Initial Problem
Start: evalEx4start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: evalEx4bb1in, evalEx4bb2in, evalEx4bb3in, evalEx4bb4in, evalEx4entryin, evalEx4returnin, evalEx4start, evalEx4stop
Transitions:
t₁₀: evalEx4bb1in(X₀, X₁, X₂, X₃) → evalEx4bb2in(X₀, X₁, 1, X₃-1)
t₆: evalEx4bb2in(X₀, X₁, X₂, X₃) → evalEx4bb3in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₅: evalEx4bb2in(X₀, X₁, X₂, X₃) → evalEx4bb4in(X₂, X₃, X₂, X₃) :|: X₃ ≤ 0
t₇: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0
t₈: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₉: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb4in(X₂, X₃, X₂, X₃)
t₂: evalEx4bb4in(X₀, X₁, X₂, X₃) → evalEx4bb2in(X₀, X₁, 0, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₃: evalEx4bb4in(X₀, X₁, X₂, X₃) → evalEx4returnin(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: evalEx4bb4in(X₀, X₁, X₂, X₃) → evalEx4returnin(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀
t₁: evalEx4entryin(X₀, X₁, X₂, X₃) → evalEx4bb4in(1, X₀, X₂, X₃)
t₁₁: evalEx4returnin(X₀, X₁, X₂, X₃) → evalEx4stop(X₀, X₁, X₂, X₃)
t₀: evalEx4start(X₀, X₁, X₂, X₃) → evalEx4entryin(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location evalEx4bb2in
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location evalEx4stop
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location evalEx4bb1in
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location evalEx4bb3in
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location evalEx4returnin
Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location evalEx4bb4in
Cut unsatisfiable transition [t₄: evalEx4bb4in→evalEx4returnin]
Problem after Preprocessing
Start: evalEx4start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: evalEx4bb1in, evalEx4bb2in, evalEx4bb3in, evalEx4bb4in, evalEx4entryin, evalEx4returnin, evalEx4start, evalEx4stop
Transitions:
t₁₀: evalEx4bb1in(X₀, X₁, X₂, X₃) → evalEx4bb2in(X₀, X₁, 1, X₃-1) :|: X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃
t₆: evalEx4bb2in(X₀, X₁, X₂, X₃) → evalEx4bb3in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₅: evalEx4bb2in(X₀, X₁, X₂, X₃) → evalEx4bb4in(X₂, X₃, X₂, X₃) :|: X₃ ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₇: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃
t₈: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃
t₉: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb4in(X₂, X₃, X₂, X₃) :|: X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃
t₂: evalEx4bb4in(X₀, X₁, X₂, X₃) → evalEx4bb2in(X₀, X₁, 0, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀
t₃: evalEx4bb4in(X₀, X₁, X₂, X₃) → evalEx4returnin(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₁: evalEx4entryin(X₀, X₁, X₂, X₃) → evalEx4bb4in(1, X₀, X₂, X₃)
t₁₁: evalEx4returnin(X₀, X₁, X₂, X₃) → evalEx4stop(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₀: evalEx4start(X₀, X₁, X₂, X₃) → evalEx4entryin(X₀, X₁, X₂, X₃)
MPRF for transition t₆: evalEx4bb2in(X₀, X₁, X₂, X₃) → evalEx4bb3in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₀+3 {O(n)}
MPRF:
• evalEx4bb1in: [2⋅X₃-2]
• evalEx4bb2in: [X₀+X₂+2⋅X₃-2]
• evalEx4bb3in: [X₀+X₂+2⋅X₃-3]
• evalEx4bb4in: [X₀+2⋅X₁-2]
MPRF for transition t₇: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
• evalEx4bb1in: [X₃-X₀]
• evalEx4bb2in: [X₃]
• evalEx4bb3in: [1+X₃-X₀]
• evalEx4bb4in: [X₁]
MPRF for transition t₈: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb1in(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
• evalEx4bb1in: [X₃-X₀]
• evalEx4bb2in: [X₀+X₃-1]
• evalEx4bb3in: [1+X₃-X₀]
• evalEx4bb4in: [X₀+X₁-1]
MPRF for transition t₉: evalEx4bb3in(X₀, X₁, X₂, X₃) → evalEx4bb4in(X₂, X₃, X₂, X₃) :|: X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
