Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0)
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄)
t₁₂: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁
t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄
t₁₄: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄+1)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, 0, X₄)
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃
Preprocessing
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l11
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12
Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l10
Found invariant 0 ≤ X₃ for location l9
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₂ ≤ X₃
t₁₂: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₄: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, 0, X₄)
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃
MPRF for transition t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
TWN: t₁₂: l12→l13
cycle: [t₁₂: l12→l13; t₁₄: l13→l12]
loop: (X₄ < X₁,(X₁,X₄) -> (X₁,X₄+1)
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₄ < X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}
TWN - Lifting for t₁₂: l12→l13 of 2⋅X₁+2⋅X₄+4 {O(n)}
relevant size-bounds w.r.t. t₁₁:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₁₁: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
TWN: t₁₄: l13→l12
TWN - Lifting for t₁₄: l13→l12 of 2⋅X₁+2⋅X₄+4 {O(n)}
relevant size-bounds w.r.t. t₁₁:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₁₁: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
Chain transitions t₉: l9→l10 and t₁₁: l10→l12 to t₈₈: l9→l12
Chain transitions t₈₈: l9→l12 and t₁₃: l12→l9 to t₈₉: l9→l9
Chain transitions t₁₄: l13→l12 and t₁₃: l12→l9 to t₉₀: l13→l9
Chain transitions t₁₄: l13→l12 and t₁₂: l12→l13 to t₉₁: l13→l13
Chain transitions t₈₈: l9→l12 and t₁₂: l12→l13 to t₉₂: l9→l13
Analysing control-flow refined program
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l11
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12
Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l10
Found invariant 0 ≤ X₃ for location l9
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l14
MPRF for transition t₈₉: l9(X₀, X₁, X₂, X₃, X₄) -{3}> l9(1+X₃, X₁, X₂, 1+X₃, 0) :|: X₃ < X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₃+X₂ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₉₀: l13(X₀, X₁, X₂, X₃, X₄) -{2}> l9(X₀, X₁, X₂, X₀, 1+X₄) :|: X₁ ≤ X₄+1 ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ X₃+X₄+1 ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₉₂: l9(X₀, X₁, X₂, X₃, X₄) -{3}> l13(1+X₃, X₁, X₂, X₃, 0) :|: X₃ < X₂ ∧ 0 < X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ 2⋅X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₃+X₂ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₂ {O(n)}
TWN: t₉₁: l13→l13
cycle: [t₉₁: l13→l13]
loop: (1+X₄ < X₁,(X₁,X₄) -> (X₁,1+X₄)
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 1+X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 1+X₄ < X₁
alphas_abs: 1+X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+4 {O(n)}
TWN - Lifting for t₉₁: l13→l13 of 2⋅X₁+2⋅X₄+6 {O(n)}
relevant size-bounds w.r.t. t₉₂:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₉₂: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+6⋅X₂ {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 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l11
Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___3
Found invariant 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___1
Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l12___2
Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l10
Found invariant 0 ≤ X₃ for location l9
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l14
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₇₅: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₃+1 ∧ X₄ ≤ 0 ∧ X₄ < X₁ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₇₇: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: 0 < X₁ ∧ X₀ ≤ X₃+1 ∧ X₄ ≤ 0 ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₁₇₄: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₃+1 ∧ 1 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₄ < X₁ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₂+2⋅X₂ {O(n^2)}
MPRF for transition t₁₇₆: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: X₄ < X₁ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₂+X₂ {O(n^2)}
MPRF for transition t₁₈₁: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₁⋅X₂+11⋅X₂+11 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₂ {O(n)}
t₁₂: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₃: X₂ {O(n)}
t₁₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₅: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₁⋅X₂+11⋅X₂+11 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₂ {O(n)}
t₁₂: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₃: X₂ {O(n)}
t₁₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₅: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: 2⋅X₂+X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂ {O(n)}
t₉, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₁₀, X₀: 2⋅X₂+X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₂ {O(n)}
t₁₀, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂ {O(n)}
t₁₁, X₄: 0 {O(1)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂ {O(n)}
t₁₂, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₃, X₀: 2⋅X₂ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂ {O(n)}
t₁₃, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂ {O(n)}
t₁₄, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₁₅, X₀: 2⋅X₂+X₀ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: X₂ {O(n)}
t₁₅, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}