KoAT2 Proof Output

Initial Problem

Start: eval_gcd_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_gcd_bb0_in, eval_gcd_bb1_in, eval_gcd_bb2_in, eval_gcd_bb3_in, eval_gcd_start, eval_gcd_stop
Transitions:
t₃: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₂, X₃, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃
t₁: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₄: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁
t₅: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₆: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁
t₈: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀-X₁, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₉: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁₁: eval_gcd_bb3_in(X₀, X₁, X₂, X₃) → eval_gcd_stop(X₀, X₁, X₂, X₃)
t₀: eval_gcd_start(X₀, X₁, X₂, X₃) → eval_gcd_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition [t₈: eval_gcd_bb2_in→eval_gcd_bb1_in; t₉: eval_gcd_bb2_in→eval_gcd_bb1_in]

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location eval_gcd_bb2_in

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₁ for location eval_gcd_bb1_in

Problem after Preprocessing

Start: eval_gcd_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_gcd_bb0_in, eval_gcd_bb1_in, eval_gcd_bb2_in, eval_gcd_bb3_in, eval_gcd_start, eval_gcd_stop
Transitions:
t₃: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₂, X₃, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃
t₁: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₄: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁
t₅: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁
t₆: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁
t₇: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁
t₁₀: eval_gcd_bb2_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁
t₁₁: eval_gcd_bb3_in(X₀, X₁, X₂, X₃) → eval_gcd_stop(X₀, X₁, X₂, X₃)
t₀: eval_gcd_start(X₀, X₁, X₂, X₃) → eval_gcd_bb0_in(X₀, X₁, X₂, X₃)

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 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 eval_gcd_bb2_in_v1

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 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 eval_gcd_bb2_in_v3

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ for location eval_gcd_bb1_in_v3

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_gcd_bb1_in_v1

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_gcd_bb1_in

Found invariant 2+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_gcd_bb2_in_v6

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 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 eval_gcd_bb2_in_v4

Found invariant 2 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_gcd_bb2_in_v5

Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 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 eval_gcd_bb2_in_v2

Found invariant 2 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₀+X₁ for location eval_gcd_bb1_in_v2

Analysing control-flow refined program

MPRF for transition t₇₇: eval_gcd_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v6(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_gcd_bb1_in_v3: [1+X₀]
• eval_gcd_bb2_in_v6: [X₀]

MPRF for transition t₇₉: eval_gcd_bb2_in_v6(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v3(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₂ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_gcd_bb1_in_v3: [X₀-1]
• eval_gcd_bb2_in_v6: [X₀-1]

MPRF for transition t₆₈: eval_gcd_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_gcd_bb1_in_v1: [1+X₁]
• eval_gcd_bb2_in_v4: [X₁]

MPRF for transition t₆₉: eval_gcd_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v1(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

• eval_gcd_bb1_in_v1: [X₁+X₂-2]
• eval_gcd_bb2_in_v4: [X₁-1]

MPRF for transition t₇₀: eval_gcd_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v2(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₂ of depth 1:

new bound:

2⋅X₂+2⋅X₃+3 {O(n)}

MPRF:

• eval_gcd_bb1_in_v2: [X₀+X₁-2]
• eval_gcd_bb2_in_v3: [X₀-1]
• eval_gcd_bb2_in_v5: [X₁-2]

MPRF for transition t₇₂: eval_gcd_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₂+1 {O(n)}

MPRF:

• eval_gcd_bb1_in_v2: [1+X₀]
• eval_gcd_bb2_in_v3: [X₀]
• eval_gcd_bb2_in_v5: [1+X₀]

MPRF for transition t₇₃: eval_gcd_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v5(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₃+3 {O(n)}

MPRF:

• eval_gcd_bb1_in_v2: [X₁-1]
• eval_gcd_bb2_in_v3: [X₁-1]
• eval_gcd_bb2_in_v5: [X₁-2]

