KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb4in

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicreturnin

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbbin

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb3in

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicstop

Problem after Preprocessing

Start: evalcyclicstart
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: evalcyclicbb3in, evalcyclicbb4in, evalcyclicbbin, evalcyclicentryin, evalcyclicreturnin, evalcyclicstart, evalcyclicstop
Transitions:
t₃: evalcyclicbb3in(X₀, X₁, X₂) → evalcyclicbb4in(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₄: evalcyclicbb3in(X₀, X₁, X₂) → evalcyclicbb4in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₂: evalcyclicbb3in(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₅: evalcyclicbb4in(X₀, X₁, X₂) → evalcyclicbbin(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₆: evalcyclicbb4in(X₀, X₁, X₂) → evalcyclicbbin(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₇: evalcyclicbb4in(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₈: evalcyclicbbin(X₀, X₁, X₂) → evalcyclicbb3in(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₉: evalcyclicbbin(X₀, X₁, X₂) → evalcyclicbb3in(X₀, X₁, 0) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₁: evalcyclicentryin(X₀, X₁, X₂) → evalcyclicbb3in(X₀, X₁, 1+X₀) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: evalcyclicreturnin(X₀, X₁, X₂) → evalcyclicstop(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₀: evalcyclicstart(X₀, X₁, X₂) → evalcyclicentryin(X₀, X₁, X₂)

Cut unreachable locations [evalcyclicbb4in] from the program graph

Cut unsatisfiable transition [t₂: evalcyclicbb3in→evalcyclicreturnin; t₆₆: evalcyclicbb3in→evalcyclicreturnin; t₆₈: evalcyclicbb3in→evalcyclicbb4in_v2]

Cut unreachable locations [evalcyclicbb3in_v1; evalcyclicbb4in_v2; evalcyclicbbin_v1] from the program graph

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location evalcyclicbb4in_v6

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb3in_v2

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb4in_v3

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicstop

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbbin_v3

Found invariant X₂ ≤ 1 ∧ 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 evalcyclicbbin_v5

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location evalcyclicbbin_v6

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbbin_v2

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb3in

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb4in_v1

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicreturnin

Found invariant X₂ ≤ 1 ∧ 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 evalcyclicbb4in_v5

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalcyclicbb3in_v5

Found invariant X₂ ≤ 1 ∧ 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 evalcyclicbb3in_v4

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 evalcyclicbb4in_v4

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 evalcyclicbbin_v4

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalcyclicbb3in_v3

Cut unsatisfiable transition [t₇₈: evalcyclicbbin_v2→evalcyclicbb3in_v2]

Analysing control-flow refined program

MPRF for transition t₈₀: evalcyclicbb3in_v3(X₀, X₁, X₂) → evalcyclicbb4in_v3(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

• evalcyclicbb3in_v3: [2+X₁-X₂]
• evalcyclicbb4in_v3: [1+X₁-X₂]
• evalcyclicbbin_v3: [1+X₁-X₂]

MPRF for transition t₈₂: evalcyclicbb4in_v3(X₀, X₁, X₂) → evalcyclicbbin_v3(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

• evalcyclicbb3in_v3: [2+X₁-X₂]
• evalcyclicbb4in_v3: [2+X₁-X₂]
• evalcyclicbbin_v3: [1+X₁-X₂]

MPRF for transition t₈₃: evalcyclicbb4in_v3(X₀, X₁, X₂) → evalcyclicbbin_v3(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

• evalcyclicbb3in_v3: [2+X₁-X₂]
• evalcyclicbb4in_v3: [2+X₁-X₂]
• evalcyclicbbin_v3: [1+X₁-X₂]

MPRF for transition t₈₅: evalcyclicbbin_v3(X₀, X₁, X₂) → evalcyclicbb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+5 {O(n)}

MPRF:

• evalcyclicbb3in_v3: [1+X₁-X₂]
• evalcyclicbb4in_v3: [1+X₁-X₂]
• evalcyclicbbin_v3: [1+X₁-X₂]

MPRF for transition t₉₉: evalcyclicbb3in_v5(X₀, X₁, X₂) → evalcyclicbb4in_v6(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