• evalEx4bb1in: [1+X₃]
• evalEx4bb2in: [X₀+X₂+X₃]
• evalEx4bb3in: [1+X₂+X₃]
• evalEx4bb4in: [X₀+X₁]
MPRF for transition t₁₀: evalEx4bb1in(X₀, X₁, X₂, X₃) → evalEx4bb2in(X₀, X₁, 1, X₃-1) :|: X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF:
• evalEx4bb1in: [2⋅X₃-X₀]
• evalEx4bb2in: [2⋅X₃]
• evalEx4bb3in: [2⋅X₃]
• evalEx4bb4in: [2⋅X₁]
TWN: t₅: evalEx4bb2in→evalEx4bb4in
cycle: [t₅: evalEx4bb2in→evalEx4bb4in; t₂: evalEx4bb4in→evalEx4bb2in]
original loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
transformed loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
order: [X₁; X₀]
closed-form:X₁: X₁
X₀: [[n == 0]]⋅X₀
Termination: true
Formula:
0 ≤ 0 ∧ X₀ ≤ 2 ∧ 0 ≤ 1 ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0
original loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
transformed loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
loop: (X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ X₀ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₀,X₁) -> (0,X₁))
order: [X₁; X₀]
closed-form:X₁: X₁
X₀: [[n == 0]]⋅X₀
Termination: true
Formula:
0 ≤ 0 ∧ X₀ ≤ 2 ∧ 0 ≤ 1 ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 0
original loop: (X₃ ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 0 ≤ X₂,(X₀,X₁,X₂,X₃) -> (X₂,X₃,0,X₃))
transformed loop: (X₃ ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 0 ≤ X₂,(X₀,X₁,X₂,X₃) -> (X₂,X₃,0,X₃))
loop: (X₃ ≤ 0 ∧ X₀+X₂ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 0 ≤ X₂,(X₀,X₁,X₂,X₃) -> (X₂,X₃,0,X₃))
order: [X₃; X₂; X₁; X₀]
closed-form:X₃: X₃
X₂: [[n == 0]]⋅X₂
X₁: [[n == 0]]⋅X₁ + [[n != 0]]⋅X₃
X₀: [[n == 0]]⋅X₀ + [[n != 0, n == 1]]⋅X₂
Termination: true
Formula:
0 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₃ ≤ 0
∨ 0 ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₃ ≤ 0
TWN - Lifting for [2: evalEx4bb4in->evalEx4bb2in; 5: evalEx4bb2in->evalEx4bb4in] of 2 {O(1)}
relevant size-bounds w.r.t. t₁: evalEx4entryin→evalEx4bb4in:
Runtime-bound of t₁: 1 {O(1)}
Results in: 2 {O(1)}
TWN - Lifting for [2: evalEx4bb4in->evalEx4bb2in; 5: evalEx4bb2in->evalEx4bb4in] of 2 {O(1)}
relevant size-bounds w.r.t. t₉: evalEx4bb3in→evalEx4bb4in:
Runtime-bound of t₉: X₀+1 {O(n)}
Results in: 2⋅X₀+2 {O(n)}
TWN - Lifting for [2: evalEx4bb4in->evalEx4bb2in; 5: evalEx4bb2in->evalEx4bb4in] of 6 {O(1)}
relevant size-bounds w.r.t. t₁₀: evalEx4bb1in→evalEx4bb2in:
Runtime-bound of t₁₀: 2⋅X₀ {O(n)}
Results in: 12⋅X₀ {O(n)}
All Bounds
Timebounds
Overall timebound:35⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 14⋅X₀+4 {O(n)}
t₃: 1 {O(1)}
t₅: 14⋅X₀+4 {O(n)}
t₆: 2⋅X₀+3 {O(n)}
t₇: X₀ {O(n)}
t₈: X₀+2 {O(n)}
t₉: X₀+1 {O(n)}
t₁₀: 2⋅X₀ {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 35⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 14⋅X₀+4 {O(n)}
t₃: 1 {O(1)}
t₅: 14⋅X₀+4 {O(n)}
t₆: 2⋅X₀+3 {O(n)}
t₇: X₀ {O(n)}
t₈: X₀+2 {O(n)}
t₉: X₀+1 {O(n)}
t₁₀: 2⋅X₀ {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 1 {O(1)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: 0 {O(1)}
t₂, X₃: X₀ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: 2 {O(1)}
t₃, X₃: 3⋅X₀ {O(n)}
t₅, X₀: 1 {O(1)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 2⋅X₀ {O(n)}
t₆, X₀: 1 {O(1)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: X₀ {O(n)}
t₇, X₀: 1 {O(1)}
t₇, X₁: X₀ {O(n)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₀ {O(n)}
t₈, X₀: 1 {O(1)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: 1 {O(1)}
t₈, X₃: X₀ {O(n)}
t₉, X₀: 1 {O(1)}
t₉, X₁: X₀ {O(n)}
t₉, X₂: 1 {O(1)}
t₉, X₃: X₀ {O(n)}
t₁₀, X₀: 1 {O(1)}
t₁₀, X₁: X₀ {O(n)}
t₁₀, X₂: 1 {O(1)}
t₁₀, X₃: X₀ {O(n)}
t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: 2⋅X₀ {O(n)}
t₁₁, X₂: 2 {O(1)}
t₁₁, X₃: 3⋅X₀ {O(n)}