Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l8(X₀, X₁)
t₈: l1(X₀, X₁) → l2(X₀, X₁)
t₉: l2(X₀, X₁) → l3(X₀, X₁+1)
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1+X₁ ≤ X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁
t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: D+1 ≤ C
t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: C ≤ D
t₁₀: l5(X₀, X₁) → l6(X₀-1, X₁)
t₂: l6(X₀, X₁) → l3(X₀, 0) :|: 0 ≤ X₀
t₃: l6(X₀, X₁) → l7(X₀, X₁) :|: X₀+1 ≤ 0
t₁₁: l7(X₀, X₁) → l9(X₀, X₁)
t₁: l8(X₀, X₁) → l6(X₀, X₁)
Preprocessing
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1+X₀ ≤ 0 for location l7
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1+X₀ ≤ 0 for location l9
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l8(X₀, X₁)
t₈: l1(X₀, X₁) → l2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁) → l3(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: D+1 ≤ C ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: C ≤ D ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁) → l6(X₀-1, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l6(X₀, X₁) → l3(X₀, 0) :|: 0 ≤ X₀
t₃: l6(X₀, X₁) → l7(X₀, X₁) :|: X₀+1 ≤ 0
t₁₁: l7(X₀, X₁) → l9(X₀, X₁) :|: 1+X₀ ≤ 0
t₁: l8(X₀, X₁) → l6(X₀, X₁)
MPRF for transition t₂: l6(X₀, X₁) → l3(X₀, 0) :|: 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₀: l5(X₀, X₁) → l6(X₀-1, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+3 {O(n^2)}
MPRF for transition t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: D+1 ≤ C ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+3 {O(n^2)}
MPRF for transition t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: C ≤ D ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+3 {O(n^2)}
MPRF for transition t₈: l1(X₀, X₁) → l2(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+3 {O(n^2)}
MPRF for transition t₉: l2(X₀, X₁) → l3(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+3 {O(n^2)}
Chain transitions t₆: l4→l1 and t₈: l1→l2 to t₁₀₁: l4→l2
Chain transitions t₁₀₁: l4→l2 and t₉: l2→l3 to t₁₀₂: l4→l3
Chain transitions t₇: l4→l2 and t₉: l2→l3 to t₁₀₃: l4→l3
Chain transitions t₂: l6→l3 and t₅: l3→l5 to t₁₀₄: l6→l5
Chain transitions t₁₀₃: l4→l3 and t₅: l3→l5 to t₁₀₅: l4→l5
Chain transitions t₁₀₃: l4→l3 and t₄: l3→l4 to t₁₀₆: l4→l4
Chain transitions t₂: l6→l3 and t₄: l3→l4 to t₁₀₇: l6→l4
Chain transitions t₁₀₂: l4→l3 and t₄: l3→l4 to t₁₀₈: l4→l4
Chain transitions t₁₀₂: l4→l3 and t₅: l3→l5 to t₁₀₉: l4→l5
Chain transitions t₁₀₄: l6→l5 and t₁₀: l5→l6 to t₁₁₀: l6→l6
Chain transitions t₁₀₉: l4→l5 and t₁₀: l5→l6 to t₁₁₁: l4→l6
Chain transitions t₁₀₅: l4→l5 and t₁₀: l5→l6 to t₁₁₂: l4→l6
Analysing control-flow refined program
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1+X₀ ≤ 0 for location l7
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1+X₀ ≤ 0 for location l9
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
MPRF for transition t₁₀₇: l6(X₀, X₁) -{2}> l4(X₀, 0) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₁₀: l6(X₀, X₁) -{3}> l6(X₀-1, 0) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₁₁: l4(X₀, X₁) -{5}> l6(X₀-1, 1+X₁) :|: D+1 ≤ C ∧ X₀ ≤ X₁+1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+1+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₁₁₂: l4(X₀, X₁) -{4}> l6(X₀-1, 1+X₁) :|: C ≤ D ∧ X₀ ≤ X₁+1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+1+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
TWN: t₁₀₆: l4→l4
cycle: [t₁₀₆: l4→l4; t₁₀₈: l4→l4]
