KoAT2 Proof Output

Initial Problem

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 evalEx7returnin

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 evalEx7stop

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 evalEx7bbin

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 evalEx7bb3in

Problem after Preprocessing

Start: evalEx7start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: evalEx7bb3in, evalEx7bbin, evalEx7entryin, evalEx7returnin, evalEx7start, evalEx7stop
Transitions:
t₂: evalEx7bb3in(X₀, X₁, X₂) → evalEx7bbin(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₃: evalEx7bb3in(X₀, X₁, X₂) → evalEx7bbin(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₄: evalEx7bb3in(X₀, X₁, X₂) → evalEx7returnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₅: evalEx7bbin(X₀, X₁, X₂) → evalEx7bb3in(X₀, X₁, 0) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₆: evalEx7bbin(X₀, X₁, X₂) → evalEx7bb3in(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₁: evalEx7entryin(X₀, X₁, X₂) → evalEx7bb3in(X₀, X₁, 1+X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇: evalEx7returnin(X₀, X₁, X₂) → evalEx7stop(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₀: evalEx7start(X₀, X₁, X₂) → evalEx7entryin(X₀, X₁, X₂)

Cut unsatisfiable transition [t₄: evalEx7bb3in→evalEx7returnin; t₄₈: evalEx7bb3in→evalEx7returnin; t₅₀: evalEx7bb3in→evalEx7bbin_v2]

Cut unreachable locations [evalEx7bb3in_v1; evalEx7bb3in_v2; evalEx7bbin_v2; evalEx7bbin_v3; evalEx7bbin_v4] from the program graph

Found invariant X₂ ≤ 2 ∧ 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 evalEx7bb3in_v7

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 evalEx7bbin_v9

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 evalEx7bb3in_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 evalEx7bb3in_v6

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 evalEx7bbin_v6

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 3 ≤ X₂ ∧ 8 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₂ ∧ 5 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 4 ≤ X₀ for location evalEx7bbin_v5

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 evalEx7bb3in_v4

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 3 ≤ X₂ ∧ 7 ≤ X₁+X₂ ∧ 6 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location evalEx7bb3in_v3

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 evalEx7bb3in

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 evalEx7bbin_v1

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 evalEx7bbin_v7

Found invariant X₂ ≤ 2 ∧ 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 evalEx7bbin_v8

Cut unsatisfiable transition [t₆₂: evalEx7bbin_v1→evalEx7bb3in_v5]

Analysing control-flow refined program

MPRF for transition t₇₁: evalEx7bb3in_v4(X₀, X₁, X₂) → evalEx7bbin_v9(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₁+4 {O(n)}

MPRF:

• evalEx7bb3in_v4: [2+X₁-X₂]
• evalEx7bbin_v9: [1+X₁-X₂]

MPRF for transition t₇₂: evalEx7bbin_v9(X₀, X₁, X₂) → evalEx7bb3in_v4(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₁+3 {O(n)}

MPRF:

• evalEx7bb3in_v4: [1+X₁-X₂]
• evalEx7bbin_v9: [1+X₁-X₂]

MPRF for transition t₅₉: evalEx7bb3in_v3(X₀, X₁, X₂) → evalEx7bbin_v5(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₂ ∧ 7 ≤ X₀+X₁ ∧ 7 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+4 {O(n)}

MPRF:

• evalEx7bb3in_v3: [1+X₁-X₂]
• evalEx7bbin_v5: [X₁-X₂]

MPRF for transition t₆₀: evalEx7bbin_v5(X₀, X₁, X₂) → evalEx7bb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀ ∧ 5 ≤ X₁ ∧ 7 ≤ X₀+X₂ ∧ 8 ≤ X₁+X₂ ∧ 9 ≤ X₀+X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+4 {O(n)}

MPRF:

