Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E, F
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1)
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F
t₁₁: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ 0
t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)
t₁₄: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁: l9(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7
Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
Cut unsatisfiable transition t₁₁: l5→l7
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E, F
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₄: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁: l9(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
l5 [X₀ ]
l3 [X₀+1 ]
l7 [X₀ ]
l6 [X₀+1 ]
MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀ ]
l4 [X₀ ]
l2 [X₀ ]
l5 [X₁ ]
l3 [X₀ ]
l7 [X₁-1 ]
l6 [X₀ ]
MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀-1 ]
l4 [X₀-1 ]
l2 [X₀-1 ]
l5 [X₀-1 ]
l3 [X₀-1 ]
l7 [X₀-1 ]
l6 [X₀ ]
MPRF for transition t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀ ]
l4 [X₀ ]
l2 [X₀ ]
l5 [X₀ ]
l3 [X₀ ]
l7 [X₁+1-X₂ ]
l6 [X₀ ]
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+3⋅X₀+2 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l2 [X₀-X₁-1 ]
l5 [X₀-X₁ ]
l7 [0 ]
l6 [X₀ ]
l3 [X₀-X₁ ]
MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+3⋅X₀+2 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l2 [X₀-X₁ ]
l5 [X₀-X₁ ]
l7 [X₀-X₁ ]
l6 [X₀ ]
l3 [X₀-X₁ ]
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+3⋅X₀+2 {O(n^2)}
MPRF:
l1 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]
l2 [X₀-X₁-1 ]
l5 [0 ]
l7 [X₀-X₁ ]
l6 [X₀ ]
l3 [X₀-X₁ ]
MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+6⋅X₀+4 {O(n^2)}
MPRF:
l1 [2⋅X₀-X₁-X₂-1 ]
l4 [2⋅X₀-X₁-X₂ ]
l2 [2⋅X₀-X₁-X₂-X₃ ]
l5 [2⋅X₀-X₁-1 ]
l7 [2⋅X₀-X₁-X₂ ]
l6 [2⋅X₀ ]
l3 [2⋅X₀-X₁-X₂ ]
MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+3⋅X₀+2 {O(n^2)}
MPRF:
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l2 [X₀-X₁-1 ]
l5 [0 ]
l7 [0 ]
l6 [X₀ ]
l3 [X₀-X₁ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₅: l3→l5
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₁+X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___6
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___7
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___9
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___4
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___5
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___1
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___8
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___2
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₂₅: l3(X₀, X₁, X₂, X₃) → n_l4___9(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₂₉: n_l4___9(X₀, X₁, X₂, X₃) → n_l1___8(X₀, X₁, Arg2_P, X₃) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₃₀: n_l4___9(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, Arg2_P, Arg3_P) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ Arg2_P ≤ Arg3_P ∧ Arg3_P ≤ Arg2_P ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₂₀: n_l1___8(X₀, X₁, X₂, X₃) → n_l2___6(X₀, X₁, X₂, 1) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₂₃: n_l2___6(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₁+X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₂₄: n_l2___7(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₁₁₉: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, 1) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+4⋅X₀+2 {O(n^2)}
MPRF:
n_l4___9 [-1 ]
l3 [-1 ]
l7 [0 ]
l6 [0 ]
n_l1___8 [X₀ ]
n_l2___1 [X₀-X₁-X₃ ]
n_l2___6 [X₀ ]
n_l2___7 [X₀ ]
n_l3___5 [X₀-X₁ ]
l5 [X₀-X₁ ]
n_l1___3 [X₀-X₁ ]
n_l4___4 [X₀-X₁ ]
n_l2___2 [X₀-X₁-1 ]
MPRF for transition t₁₂₁: n_l2___1(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+4⋅X₀+2 {O(n^2)}
MPRF:
n_l4___9 [0 ]
l3 [0 ]
l7 [0 ]
l6 [0 ]
n_l1___8 [X₀ ]
n_l2___1 [X₀-X₁ ]
n_l2___6 [X₀ ]
n_l2___7 [X₀ ]
n_l3___5 [X₀-X₁ ]
l5 [0 ]
n_l1___3 [X₀-X₁ ]
n_l4___4 [X₀-X₁ ]
