
l1 [X₀-X₂ ]
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+X₀+1 {O(n^2)}
MPRF:
l2 [X₁ ]
l3 [X₀+1-X₂ ]
l4 [X₀-X₂ ]
l1 [X₀-X₂ ]
MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₁+X₀+X₁+1 {O(n^2)}
MPRF:
l2 [X₀+1 ]
l3 [X₀+1-X₂ ]
l4 [X₀+1-X₂ ]
l1 [X₀-X₂ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₅: l3→l5
Cut unsatisfiable transition t₁₀₂: n_l3___7→l5
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___9
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___8
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___5
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___1
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___4
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___7
MPRF for transition t₈₂: n_l1___1(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l3___3 [X₁-X₃ ]
n_l3___7 [X₁-X₃-1 ]
n_l4___2 [X₁-X₃ ]
n_l1___1 [X₁-X₃ ]
n_l1___5 [X₁-X₃-1 ]
n_l4___6 [X₁-X₃-1 ]
n_l2___4 [X₁-X₃-1 ]
MPRF for transition t₈₅: n_l2___4(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l3___3 [X₁-X₃ ]
n_l3___7 [X₁-X₃ ]
n_l4___2 [X₁-X₃ ]
n_l1___1 [X₁-X₃ ]
n_l1___5 [X₁-X₃ ]
n_l4___6 [X₁-X₃ ]
n_l2___4 [X₁-X₃ ]
MPRF for transition t₈₇: n_l3___3(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l3___3 [X₁+1-X₃ ]
n_l3___7 [X₁-X₃ ]
n_l4___2 [X₁-X₃ ]
n_l1___1 [X₁-X₃ ]
n_l1___5 [X₁-X₃ ]
n_l4___6 [X₁-X₃ ]
n_l2___4 [X₁-X₃ ]
MPRF for transition t₈₉: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___1(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l3___3 [X₁-X₃ ]
n_l3___7 [X₁-X₃-1 ]
n_l4___2 [X₁-X₃ ]
n_l1___1 [X₁-X₃-1 ]
n_l1___5 [X₁-X₃-1 ]
n_l4___6 [X₁-X₃-1 ]
n_l2___4 [X₁-X₃-1 ]
MPRF for transition t₉₁: n_l4___6(X₀, X₁, X₂, X₃) → n_l2___4(X₀, X₁, X₀, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l3___3 [X₁-X₃ ]
n_l3___7 [X₁-X₃ ]
n_l4___2 [X₁-X₃ ]
n_l1___1 [X₁-X₃ ]
n_l1___5 [X₁-X₃ ]
n_l4___6 [X₁-X₃ ]
n_l2___4 [X₁-X₃-1 ]
MPRF for transition t₈₃: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀⋅X₁+X₀+1 {O(n^2)}
MPRF:
n_l2___4 [X₀ ]
n_l3___3 [X₀ ]
n_l3___7 [X₀-X₂ ]
n_l4___2 [X₀ ]
n_l1___1 [X₀ ]
n_l4___6 [X₀-X₂ ]
n_l1___5 [X₀-X₂ ]
MPRF for transition t₈₈: n_l3___7(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₁+X₀+2 {O(n^2)}
MPRF:
n_l2___4 [X₀ ]
n_l3___3 [X₀ ]
n_l3___7 [X₀+1-X₂ ]
n_l4___2 [X₀ ]
n_l1___1 [X₀ ]
n_l4___6 [X₀-X₂ ]
n_l1___5 [X₀-X₂ ]
MPRF for transition t₉₀: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₁+X₀+2 {O(n^2)}
MPRF:
n_l2___4 [X₀ ]
n_l3___3 [X₀ ]
n_l3___7 [X₀+1-X₂ ]
n_l4___2 [X₀ ]
n_l1___1 [X₀ ]
n_l4___6 [X₀+1-X₂ ]
n_l1___5 [X₀-X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₀⋅X₁+X₁⋅X₁+3⋅X₀+4⋅X₁+8 {O(n^2)}
t₀: 1 {O(1)}
t₈: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₉: X₁ {O(n)}
t₄: X₁⋅X₁+X₀+1 {O(n^2)}
t₅: 1 {O(1)}
t₆: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₇: X₁ {O(n)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₀⋅X₁+X₁⋅X₁+3⋅X₀+4⋅X₁+8 {O(n^2)}
t₀: 1 {O(1)}
t₈: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₉: X₁ {O(n)}
t₄: X₁⋅X₁+X₀+1 {O(n^2)}
t₅: 1 {O(1)}
t₆: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₇: X₁ {O(n)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₈, X₃: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₄, X₃: X₁ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₅, X₃: 2⋅X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₆, X₃: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₀⋅X₁+X₀+X₁ {O(n^2)}
t₇, X₃: X₁ {O(n)}
t₁₀, X₀: 4⋅X₀ {O(n)}
t₁₀, X₁: 4⋅X₁ {O(n)}
t₁₀, X₂: X₀⋅X₁+2⋅X₂+X₀+X₁ {O(n^2)}
t₁₀, X₃: 2⋅X₁+2⋅X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 0 {O(1)}
t₃, X₃: 0 {O(1)}