Initial Problem
Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀) → l1(B)
t₁: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀
Preprocessing
Found invariant 4 ≤ X₀ for location l2
Problem after Preprocessing
Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀) → l1(B)
t₁: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l1
Found invariant 4 ≤ X₀ for location l2
Analysing control-flow refined program
Cut unsatisfiable transition t₆₃: n_l1___1→l2
Cut unsatisfiable transition t₆₄: n_l1___2→l2
Found invariant 4 ≤ X₀ for location l2
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 4 ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___1
Found invariant 4 ≤ X₀ for location l2
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 4 ∧ 3 ≤ X₀ for location n_l1___3
Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___1
Found invariant 4 ≤ X₀ for location l2
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 4 ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₅₄ 100 {O(1)}
TWN-Loops:
entry: t₅₂: n_l1___1(X₀) → n_l1___3(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
results in twn-loop: twn:Inv: [X₀ ≤ 4 ∧ 2 ≤ X₀] , (X₀) -> (X₀+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3
entry: t₅₆: l1(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ X₀ ≤ 3
results in twn-loop: twn:Inv: [X₀ ≤ 4 ∧ 2 ≤ X₀] , (X₀) -> (X₀+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ 0 < 1
∨ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
Stabilization-Threshold for: X₀ ≤ 3
alphas_abs: 3+X₀
M: 0
N: 1
Bound: 2⋅X₀+8 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+X₀
M: 0
N: 1
Bound: 2⋅X₀+4 {O(n)}
Stabilization-Threshold for: X₀ ≤ 4
alphas_abs: 4+X₀
M: 0
N: 1
Bound: 2⋅X₀+10 {O(n)}
Stabilization-Threshold for: 2 ≤ X₀
alphas_abs: 2+X₀
M: 0
N: 1
Bound: 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₅₂:
X₀: 3 {O(1)}
Runtime-bound of t₅₂: 1 {O(1)}
Results in: 54 {O(1)}
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ 0 < 1
∨ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ < 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 2 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₀ ≤ 4 ∧ 4 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
Stabilization-Threshold for: X₀ ≤ 3
alphas_abs: 3
M: 0
N: 1
Bound: 8 {O(1)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+X₀
M: 0
N: 1
Bound: 2⋅X₀+4 {O(n)}
Stabilization-Threshold for: X₀ ≤ 4
alphas_abs: 4
M: 0
N: 1
Bound: 10 {O(1)}
Stabilization-Threshold for: 2 ≤ X₀
alphas_abs: 2+X₀
M: 0
N: 1
Bound: 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₅₆:
X₀: 4 {O(1)}
Runtime-bound of t₅₆: 1 {O(1)}
Results in: 46 {O(1)}
100 {O(1)}
CFR: Improvement to new bound with the following program:
new bound:
100 {O(1)}
cfr-program:
Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, n_l1___1, n_l1___2, n_l1___3
Transitions:
t₀: l0(X₀) → l1(B)
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀
t₅₅: l1(X₀) → n_l1___2(1) :|: X₀ ≤ 0
t₅₆: l1(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ X₀ ≤ 3
t₅₂: n_l1___1(X₀) → n_l1___3(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₅₃: n_l1___2(X₀) → n_l1___1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₆₅: n_l1___3(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 2 ≤ X₀
t₅₄: n_l1___3(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 2 ≤ X₀
All Bounds
Timebounds
Overall timebound:107 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 100 {O(1)}
t₆₅: 1 {O(1)}
Costbounds
Overall costbound: 107 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 100 {O(1)}
t₆₅: 1 {O(1)}
Sizebounds
t₅₅, X₀: 1 {O(1)}
t₅₆, X₀: 4 {O(1)}
t₅₂, X₀: 3 {O(1)}
t₅₃, X₀: 2 {O(1)}
t₅₄, X₀: 4 {O(1)}
t₆₅, X₀: 4 {O(1)}