16⋅X₀+3 {O(n)}

MPRF:

• evalcyclicbb3in_v5: [1+X₀-X₂]
• evalcyclicbb4in_v6: [X₀-X₂]
• evalcyclicbbin_v6: [X₀-X₂]

MPRF for transition t₁₀₁: evalcyclicbb4in_v6(X₀, X₁, X₂) → evalcyclicbbin_v6(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

16⋅X₁+3 {O(n)}

MPRF:

• evalcyclicbb3in_v5: [X₁-1-X₂]
• evalcyclicbb4in_v6: [X₁-1-X₂]
• evalcyclicbbin_v6: [X₁-2-X₂]

MPRF for transition t₁₀₂: evalcyclicbb4in_v6(X₀, X₁, X₂) → evalcyclicbbin_v6(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

16⋅X₀+2 {O(n)}

MPRF:

• evalcyclicbb3in_v5: [X₀-X₂]
• evalcyclicbb4in_v6: [X₀-X₂]
• evalcyclicbbin_v6: [X₀-1-X₂]

MPRF for transition t₁₀₃: evalcyclicbbin_v6(X₀, X₁, X₂) → evalcyclicbb3in_v5(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

16⋅X₀+2 {O(n)}

MPRF:

• evalcyclicbb3in_v5: [X₀-X₂]
• evalcyclicbb4in_v6: [X₀-X₂]
• evalcyclicbbin_v6: [X₀-X₂]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: evalcyclicstart
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: evalcyclicbb3in, evalcyclicbb3in_v2, evalcyclicbb3in_v3, evalcyclicbb3in_v4, evalcyclicbb3in_v5, evalcyclicbb4in_v1, evalcyclicbb4in_v3, evalcyclicbb4in_v4, evalcyclicbb4in_v5, evalcyclicbb4in_v6, evalcyclicbbin_v2, evalcyclicbbin_v3, evalcyclicbbin_v4, evalcyclicbbin_v5, evalcyclicbbin_v6, evalcyclicentryin, evalcyclicreturnin, evalcyclicstart, evalcyclicstop
Transitions:
t₆₇: evalcyclicbb3in(X₀, X₁, X₂) → evalcyclicbb4in_v1(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁
t₈₇: evalcyclicbb3in_v2(X₀, X₁, X₂) → evalcyclicbb4in_v4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₆: evalcyclicbb3in_v2(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₀: evalcyclicbb3in_v3(X₀, X₁, X₂) → evalcyclicbb4in_v3(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
t₉₃: evalcyclicbb3in_v4(X₀, X₁, X₂) → evalcyclicbb4in_v5(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂
t₉₂: evalcyclicbb3in_v4(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂
t₉₉: evalcyclicbb3in_v5(X₀, X₁, X₂) → evalcyclicbb4in_v6(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂
t₉₈: evalcyclicbb3in_v5(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂
t₇₆: evalcyclicbb4in_v1(X₀, X₁, X₂) → evalcyclicbbin_v2(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁
t₇₇: evalcyclicbb4in_v1(X₀, X₁, X₂) → evalcyclicbbin_v2(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁
t₇₅: evalcyclicbb4in_v1(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁
t₈₂: evalcyclicbb4in_v3(X₀, X₁, X₂) → evalcyclicbbin_v3(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₈₃: evalcyclicbb4in_v3(X₀, X₁, X₂) → evalcyclicbbin_v3(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₈₁: evalcyclicbb4in_v3(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₈₉: evalcyclicbb4in_v4(X₀, X₁, X₂) → evalcyclicbbin_v4(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₀: evalcyclicbb4in_v4(X₀, X₁, X₂) → evalcyclicbbin_v4(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₈: evalcyclicbb4in_v4(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₅: evalcyclicbb4in_v5(X₀, X₁, X₂) → evalcyclicbbin_v5(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉₆: evalcyclicbb4in_v5(X₀, X₁, X₂) → evalcyclicbbin_v5(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉₄: evalcyclicbb4in_v5(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₁: evalcyclicbb4in_v6(X₀, X₁, X₂) → evalcyclicbbin_v6(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₂: evalcyclicbb4in_v6(X₀, X₁, X₂) → evalcyclicbbin_v6(X₀, X₁, X₂) :|: 1+D ≤ 0 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₀: evalcyclicbb4in_v6(X₀, X₁, X₂) → evalcyclicreturnin(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇₉: evalcyclicbbin_v2(X₀, X₁, X₂) → evalcyclicbb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₈₄: evalcyclicbbin_v3(X₀, X₁, X₂) → evalcyclicbb3in_v2(X₀, X₁, 0) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₈₅: evalcyclicbbin_v3(X₀, X₁, X₂) → evalcyclicbb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₉₁: evalcyclicbbin_v4(X₀, X₁, X₂) → evalcyclicbb3in_v4(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₇: evalcyclicbbin_v5(X₀, X₁, X₂) → evalcyclicbb3in_v5(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₃: evalcyclicbbin_v6(X₀, X₁, X₂) → evalcyclicbb3in_v5(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: evalcyclicentryin(X₀, X₁, X₂) → evalcyclicbb3in(X₀, X₁, 1+X₀) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: evalcyclicreturnin(X₀, X₁, X₂) → evalcyclicstop(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₀: evalcyclicstart(X₀, X₁, X₂) → evalcyclicentryin(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:24⋅X₁+56⋅X₀+57 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₀: 1 {O(1)}
t₆₇: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₃: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 2⋅X₀+2⋅X₁+5 {O(n)}
t₈₆: 1 {O(1)}
t₈₇: 1 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}
t₉₃: 1 {O(1)}
t₉₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₉₆: 1 {O(1)}
t₉₇: 1 {O(1)}
t₉₈: 1 {O(1)}
t₉₉: 16⋅X₀+3 {O(n)}
t₁₀₀: 1 {O(1)}
t₁₀₁: 16⋅X₁+3 {O(n)}
t₁₀₂: 16⋅X₀+2 {O(n)}
t₁₀₃: 16⋅X₀+2 {O(n)}