n_l2___2 [X₀-X₁-1 ]
MPRF for transition t₁₂₂: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+6 {O(n^2)}
MPRF:
n_l4___9 [X₀-1 ]
l3 [X₀-1 ]
l7 [X₁-2⋅X₃ ]
l6 [X₀-1 ]
n_l1___8 [2⋅X₀ ]
n_l2___1 [2⋅X₀-X₁-3⋅X₃ ]
n_l2___6 [2⋅X₀ ]
n_l2___7 [2⋅X₀ ]
n_l3___5 [2⋅X₀-X₁-2 ]
l5 [X₁+2⋅X₂-2⋅X₃-2 ]
n_l1___3 [2⋅X₀-X₁-3 ]
n_l4___4 [2⋅X₀-X₁-2 ]
n_l2___2 [2⋅X₀-X₁-2 ]
MPRF for transition t₁₂₆: n_l3___5(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+5 {O(n^2)}
MPRF:
n_l4___9 [X₀ ]
l3 [X₀ ]
l7 [X₀+X₂-X₃ ]
l6 [X₀ ]
n_l1___8 [2⋅X₀ ]
n_l2___1 [2⋅X₀-X₁-X₃ ]
n_l2___6 [2⋅X₀ ]
n_l2___7 [2⋅X₀ ]
n_l3___5 [2⋅X₀+1-X₁-X₃ ]
l5 [X₁+1-X₃ ]
n_l1___3 [2⋅X₀-X₁-1 ]
n_l4___4 [2⋅X₀-X₁-X₂ ]
n_l2___2 [2⋅X₀-X₁-X₂ ]
MPRF for transition t₁₃₈: n_l3___5(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l3 [X₀+1 ]
l7 [X₁ ]
l6 [X₀+1 ]
n_l2___1 [X₀+1 ]
n_l2___6 [X₀+X₃ ]
n_l3___5 [X₀+1 ]
l5 [X₀ ]
n_l1___3 [X₀+1 ]
n_l4___4 [X₀+1 ]
n_l2___2 [X₀+1 ]
n_l1___8 [X₀+1 ]
n_l4___9 [X₀+1 ]
n_l2___7 [X₀+1 ]
MPRF for transition t₁₂₇: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, Arg2_P, X₃) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+6 {O(n^2)}
MPRF:
n_l4___9 [X₀-1 ]
l3 [X₀-1 ]
l7 [2⋅X₀-X₁-2 ]
l6 [X₀-1 ]
n_l1___8 [2⋅X₀ ]
n_l2___1 [2⋅X₀-X₁-2⋅X₃-1 ]
n_l2___6 [2⋅X₀ ]
n_l2___7 [2⋅X₀-X₁ ]
n_l3___5 [2⋅X₀-X₁-2⋅X₂ ]
l5 [2⋅X₀-X₁-2 ]
n_l1___3 [2⋅X₀-X₁-X₃-2 ]
n_l4___4 [2⋅X₀-X₁-X₃-1 ]
n_l2___2 [2⋅X₀-X₁-X₂-1 ]
MPRF for transition t₁₂₈: n_l4___4(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, Arg2_P, Arg3_P) :|: X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ Arg2_P ≤ Arg3_P ∧ Arg3_P ≤ Arg2_P ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+4⋅X₀+2 {O(n^2)}
MPRF:
n_l4___9 [0 ]
l3 [0 ]
l7 [0 ]
l6 [0 ]
n_l1___8 [X₀ ]
n_l2___1 [X₀-X₁ ]
n_l2___6 [X₀ ]
n_l2___7 [X₀ ]
n_l3___5 [X₀-X₁ ]
l5 [X₀-X₁ ]
n_l1___3 [X₀-X₁ ]
n_l4___4 [X₀-X₁ ]
n_l2___2 [X₀-X₁-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:6⋅X₀⋅X₀+22⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₈: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₉: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₄: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₅: X₀+2 {O(n)}
t₆: 2⋅X₀⋅X₀+6⋅X₀+4 {O(n^2)}
t₇: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₂: X₀+1 {O(n)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 6⋅X₀⋅X₀+22⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₈: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₉: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₄: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₅: X₀+2 {O(n)}
t₆: 2⋅X₀⋅X₀+6⋅X₀+4 {O(n^2)}
t₇: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₂: X₀+1 {O(n)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: 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)}
t₈, X₀: X₀+1 {O(n)}
t₈, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₈, X₂: 1 {O(1)}
t₈, X₃: 1 {O(1)}
t₉, X₀: X₀+1 {O(n)}
t₉, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₉, X₂: 1 {O(1)}
t₉, X₃: 1 {O(1)}
t₄, X₀: X₀+1 {O(n)}
t₄, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₄, X₂: 1 {O(1)}
t₄, X₃: X₃+2 {O(n)}
t₅, X₀: X₀+1 {O(n)}
t₅, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 1 {O(1)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₆, X₂: 1 {O(1)}
t₆, X₃: X₃+2 {O(n)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₇, X₂: 1 {O(1)}
t₇, X₃: 1 {O(1)}
t₁₀, X₀: X₀+1 {O(n)}
t₁₀, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₁₀, X₂: 0 {O(1)}
t₁₀, X₃: 1 {O(1)}
t₁₂, X₀: X₀+1 {O(n)}
t₁₂, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₁₂, X₂: 1 {O(1)}
t₁₂, X₃: 1 {O(1)}
t₂, X₀: X₀+1 {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: 0 {O(1)}
t₂, X₃: X₃+1 {O(n)}
t₃, X₀: 2⋅X₀+2 {O(n)}
t₃, X₁: X₀⋅X₀+3⋅X₀+X₁+2 {O(n^2)}
t₃, X₂: X₂+1 {O(n)}
t₃, X₃: X₃+1 {O(n)}
t₁₃, X₀: X₀+1 {O(n)}
t₁₃, X₁: X₀⋅X₀+3⋅X₀+2 {O(n^2)}
t₁₃, X₂: 1 {O(1)}
t₁₃, X₃: 1 {O(1)}
t₁₄, X₀: 3⋅X₀+3 {O(n)}
t₁₄, X₁: 2⋅X₀⋅X₀+6⋅X₀+X₁+4 {O(n^2)}
t₁₄, X₂: X₂+1 {O(n)}
t₁₄, X₃: X₃+2 {O(n)}
t₁, X₀: X₀+1 {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}