• evalEx7bb3in_v3: [1+X₁-X₂]
• evalEx7bbin_v5: [1+X₁-X₂]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: evalEx7start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: evalEx7bb3in, evalEx7bb3in_v3, evalEx7bb3in_v4, evalEx7bb3in_v5, evalEx7bb3in_v6, evalEx7bb3in_v7, evalEx7bbin_v1, evalEx7bbin_v5, evalEx7bbin_v6, evalEx7bbin_v7, evalEx7bbin_v8, evalEx7bbin_v9, evalEx7entryin, evalEx7returnin, evalEx7start, evalEx7stop
Transitions:
t₄₉: evalEx7bb3in(X₀, X₁, X₂) → evalEx7bbin_v1(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₅₉: evalEx7bb3in_v3(X₀, X₁, X₂) → evalEx7bbin_v5(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₂ ∧ 7 ≤ X₀+X₁ ∧ 7 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₅₈: evalEx7bb3in_v3(X₀, X₁, X₂) → evalEx7returnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₂ ∧ 7 ≤ X₀+X₁ ∧ 7 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₇₁: evalEx7bb3in_v4(X₀, X₁, X₂) → evalEx7bbin_v9(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
t₆₃: evalEx7bb3in_v5(X₀, X₁, X₂) → evalEx7bbin_v6(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₆₆: evalEx7bb3in_v6(X₀, X₁, X₂) → evalEx7bbin_v7(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₆₅: evalEx7bb3in_v6(X₀, X₁, X₂) → evalEx7returnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₆₉: evalEx7bb3in_v7(X₀, X₁, X₂) → evalEx7bbin_v8(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₆₈: evalEx7bb3in_v7(X₀, X₁, X₂) → evalEx7returnin(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₆₁: evalEx7bbin_v1(X₀, X₁, X₂) → evalEx7bb3in_v4(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₆₀: evalEx7bbin_v5(X₀, X₁, X₂) → evalEx7bb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀ ∧ 5 ≤ X₁ ∧ 7 ≤ X₀+X₂ ∧ 8 ≤ X₁+X₂ ∧ 9 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₆₄: evalEx7bbin_v6(X₀, X₁, X₂) → evalEx7bb3in_v6(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₆₇: evalEx7bbin_v7(X₀, X₁, X₂) → evalEx7bb3in_v7(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₇₀: evalEx7bbin_v8(X₀, X₁, X₂) → evalEx7bb3in_v3(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₂ ∧ 6 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₁ ∧ 0 ≤ X₂
t₇₂: evalEx7bbin_v9(X₀, X₁, X₂) → evalEx7bb3in_v4(X₀, X₁, 1+X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₇₃: evalEx7bbin_v9(X₀, X₁, X₂) → evalEx7bb3in_v5(X₀, X₁, 0) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₁: evalEx7entryin(X₀, X₁, X₂) → evalEx7bb3in(X₀, X₁, 1+X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇: evalEx7returnin(X₀, X₁, X₂) → evalEx7stop(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₀: evalEx7start(X₀, X₁, X₂) → evalEx7entryin(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:2⋅X₀+4⋅X₁+30 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: X₁+4 {O(n)}
t₆₀: X₁+4 {O(n)}
t₆₁: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 1 {O(1)}
t₇₀: 1 {O(1)}
t₇₁: X₀+X₁+4 {O(n)}
t₇₂: X₀+X₁+3 {O(n)}
t₇₃: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+4⋅X₁+30 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: X₁+4 {O(n)}
t₆₀: X₁+4 {O(n)}
t₆₁: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 1 {O(1)}
t₇₀: 1 {O(1)}
t₇₁: X₀+X₁+4 {O(n)}
t₇₂: X₀+X₁+3 {O(n)}
t₇₃: 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: 2⋅X₀+3 {O(n)}
t₇, X₁: 4⋅X₁ {O(n)}
t₇, X₂: X₁+13 {O(n)}
t₄₉, X₀: X₀ {O(n)}
t₄₉, X₁: X₁ {O(n)}
t₄₉, X₂: X₀+1 {O(n)}
t₅₈, X₀: 2⋅X₀ {O(n)}
t₅₈, X₁: 2⋅X₁ {O(n)}
t₅₈, X₂: X₁+10 {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: X₁ {O(n)}
t₅₉, X₂: X₁+7 {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: X₁ {O(n)}
t₆₀, X₂: X₁+7 {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: X₁ {O(n)}
t₆₁, X₂: X₀+2 {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: X₁ {O(n)}
t₆₃, X₂: 0 {O(1)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: X₁ {O(n)}
t₆₄, X₂: 1 {O(1)}
t₆₅, X₀: 1 {O(1)}
t₆₅, X₁: X₁ {O(n)}
t₆₅, X₂: 1 {O(1)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: X₁ {O(n)}
t₆₆, X₂: 1 {O(1)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: X₁ {O(n)}
t₆₇, X₂: 2 {O(1)}
t₆₈, X₀: 2 {O(1)}
t₆₈, X₁: X₁ {O(n)}
t₆₈, X₂: 2 {O(1)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: X₁ {O(n)}
t₆₉, X₂: 2 {O(1)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: X₁ {O(n)}
t₇₀, X₂: 3 {O(1)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: X₁ {O(n)}
t₇₁, X₂: 2⋅X₀+X₁+5 {O(n)}
t₇₂, X₀: X₀ {O(n)}
t₇₂, X₁: X₁ {O(n)}
t₇₂, X₂: 2⋅X₀+X₁+5 {O(n)}
t₇₃, X₀: X₀ {O(n)}
t₇₃, X₁: X₁ {O(n)}
t₇₃, X₂: 0 {O(1)}