Costbounds

Overall costbound: 24⋅X₁+56⋅X₀+57 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₀: 1 {O(1)}
t₆₇: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₃: 2⋅X₀+2⋅X₁+6 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 2⋅X₀+2⋅X₁+5 {O(n)}
t₈₆: 1 {O(1)}
t₈₇: 1 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}
t₉₃: 1 {O(1)}
t₉₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₉₆: 1 {O(1)}
t₉₇: 1 {O(1)}
t₉₈: 1 {O(1)}
t₉₉: 16⋅X₀+3 {O(n)}
t₁₀₀: 1 {O(1)}
t₁₀₁: 16⋅X₁+3 {O(n)}
t₁₀₂: 16⋅X₀+2 {O(n)}
t₁₀₃: 16⋅X₀+2 {O(n)}

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)}
t₁₀, X₀: 63⋅X₀+1 {O(n)}
t₁₀, X₁: 75⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+37⋅X₀+22 {O(n)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: X₁ {O(n)}
t₆₇, X₂: X₀+1 {O(n)}
t₇₅, X₀: X₀ {O(n)}
t₇₅, X₁: X₁ {O(n)}
t₇₅, X₂: X₀+1 {O(n)}
t₇₆, X₀: X₀ {O(n)}
t₇₆, X₁: X₁ {O(n)}
t₇₆, X₂: X₀+1 {O(n)}
t₇₇, X₀: X₀ {O(n)}
t₇₇, X₁: X₁ {O(n)}
t₇₇, X₂: X₀+1 {O(n)}
t₇₉, X₀: 2⋅X₀ {O(n)}
t₇₉, X₁: 2⋅X₁ {O(n)}
t₇₉, X₂: 2⋅X₀+4 {O(n)}
t₈₀, X₀: 2⋅X₀ {O(n)}
t₈₀, X₁: 2⋅X₁ {O(n)}
t₈₀, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₈₁, X₀: 2⋅X₀ {O(n)}
t₈₁, X₁: 2⋅X₁ {O(n)}
t₈₁, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₈₂, X₀: 2⋅X₀ {O(n)}
t₈₂, X₁: 2⋅X₁ {O(n)}
t₈₂, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₈₃, X₀: 2⋅X₀ {O(n)}
t₈₃, X₁: 2⋅X₁ {O(n)}
t₈₃, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₈₄, X₀: 4⋅X₀ {O(n)}
t₈₄, X₁: 4⋅X₁ {O(n)}
t₈₄, X₂: 0 {O(1)}
t₈₅, X₀: 2⋅X₀ {O(n)}
t₈₅, X₁: 2⋅X₁ {O(n)}
t₈₅, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₈₆, X₀: 0 {O(1)}
t₈₆, X₁: 4⋅X₁ {O(n)}
t₈₆, X₂: 0 {O(1)}
t₈₇, X₀: 4⋅X₀ {O(n)}
t₈₇, X₁: 4⋅X₁ {O(n)}
t₈₇, X₂: 0 {O(1)}
t₈₈, X₀: 4⋅X₀ {O(n)}
t₈₈, X₁: 4⋅X₁ {O(n)}
t₈₈, X₂: 0 {O(1)}
t₈₉, X₀: 4⋅X₀ {O(n)}
t₈₉, X₁: 4⋅X₁ {O(n)}
t₈₉, X₂: 0 {O(1)}
t₉₀, X₀: 4⋅X₀ {O(n)}
t₉₀, X₁: 4⋅X₁ {O(n)}
t₉₀, X₂: 0 {O(1)}
t₉₁, X₀: 8⋅X₀ {O(n)}
t₉₁, X₁: 8⋅X₁ {O(n)}
t₉₁, X₂: 1 {O(1)}
t₉₂, X₀: 1 {O(1)}
t₉₂, X₁: 8⋅X₁ {O(n)}
t₉₂, X₂: 1 {O(1)}
t₉₃, X₀: 8⋅X₀ {O(n)}
t₉₃, X₁: 8⋅X₁ {O(n)}
t₉₃, X₂: 1 {O(1)}
t₉₄, X₀: 8⋅X₀ {O(n)}
t₉₄, X₁: 8⋅X₁ {O(n)}
t₉₄, X₂: 1 {O(1)}
t₉₅, X₀: 8⋅X₀ {O(n)}
t₉₅, X₁: 8⋅X₁ {O(n)}
t₉₅, X₂: 1 {O(1)}
t₉₆, X₀: 8⋅X₀ {O(n)}
t₉₆, X₁: 8⋅X₁ {O(n)}
t₉₆, X₂: 1 {O(1)}
t₉₇, X₀: 16⋅X₀ {O(n)}
t₉₇, X₁: 16⋅X₁ {O(n)}
t₉₇, X₂: 2 {O(1)}
t₉₈, X₀: 32⋅X₀ {O(n)}
t₉₈, X₁: 32⋅X₁ {O(n)}
t₉₈, X₂: 16⋅X₀+6 {O(n)}
t₉₉, X₀: 16⋅X₀ {O(n)}
t₉₉, X₁: 16⋅X₁ {O(n)}
t₉₉, X₂: 16⋅X₀+4 {O(n)}
t₁₀₀, X₀: 16⋅X₀ {O(n)}
t₁₀₀, X₁: 16⋅X₁ {O(n)}
t₁₀₀, X₂: 16⋅X₀+4 {O(n)}
t₁₀₁, X₀: 16⋅X₀ {O(n)}
t₁₀₁, X₁: 16⋅X₁ {O(n)}
t₁₀₁, X₂: 16⋅X₀+4 {O(n)}
t₁₀₂, X₀: 16⋅X₀ {O(n)}
t₁₀₂, X₁: 16⋅X₁ {O(n)}
t₁₀₂, X₂: 16⋅X₀+4 {O(n)}
t₁₀₃, X₀: 16⋅X₀ {O(n)}
t₁₀₃, X₁: 16⋅X₁ {O(n)}
t₁₀₃, X₂: 16⋅X₀+4 {O(n)}