MPRF for transition t₇₄: eval_gcd_bb2_in_v5(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v2(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₁+X₂ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

2⋅X₂+2⋅X₃+2 {O(n)}

MPRF:

• eval_gcd_bb1_in_v2: [X₀+X₁-2]
• eval_gcd_bb2_in_v3: [X₀-1]
• eval_gcd_bb2_in_v5: [X₁-1]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: eval_gcd_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_gcd_bb0_in, eval_gcd_bb1_in, eval_gcd_bb1_in_v1, eval_gcd_bb1_in_v2, eval_gcd_bb1_in_v3, eval_gcd_bb2_in_v1, eval_gcd_bb2_in_v2, eval_gcd_bb2_in_v3, eval_gcd_bb2_in_v4, eval_gcd_bb2_in_v5, eval_gcd_bb2_in_v6, eval_gcd_bb3_in, eval_gcd_start, eval_gcd_stop
Transitions:
t₃: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in(X₂, X₃, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃
t₁: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: eval_gcd_bb0_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₆₃: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v1(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₄: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v2(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₂: eval_gcd_bb1_in(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₇: eval_gcd_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₆₈: eval_gcd_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₆₆: eval_gcd_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₇₂: eval_gcd_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₇₃: eval_gcd_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v5(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₇₁: eval_gcd_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₇₈: eval_gcd_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v5(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₇₇: eval_gcd_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb2_in_v6(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₇₆: eval_gcd_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₇₅: eval_gcd_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v3(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₅: eval_gcd_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v1(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₇₀: eval_gcd_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v2(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₂
t₆₉: eval_gcd_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v1(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₇₄: eval_gcd_bb2_in_v5(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v2(X₀, X₁-X₀, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₁+X₂ ∧ 5 ≤ X₂+X₃ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₃
t₇₉: eval_gcd_bb2_in_v6(X₀, X₁, X₂, X₃) → eval_gcd_bb1_in_v3(X₀-X₁, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₂ ∧ 0 ≤ X₀+2⋅X₁ ∧ 0 ≤ X₀+X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₁₁: eval_gcd_bb3_in(X₀, X₁, X₂, X₃) → eval_gcd_stop(X₀, X₁, X₂, X₃)
t₀: eval_gcd_start(X₀, X₁, X₂, X₃) → eval_gcd_bb0_in(X₀, X₁, X₂, X₃)

All Bounds

Timebounds

Overall timebound:10⋅X₃+11⋅X₂+30 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: X₃+1 {O(n)}
t₆₉: X₂+X₃+2 {O(n)}
t₇₀: 2⋅X₂+2⋅X₃+3 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 4⋅X₂+1 {O(n)}
t₇₃: 4⋅X₃+3 {O(n)}
t₇₄: 2⋅X₂+2⋅X₃+2 {O(n)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: X₂+1 {O(n)}
t₇₈: 1 {O(1)}
t₇₉: X₂+1 {O(n)}

