Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁₂: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆
t₁₈: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆)
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < X₅
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
Preprocessing
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l6
Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l15
Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l17
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l7
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l5
Found invariant X₁ ≤ X₅ for location l8
Found invariant X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location l16
Found invariant X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁₂: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₈: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < X₅ ∧ X₁ ≤ X₅
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
MPRF for transition t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₅+1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF for transition t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
TWN: t₁₂: l14→l16
cycle: [t₁₂: l14→l16; t₁₄: l16→l14]
loop: (X₆ ≤ X₄,(X₄,X₆) -> (X₄,X₆+1)
order: [X₄; X₆]
closed-form:
X₄: X₄
X₆: X₆ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ X₆ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₆ ≤ X₄ ∧ X₄ ≤ X₆
Stabilization-Threshold for: X₆ ≤ X₄
alphas_abs: X₆+X₄
M: 0
N: 1
Bound: 2⋅X₄+2⋅X₆+2 {O(n)}
TWN - Lifting for t₁₂: l14→l16 of 2⋅X₄+2⋅X₆+4 {O(n)}
relevant size-bounds w.r.t. t₁₀:
X₄: X₄ {O(n)}
X₆: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀: X₁+X₂+1 {O(n)}
Results in: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
TWN: t₁₄: l16→l14
TWN - Lifting for t₁₄: l16→l14 of 2⋅X₄+2⋅X₆+4 {O(n)}
relevant size-bounds w.r.t. t₁₀:
X₄: X₄ {O(n)}
X₆: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀: X₁+X₂+1 {O(n)}
Results in: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
Chain transitions t₁₀: l8→l14 and t₁₃: l14→l6 to t₁₀₃: l8→l6
Chain transitions t₁₄: l16→l14 and t₁₃: l14→l6 to t₁₀₄: l16→l6
Chain transitions t₁₄: l16→l14 and t₁₂: l14→l16 to t₁₀₅: l16→l16
Chain transitions t₁₀: l8→l14 and t₁₂: l14→l16 to t₁₀₆: l8→l16
Chain transitions t₁₆: l7→l5 and t₁₇: l5→l8 to t₁₀₇: l7→l8
Chain transitions t₁₀₃: l8→l6 and t₁₅: l6→l7 to t₁₀₈: l8→l7
Chain transitions t₁₀₄: l16→l6 and t₁₅: l6→l7 to t₁₀₉: l16→l7
Chain transitions t₁₀₈: l8→l7 and t₁₀₇: l7→l8 to t₁₁₀: l8→l8
Chain transitions t₁₀₉: l16→l7 and t₁₀₇: l7→l8 to t₁₁₁: l16→l8
Chain transitions t₁₀₉: l16→l7 and t₁₆: l7→l5 to t₁₁₂: l16→l5
Chain transitions t₁₀₈: l8→l7 and t₁₆: l7→l5 to t₁₁₃: l8→l5
Analysing control-flow refined program
Eliminate variables {X₀} that do not contribute to the problem
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l6
Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l15
Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l17
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l7
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l5
Found invariant X₀ ≤ X₄ for location l8
Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l16
Found invariant X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l14
MPRF for transition t₁₅₂: l16(X₀, X₁, X₂, X₃, X₄, X₅) -{5}> l8(X₀, X₁, X₂, X₃, 1+X₄, 1+X₅) :|: X₃ < X₅+1 ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₅₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l16(X₀, X₁, X₂, X₃, X₄, X₂) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₄ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF for transition t₁₆₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) -{5}> l8(X₀, X₁, X₂, X₃, 1+X₄, X₂) :|: X₄ ≤ X₁ ∧ X₃ < X₂ ∧ X₀ ≤ X₄ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
TWN: t₁₄₈: l16→l16
cycle: [t₁₄₈: l16→l16]
loop: (1+X₅ ≤ X₃,(X₃,X₅) -> (X₃,1+X₅)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 1+X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₅ ≤ X₃ ∧ X₃ ≤ 1+X₅
Stabilization-Threshold for: 1+X₅ ≤ X₃
alphas_abs: 1+X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+4 {O(n)}
TWN - Lifting for t₁₄₈: l16→l16 of 2⋅X₃+2⋅X₅+6 {O(n)}
relevant size-bounds w.r.t. t₁₅₈:
X₃: X₃ {O(n)}
X₅: 2⋅X₂ {O(n)}
Runtime-bound of t₁₅₈: X₀+X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₂+6⋅X₀+6⋅X₁+6 {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 X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l14___2
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l6
Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l15
Found invariant X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l16___3
Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location l17
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l7
Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location l5
Found invariant X₁ ≤ X₅ for location l8
Found invariant X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location n_l16___1
Found invariant X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location l14
knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₂₄₆: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l16___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₃ ∧ X₆ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂
knowledge_propagation leads to new time bound X₁+X₂+1 {O(n)} for transition t₂₄₈: n_l16___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂
MPRF for transition t₂₄₅: n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l16___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₆ ∧ X₆ ≤ 1+X₄ ∧ X₆ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₁⋅X₃+2⋅X₂⋅X₃+X₁⋅X₄+X₂⋅X₄+2⋅X₁+2⋅X₂+2⋅X₃+X₄+2 {O(n^2)}
MPRF for transition t₂₄₇: n_l16___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1) :|: 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₁⋅X₃+2⋅X₂⋅X₃+X₁⋅X₄+X₂⋅X₄+2⋅X₁+2⋅X₂+2⋅X₃+X₄+2 {O(n^2)}
MPRF for transition t₂₅₂: n_l14___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₁+X₂+1 {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⋅X₄+4⋅X₂⋅X₄+8⋅X₁⋅X₃+8⋅X₂⋅X₃+13⋅X₁+13⋅X₂+4⋅X₄+8⋅X₃+25 {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: 1 {O(1)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₄: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₈: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₁⋅X₄+4⋅X₂⋅X₄+8⋅X₁⋅X₃+8⋅X₂⋅X₃+13⋅X₁+13⋅X₂+4⋅X₄+8⋅X₃+25 {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: 1 {O(1)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₄: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+4⋅X₃+4 {O(n^2)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₈: 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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {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)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {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)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {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)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {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)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {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)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {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)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {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)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₁ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₀, X₆: 2⋅X₃ {O(n)}
t₁₁, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₁, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+X₆+4 {O(n^2)}
t₁₂, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₂, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+6⋅X₃+4 {O(n^2)}
t₁₃, X₀: 2⋅X₀+2⋅X₂+4⋅X₁+2 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₃, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₄, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₄, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+6⋅X₃+4 {O(n^2)}
t₁₅, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₆, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₇, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+4 {O(n^2)}
t₁₈, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₈, X₁: 2⋅X₁ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₈, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₈, X₆: 2⋅X₁⋅X₄+2⋅X₂⋅X₄+4⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃+X₆+4 {O(n^2)}