Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
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) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃)
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, 1, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₁, X₃) :|: X₁ ≤ X₃
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃)
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+1, X₁, X₂, X₃)
Preprocessing
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l11
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l12
Found invariant 1 ≤ X₁ for location l7
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l9
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
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) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, 1, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₁, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < X₁ ∧ 1 ≤ X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁
MPRF for transition t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
l13 [X₃+1-X₁ ]
l11 [X₃+1-X₁ ]
l8 [X₃-X₁ ]
l7 [X₃+1-X₁ ]
l9 [X₃+1-X₁ ]
l10 [X₃+1-X₁ ]
MPRF for transition t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃+3 {O(n)}
MPRF:
l13 [X₃+2-X₁ ]
l11 [X₃+2-X₁ ]
l8 [2⋅X₂-X₀-X₃ ]
l7 [X₃+2-X₁ ]
l9 [2⋅X₂-X₁-X₃-1 ]
l10 [2⋅X₂-X₁-X₃-1 ]
MPRF for transition t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₁, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
l13 [X₃-X₁ ]
l11 [X₃-X₁ ]
l8 [X₂-X₀ ]
l7 [X₃+1-X₁ ]
l9 [X₂-X₁-1 ]
l10 [X₂-X₁-1 ]
MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₃+1 {O(n)}
MPRF:
l13 [2⋅X₃-X₁ ]
l11 [2⋅X₃-X₁ ]
l8 [2⋅X₃+1-X₀ ]
l7 [2⋅X₃-X₁ ]
l9 [2⋅X₃-X₁ ]
l10 [2⋅X₃+1-X₀ ]
MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
l13 [X₃+1-X₁ ]
l11 [X₃+1-X₁ ]
l8 [X₂-X₀ ]
l7 [X₃+1-X₁ ]
l9 [X₃+1-X₁ ]
l10 [X₃+1-X₀ ]
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l11
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l12
Found invariant 1 ≤ X₁ for location l7
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l9
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l14
Time-Bound by TWN-Loops:
TWN-Loops: t₉ 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
TWN-Loops:
entry: t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₁, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂+1,X₃) :|: X₂ ≤ X₃
order: [X₁; X₂; X₃]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃
Termination: true
Formula:
1 < 0
∨ X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂
Stabilization-Threshold for: X₂ ≤ X₃
alphas_abs: X₃
M: 0
N: 1
Bound: 2⋅X₃+2 {O(n)}
relevant size-bounds w.r.t. t₇:
X₃: X₃ {O(n)}
Runtime-bound of t₇: X₃+2 {O(n)}
Results in: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁ 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
relevant size-bounds w.r.t. t₇:
X₃: X₃ {O(n)}
Runtime-bound of t₇: X₃+2 {O(n)}
Results in: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀: l11→l9
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l11
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l13___3
Found invariant 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l13___1
Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l11___2
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l12
Found invariant 1 ≤ X₁ for location l7
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l9
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ for location l14
knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₁₁₄: l11(X₀, X₁, X₂, X₃) → n_l13___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₁₁₆: n_l13___3(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+1, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
MPRF for transition t₁₁₃: n_l11___2(X₀, X₁, X₂, X₃) → n_l13___1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₃⋅X₃+11⋅X₃+14 {O(n^2)}
MPRF:
n_l13___3 [2⋅X₁-2⋅X₂ ]
l11 [2⋅X₁-2⋅X₂ ]
l8 [X₃+1-X₂ ]
l7 [0 ]
l10 [X₃+1-X₂ ]
l9 [X₃+1-X₂ ]
n_l13___1 [X₃+1-X₂ ]
n_l11___2 [X₃+2-X₂ ]
MPRF for transition t₁₂₀: n_l11___2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF:
l11 [X₃+1-X₂ ]
l8 [X₃-X₁ ]
l7 [X₃+1-X₁ ]
l10 [X₃-X₁ ]
l9 [X₃-X₁ ]
n_l13___1 [X₃+1-X₁ ]
n_l13___3 [X₃+1-X₁ ]
n_l11___2 [X₃+1-X₁ ]
MPRF for transition t₁₁₅: n_l13___1(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+1, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₃⋅X₃+10⋅X₃+13 {O(n^2)}
MPRF:
n_l13___3 [-X₁ ]
l11 [-X₂ ]
l8 [2⋅X₃-2⋅X₂ ]
l7 [-X₁ ]
l10 [2⋅X₃-2⋅X₂ ]
l9 [2⋅X₃-2⋅X₂ ]
n_l13___1 [X₃+1-X₂ ]
n_l11___2 [X₃+1-X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₃⋅X₃+22⋅X₃+35 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: X₃+2 {O(n)}
t₉: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
t₁₀: X₃+3 {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃+2 {O(n)}
t₈: 1 {O(1)}
t₁₄: 2⋅X₃+1 {O(n)}
t₁₂: X₃+2 {O(n)}
Costbounds
Overall costbound: 4⋅X₃⋅X₃+22⋅X₃+35 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: X₃+2 {O(n)}
t₉: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
t₁₀: X₃+3 {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 2⋅X₃⋅X₃+8⋅X₃+8 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃+2 {O(n)}
t₈: 1 {O(1)}
t₁₄: 2⋅X₃+1 {O(n)}
t₁₂: X₃+2 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₃, X₀: X₃+3 {O(n)}
t₁₃, X₁: X₃+3 {O(n)}
t₁₃, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₉, X₀: X₀+X₃+3 {O(n)}
t₉, X₁: X₃+3 {O(n)}
t₉, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₀+X₃+3 {O(n)}
t₁₀, X₁: X₃+3 {O(n)}
t₁₀, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₅, X₀: X₀+X₃+3 {O(n)}
t₁₅, X₁: X₃+4 {O(n)}
t₁₅, X₂: 2⋅X₃⋅X₃+9⋅X₃+X₂+12 {O(n^2)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₁, X₀: X₀+X₃+3 {O(n)}
t₁₁, X₁: X₃+3 {O(n)}
t₁₁, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 1 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀+X₃+3 {O(n)}
t₇, X₁: X₃+3 {O(n)}
t₇, X₂: X₃+4 {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀+X₃+3 {O(n)}
t₈, X₁: X₃+4 {O(n)}
t₈, X₂: 2⋅X₃⋅X₃+9⋅X₃+X₂+12 {O(n^2)}
t₈, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₃+3 {O(n)}
t₁₄, X₁: X₃+3 {O(n)}
t₁₄, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₂, X₀: X₃+3 {O(n)}
t₁₂, X₁: X₃+3 {O(n)}
t₁₂, X₂: 2⋅X₃⋅X₃+9⋅X₃+12 {O(n^2)}
t₁₂, X₃: X₃ {O(n)}