loop: (2+X₁ ≤ X₀ ∨ 2+X₁ ≤ X₀,(X₀,X₁) -> (X₀,1+X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁
∨ 1 < 0
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁
Stabilization-Threshold for: 2+X₁ ≤ X₀
alphas_abs: 2+X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+6 {O(n)}
TWN - Lifting for t₁₀₆: l4→l4 of 2⋅X₀+2⋅X₁+8 {O(n)}
relevant size-bounds w.r.t. t₁₀₇:
X₀: X₀ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₁₀₇: X₀+1 {O(n)}
Results in: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}
TWN: t₁₀₈: l4→l4
TWN - Lifting for t₁₀₈: l4→l4 of 2⋅X₀+2⋅X₁+8 {O(n)}
relevant size-bounds w.r.t. t₁₀₇:
X₀: X₀ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₁₀₇: X₀+1 {O(n)}
Results in: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___3
Found invariant X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___1
Found invariant 1+X₀ ≤ 0 for location l7
Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₀ ≤ 0 for location l9
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Found invariant X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___7
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂₄₀: l3(X₀, X₁) → n_l4___7(X₀, X₁) :|: X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂₄₃: n_l4___7(X₀, X₁) → n_l1___6(X₀, Arg1_P) :|: X₁ ≤ 0 ∧ 1+Arg1_P ≤ X₀ ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂₄₄: n_l4___7(X₀, X₁) → n_l2___5(X₀, Arg1_P) :|: X₁ ≤ 0 ∧ 1+Arg1_P ≤ X₀ ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂₃₆: n_l1___6(X₀, X₁) → n_l2___5(X₀, X₁) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₀+2 {O(n)} for transition t₂₃₈: n_l2___5(X₀, X₁) → n_l3___4(X₀, X₁+1) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₂₃₅: n_l1___2(X₀, X₁) → n_l2___1(X₀, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀+14⋅X₀+6 {O(n^2)}
MPRF for transition t₂₃₇: n_l2___1(X₀, X₁) → n_l3___4(X₀, X₁+1) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+4⋅X₀+2 {O(n^2)}
MPRF for transition t₂₃₉: n_l3___4(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+4 {O(n^2)}
MPRF for transition t₂₄₁: n_l4___3(X₀, X₁) → n_l1___2(X₀, Arg1_P) :|: 1 ≤ X₁ ∧ 1+Arg1_P ≤ X₀ ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+4 {O(n^2)}
MPRF for transition t₂₄₂: n_l4___3(X₀, X₁) → n_l2___1(X₀, Arg1_P) :|: 1 ≤ X₁ ∧ 1+Arg1_P ≤ X₀ ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+9⋅X₀+4 {O(n^2)}
MPRF for transition t₂₅₂: n_l3___4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:5⋅X₀⋅X₀+23⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₅: X₀+1 {O(n)}
t₆: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₇: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₈: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₉: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 5⋅X₀⋅X₀+23⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₅: X₀+1 {O(n)}
t₆: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₇: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₈: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₉: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀+1 {O(n)}
t₂, X₁: 0 {O(1)}
t₃, X₀: 2⋅X₀+1 {O(n)}
t₃, X₁: X₀⋅X₀+4⋅X₀+X₁+3 {O(n^2)}
t₄, X₀: X₀+1 {O(n)}
t₄, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₅, X₀: X₀+1 {O(n)}
t₅, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₈, X₀: X₀+1 {O(n)}
t₈, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₉, X₀: X₀+1 {O(n)}
t₉, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₁₀, X₀: X₀+1 {O(n)}
t₁₀, X₁: X₀⋅X₀+4⋅X₀+3 {O(n^2)}
t₁₁, X₀: 2⋅X₀+1 {O(n)}
t₁₁, X₁: X₀⋅X₀+4⋅X₀+X₁+3 {O(n^2)}