Costbounds

Overall costbound: 10⋅X₃+11⋅X₂+30 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₁₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: X₃+1 {O(n)}
t₆₉: X₂+X₃+2 {O(n)}
t₇₀: 2⋅X₂+2⋅X₃+3 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 4⋅X₂+1 {O(n)}
t₇₃: 4⋅X₃+3 {O(n)}
t₇₄: 2⋅X₂+2⋅X₃+2 {O(n)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: X₂+1 {O(n)}
t₇₈: 1 {O(1)}
t₇₉: X₂+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₁₁, X₀: 14⋅X₂+2⋅X₀ {O(n)}
t₁₁, X₁: 14⋅X₃+2⋅X₁ {O(n)}
t₁₁, X₂: 16⋅X₂ {O(n)}
t₁₁, X₃: 16⋅X₃ {O(n)}
t₆₂, X₀: X₂ {O(n)}
t₆₂, X₁: X₃ {O(n)}
t₆₂, X₂: X₂ {O(n)}
t₆₂, X₃: X₃ {O(n)}
t₆₃, X₀: X₂ {O(n)}
t₆₃, X₁: X₃ {O(n)}
t₆₃, X₂: X₂ {O(n)}
t₆₃, X₃: X₃ {O(n)}
t₆₄, X₀: X₂ {O(n)}
t₆₄, X₁: X₃ {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₄, X₃: X₃ {O(n)}
t₆₅, X₀: X₂ {O(n)}
t₆₅, X₁: X₃ {O(n)}
t₆₅, X₂: X₂ {O(n)}
t₆₅, X₃: X₃ {O(n)}
t₆₆, X₀: 2⋅X₂ {O(n)}
t₆₆, X₁: 2⋅X₃ {O(n)}
t₆₆, X₂: 2⋅X₂ {O(n)}
t₆₆, X₃: 2⋅X₃ {O(n)}
t₆₇, X₀: 2⋅X₂ {O(n)}
t₆₇, X₁: 2⋅X₃ {O(n)}
t₆₇, X₂: 2⋅X₂ {O(n)}
t₆₇, X₃: 2⋅X₃ {O(n)}
t₆₈, X₀: X₂ {O(n)}
t₆₈, X₁: X₃ {O(n)}
t₆₈, X₂: X₂ {O(n)}
t₆₈, X₃: X₃ {O(n)}
t₆₉, X₀: X₂ {O(n)}
t₆₉, X₁: X₃ {O(n)}
t₆₉, X₂: X₂ {O(n)}
t₆₉, X₃: X₃ {O(n)}
t₇₀, X₀: 4⋅X₂ {O(n)}
t₇₀, X₁: 4⋅X₃ {O(n)}
t₇₀, X₂: 4⋅X₂ {O(n)}
t₇₀, X₃: 4⋅X₃ {O(n)}
t₇₁, X₀: 8⋅X₂ {O(n)}
t₇₁, X₁: 8⋅X₃ {O(n)}
t₇₁, X₂: 8⋅X₂ {O(n)}
t₇₁, X₃: 8⋅X₃ {O(n)}
t₇₂, X₀: 4⋅X₂ {O(n)}
t₇₂, X₁: 4⋅X₃ {O(n)}
t₇₂, X₂: 4⋅X₂ {O(n)}
t₇₂, X₃: 4⋅X₃ {O(n)}
t₇₃, X₀: 4⋅X₂ {O(n)}
t₇₃, X₁: 4⋅X₃ {O(n)}
t₇₃, X₂: 4⋅X₂ {O(n)}
t₇₃, X₃: 4⋅X₃ {O(n)}
t₇₄, X₀: 4⋅X₂ {O(n)}
t₇₄, X₁: 4⋅X₃ {O(n)}
t₇₄, X₂: 4⋅X₂ {O(n)}
t₇₄, X₃: 4⋅X₃ {O(n)}
t₇₅, X₀: X₂ {O(n)}
t₇₅, X₁: X₃ {O(n)}
t₇₅, X₂: X₂ {O(n)}
t₇₅, X₃: X₃ {O(n)}
t₇₆, X₀: 2⋅X₂ {O(n)}
t₇₆, X₁: 2⋅X₃ {O(n)}
t₇₆, X₂: 2⋅X₂ {O(n)}
t₇₆, X₃: 2⋅X₃ {O(n)}
t₇₇, X₀: X₂ {O(n)}
t₇₇, X₁: X₃ {O(n)}
t₇₇, X₂: X₂ {O(n)}
t₇₇, X₃: X₃ {O(n)}
t₇₈, X₀: 2⋅X₂ {O(n)}
t₇₈, X₁: 2⋅X₃ {O(n)}
t₇₈, X₂: 2⋅X₂ {O(n)}
t₇₈, X₃: 2⋅X₃ {O(n)}
t₇₉, X₀: X₂ {O(n)}
t₇₉, X₁: X₃ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₇₉, X₃: X₃ {O(n)}