Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₆: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂)
t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂)
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l1(D, X₂, X₂)
Preprocessing
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l2
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l7
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5
Found invariant X₁ ≤ X₂ for location l1
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₁ ≤ X₂
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₆: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₁ ≤ 0
t₁: l6(X₀, X₁, X₂) → l1(D, X₂, X₂)
MPRF for transition t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₂ {O(n)}
Chain transitions t₁: l6→l1 and t₃: l1→l5 to t₅₇: l6→l5
Chain transitions t₇: l4→l1 and t₃: l1→l5 to t₅₈: l4→l5
Chain transitions t₇: l4→l1 and t₂: l1→l2 to t₅₉: l4→l2
Chain transitions t₁: l6→l1 and t₂: l1→l2 to t₆₀: l6→l2
Chain transitions t₆: l3→l1 and t₂: l1→l2 to t₆₁: l3→l2
Chain transitions t₆: l3→l1 and t₃: l1→l5 to t₆₂: l3→l5
Chain transitions t₆₀: l6→l2 and t₅: l2→l4 to t₆₃: l6→l4
Chain transitions t₅₉: l4→l2 and t₅: l2→l4 to t₆₄: l4→l4
Chain transitions t₅₉: l4→l2 and t₄: l2→l3 to t₆₅: l4→l3
Chain transitions t₆₀: l6→l2 and t₄: l2→l3 to t₆₆: l6→l3
Chain transitions t₆₁: l3→l2 and t₄: l2→l3 to t₆₇: l3→l3
Chain transitions t₆₁: l3→l2 and t₅: l2→l4 to t₆₈: l3→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₆₂: l3→l5
Cut unsatisfiable transition t₆₄: l4→l4
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l2
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l7
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5
Found invariant X₁ ≤ X₂ for location l1
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₆₅: l4(X₀, X₁, X₂) -{3}> l3(X₂, X₁-1, X₂) :|: 2 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₆₈: l3(X₀, X₁, X₂) -{3}> l4(X₀-1, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂+1 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₈₆: n_l1___12→l5
Cut unsatisfiable transition t₁₈₇: n_l1___3→l5
Cut unsatisfiable transition t₁₈₈: n_l1___6→l5
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___12
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l2___15
Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___9
Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___11
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___13
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___2
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l7
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___14
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5
Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___8
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___7
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___10
MPRF for transition t₁₆₂: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₆₃: n_l1___9(X₀, X₁, X₂) → n_l2___8(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2 {O(n)}
MPRF for transition t₁₆₉: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₇₀: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₇₁: n_l2___8(X₀, X₁, X₂) → n_l3___7(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₇₄: n_l3___7(X₀, X₁, X₂) → n_l1___6(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₁₇₅: n_l4___1(X₀, X₁, X₂) → n_l1___9(X₂, X₁-1, X₂) :|: 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2 {O(n)}
TWN: t₁₆₁: n_l1___3→n_l2___2
cycle: [t₁₇₃: n_l3___4→n_l1___3; t₁₆₈: n_l2___2→n_l3___4; t₁₆₁: n_l1___3→n_l2___2]
loop: (1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁,(X₀,X₁) -> (X₀-1,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+X₀
M: 0
N: 1
Bound: 2⋅X₀+4 {O(n)}
Stabilization-Threshold for: 2 ≤ X₀
alphas_abs: 2+X₀
M: 0
N: 1
Bound: 2⋅X₀+6 {O(n)}
TWN - Lifting for t₁₆₁: n_l1___3→n_l2___2 of 4⋅X₀+13 {O(n)}
relevant size-bounds w.r.t. t₁₇₀:
X₀: 4⋅X₂ {O(n)}
Runtime-bound of t₁₇₀: 2⋅X₂ {O(n)}
Results in: 32⋅X₂⋅X₂+26⋅X₂ {O(n^2)}
TWN: t₁₆₈: n_l2___2→n_l3___4
TWN - Lifting for t₁₆₈: n_l2___2→n_l3___4 of 4⋅X₀+13 {O(n)}
relevant size-bounds w.r.t. t₁₇₀:
X₀: 4⋅X₂ {O(n)}
Runtime-bound of t₁₇₀: 2⋅X₂ {O(n)}
Results in: 32⋅X₂⋅X₂+26⋅X₂ {O(n^2)}
TWN: t₁₇₃: n_l3___4→n_l1___3
TWN - Lifting for t₁₇₃: n_l3___4→n_l1___3 of 4⋅X₀+13 {O(n)}
relevant size-bounds w.r.t. t₁₇₀:
X₀: 4⋅X₂ {O(n)}
Runtime-bound of t₁₇₀: 2⋅X₂ {O(n)}
Results in: 32⋅X₂⋅X₂+26⋅X₂ {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₂ {O(n)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₂ {O(n)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₁: 2⋅X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₁: 2⋅X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}