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)
t₆: l10(X₀, X₁, X₂, X₃) → l8(X₀, 0, X₂, X₃)
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁
t₁₀: l11(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 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) → l9(X₀, X₁, X₂, X₃)
t₁₄: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₀, X₂, X₃)
t₁₂: l6(X₀, X₁, X₂, X₃) → l7(X₁+1, X₁, X₂, X₃)
t₁₃: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₇: l8(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁+1 ≤ X₃
t₈: l8(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < 1+X₁
t₅: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l11

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l6

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l12

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13

Found invariant 0 ≤ X₁ for location l8

Found invariant X₃ ≤ X₁ ∧ 0 ≤ 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)
t₆: l10(X₀, X₁, X₂, X₃) → l8(X₀, 0, X₂, X₃)
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₀: l11(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 0 ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ 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) → l9(X₀, X₁, X₂, X₃)
t₁₄: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₀, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃) → l7(X₁+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
t₇: l8(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁+1 ≤ X₃ ∧ 0 ≤ X₁
t₈: l8(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < 1+X₁ ∧ 0 ≤ X₁
t₅: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)

MPRF for transition t₁₀: l11(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l13 [X₃-X₁ ]
l6 [X₃-X₂ ]
l7 [X₃-X₂ ]
l5 [X₃-X₂ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]

MPRF for transition t₁₄: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₀, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l13 [X₃-X₁ ]
l6 [X₃-X₁ ]
l7 [X₃-X₁ ]
l5 [X₃+1-X₀ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]

MPRF for transition t₁₂: l6(X₀, X₁, X₂, X₃) → l7(X₁+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l13 [X₃-X₁ ]
l6 [X₃+1-X₂ ]
l7 [X₃-X₂ ]
l5 [X₃-X₂ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]

MPRF for transition t₁₃: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l13 [X₃-X₁ ]
l6 [X₃-X₁ ]
l7 [X₃-X₁ ]
l5 [X₃-X₁-1 ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]

MPRF for transition t₇: l8(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁+1 ≤ X₃ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l13 [X₃-X₁-1 ]
l6 [X₃-X₁-1 ]
l7 [X₃-X₀ ]
l5 [X₃-X₀ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁-1 ]

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l11

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l6

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l12

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13

Found invariant 0 ≤ X₁ for location l8

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l14

MPRF for transition t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+X₃ {O(n^2)}

MPRF:

l13 [X₃-X₂ ]
l11 [X₃+1-X₂ ]
l8 [X₃-X₁ ]
l6 [X₃-X₂ ]
l7 [X₃-X₂ ]
l5 [X₃-X₂ ]

MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₃⋅X₃+X₃ {O(n^2)}

MPRF:

l13 [X₁+X₃+1-X₂ ]
l11 [X₁+X₃+1-X₂ ]
l8 [X₃ ]
l6 [X₁+X₃+1-X₂ ]
l7 [X₁+X₃+1-X₂ ]
l5 [X₁+X₃+1-X₂ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀: l11→l6

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l11

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l13___3

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l13___1

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l11___2

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l12

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 0 ≤ X₁ for location l8

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l14

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₁₅: l11(X₀, X₁, X₂, X₃) → n_l13___3(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₁₇: n_l13___3(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+1, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

MPRF for transition t₁₁₄: n_l11___2(X₀, X₁, X₂, X₃) → n_l13___1(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+3⋅X₃ {O(n^2)}

MPRF:

n_l13___3 [X₃-X₁ ]
l7 [X₃-X₂ ]
l5 [X₃-X₀ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]
l6 [X₃-X₂ ]
n_l13___1 [X₃-X₂ ]
n_l11___2 [X₃+1-X₂ ]

MPRF for transition t₁₂₁: n_l11___2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l7 [X₃-X₀ ]
l5 [X₃-X₀ ]
l8 [X₃-X₁ ]
l11 [X₃-X₁ ]
l6 [X₃-X₁-1 ]
n_l13___1 [X₃-X₁ ]
n_l13___3 [X₃-X₁ ]
n_l11___2 [X₃-X₁ ]

MPRF for transition t₁₁₆: n_l13___1(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+1, X₃) :|: 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}

MPRF:

n_l13___3 [X₁-X₀ ]
l7 [X₁+1-X₂ ]
l5 [0 ]
l8 [X₁-X₀ ]
l11 [X₁-X₀ ]
l6 [X₁+1-X₂ ]
n_l13___1 [X₁+1-X₂ ]
n_l11___2 [X₁+1-X₂ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:3⋅X₃⋅X₃+7⋅X₃+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₉: X₃⋅X₃+X₃ {O(n^2)}
t₁₀: X₃ {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₄: X₃ {O(n)}
t₁₂: X₃ {O(n)}
t₁₃: X₃ {O(n)}
t₇: X₃ {O(n)}
t₈: 1 {O(1)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₃⋅X₃+7⋅X₃+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₉: X₃⋅X₃+X₃ {O(n^2)}
t₁₀: X₃ {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₄: X₃ {O(n)}
t₁₂: X₃ {O(n)}
t₁₃: X₃ {O(n)}
t₇: X₃ {O(n)}
t₈: 1 {O(1)}
t₅: 1 {O(1)}

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)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 0 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₉, X₀: X₀+X₃ {O(n)}
t₉, X₁: X₃ {O(n)}
t₉, X₂: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₀+X₃ {O(n)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₂: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₅, X₀: X₀+X₃ {O(n)}
t₁₅, X₁: X₃ {O(n)}
t₁₅, X₂: 2⋅X₃⋅X₃+X₂+X₃ {O(n^2)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₁, X₀: X₀+X₃ {O(n)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₂: 2⋅X₃⋅X₃+X₃ {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)}
t₁₄, X₀: X₃ {O(n)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₂, X₀: X₃ {O(n)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: X₃ {O(n)}
t₁₃, X₁: X₃ {O(n)}
t₁₃, X₂: 2⋅X₃⋅X₃+X₃ {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₇, X₀: X₀+X₃ {O(n)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: 0 {O(1)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀+X₃ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: 2⋅X₃⋅X₃+X₂+X₃ {O(n^2)}
t₈, X₃: 2⋅X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}