Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, 0) :|: X₁+1 ≤ X₂
t₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₂ ≤ X₁
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₀+1 ≤ X₂
t₄: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂
Preprocessing
Found invariant 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 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 l5
Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, 0) :|: X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 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
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
Chain transitions t₃: l4→l1 and t₆: l1→l4 to t₉₇: l4→l4
Chain transitions t₂: l4→l1 and t₆: l1→l4 to t₉₈: l4→l4
Chain transitions t₂: l4→l1 and t₅: l1→l4 to t₉₉: l4→l4
Chain transitions t₃: l4→l1 and t₅: l1→l4 to t₁₀₀: l4→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₉₉: l4→l4
Found invariant 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 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 l5
Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
MPRF for transition t₉₇: l4(X₀, X₁, X₂) -{2}> l4(X₀, X₁, X₂+1) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 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+2 {O(n)}
knowledge_propagation leads to new time bound X₀+X₁+2 {O(n)} for transition t₁₀₀: l4(X₀, X₁, X₂) -{2}> l4(X₀, X₁, 0) :|: X₀+1 ≤ X₂ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
MPRF for transition t₉₈: l4(X₀, X₁, X₂) -{2}> l4(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 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+X₁⋅X₁+2⋅X₀+4⋅X₁+4 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₄: l4→l2
Cut unsatisfiable transition t₂₀₇: n_l4___3→n_l1___1
Cut unsatisfiable transition t₂₂₃: n_l4___5→l2
Cut unsatisfiable transition t₂₂₄: n_l4___7→l2
Cut unreachable locations [n_l1___1] from the program graph
Found invariant 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 X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 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___4
Found invariant 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___3
Found invariant 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___2
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___8
Found invariant 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___5
Found invariant 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 l5
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___7
MPRF for transition t₂₀₅: n_l1___6(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+3 {O(n)}
MPRF for transition t₂₁₀: n_l4___7(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+4 {O(n)}
MPRF for transition t₂₀₂: n_l1___2(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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:
X₁+2 {O(n)}
MPRF for transition t₂₀₈: n_l4___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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+2 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2, l3, l4, l5, n_l1___2, n_l1___4, n_l1___6, n_l1___8, n_l4___3, n_l4___5, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 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 ∧ 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
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂₁₁: l4(X₀, X₁, X₂) → n_l1___8(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₂: n_l1___2(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₂₀₃: n_l1___4(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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
t₂₀₄: n_l1___6(X₀, X₁, X₂) → n_l4___5(X₀, X₁, 0) :|: 1+X₀ ≤ X₂ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₅: n_l1___6(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₆: n_l1___8(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₂₂: n_l4___3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₈: n_l4___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₉: n_l4___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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
t₂₁₀: n_l4___7(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
2⋅X₀+4⋅X₁+11 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2, l3, l4, l5, n_l1___2, n_l1___4, n_l1___6, n_l1___8, n_l4___3, n_l4___5, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₇: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 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 ∧ 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
t₁: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₀+1) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₂₁₁: l4(X₀, X₁, X₂) → n_l1___8(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₂: n_l1___2(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₂₀₃: n_l1___4(X₀, X₁, X₂) → n_l4___3(X₀, X₁, X₂+1) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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
t₂₀₄: n_l1___6(X₀, X₁, X₂) → n_l4___5(X₀, X₁, 0) :|: 1+X₀ ≤ X₂ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₅: n_l1___6(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₆: n_l1___8(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂+1) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₂₂: n_l4___3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₈: n_l4___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₀₉: n_l4___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 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
t₂₁₀: n_l4___7(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:2⋅X₀+4⋅X₁+20 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₂₀₂: X₁+2 {O(n)}
t₂₀₃: 1 {O(1)}
t₂₀₄: 1 {O(1)}
t₂₀₅: X₀+X₁+3 {O(n)}
t₂₀₆: 1 {O(1)}
t₂₀₈: X₁+2 {O(n)}
t₂₀₉: 1 {O(1)}
t₂₁₀: X₀+X₁+4 {O(n)}
t₂₁₁: 1 {O(1)}
t₂₂₂: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₀+4⋅X₁+20 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₂₀₂: X₁+2 {O(n)}
t₂₀₃: 1 {O(1)}
t₂₀₄: 1 {O(1)}
t₂₀₅: X₀+X₁+3 {O(n)}
t₂₀₆: 1 {O(1)}
t₂₀₈: X₁+2 {O(n)}
t₂₀₉: 1 {O(1)}
t₂₁₀: X₀+X₁+4 {O(n)}
t₂₁₁: 1 {O(1)}
t₂₂₂: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀+1 {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁+4 {O(n)}
t₂₀₂, X₀: X₀ {O(n)}
t₂₀₂, X₁: X₁ {O(n)}
t₂₀₂, X₂: X₁+3 {O(n)}
t₂₀₃, X₀: X₀ {O(n)}
t₂₀₃, X₁: X₁ {O(n)}
t₂₀₃, X₂: 1 {O(1)}
t₂₀₄, X₀: X₀ {O(n)}
t₂₀₄, X₁: X₁ {O(n)}
t₂₀₄, X₂: 0 {O(1)}
t₂₀₅, X₀: X₀ {O(n)}
t₂₀₅, X₁: X₁ {O(n)}
t₂₀₅, X₂: 2⋅X₀+X₁+5 {O(n)}
t₂₀₆, X₀: X₀ {O(n)}
t₂₀₆, X₁: X₁ {O(n)}
t₂₀₆, X₂: X₀+2 {O(n)}
t₂₀₈, X₀: X₀ {O(n)}
t₂₀₈, X₁: X₁ {O(n)}
t₂₀₈, X₂: X₁+3 {O(n)}
t₂₀₉, X₀: X₀ {O(n)}
t₂₀₉, X₁: X₁ {O(n)}
t₂₀₉, X₂: 0 {O(1)}
t₂₁₀, X₀: X₀ {O(n)}
t₂₁₀, X₁: X₁ {O(n)}
t₂₁₀, X₂: 2⋅X₀+X₁+5 {O(n)}
t₂₁₁, X₀: X₀ {O(n)}
t₂₁₁, X₁: X₁ {O(n)}
t₂₁₁, X₂: X₀+1 {O(n)}
t₂₂₂, X₀: 2⋅X₀ {O(n)}
t₂₂₂, X₁: 2⋅X₁ {O(n)}
t₂₂₂, X₂: X₁+4 {O(n)}