Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 1, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₂
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₀ ∧ 0 < X₂
t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄)
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 2⋅X₂, X₃, X₄)

Preprocessing

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₀ ≤ X₃ for location l7

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

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ for location l4

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₇: l3→l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 1, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 < X₁ ∧ X₀ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₀ ≤ X₃
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0 ∧ X₀ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 2⋅X₂, X₃, X₄) :|: 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 1, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 < X₁ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₉: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

TWN: t₅: l3→l6

cycle: [t₅: l3→l6; t₈: l6→l3]
loop: (X₂ < X₀ ∧ 0 < X₂,(X₀,X₂) -> (X₀,2⋅X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ * 2^n

Termination: true
Formula:

0 < X₂ ∧ X₂ < 0
∨ 0 < X₂ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂

Stabilization-Threshold for: X₂ < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

TWN - Lifting for t₅: l3→l6 of 2⋅X₀+5 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₃+1 {O(n)}
Runtime-bound of t₂: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}

TWN: t₈: l6→l3

TWN - Lifting for t₈: l6→l3 of 2⋅X₀+5 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₃+1 {O(n)}
Runtime-bound of t₂: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}

Chain transitions t₉: l5→l1 and t₄: l1→l4 to t₇₇: l5→l4

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₇₈: l2→l4

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₇₉: l2→l4

Chain transitions t₉: l5→l1 and t₃: l1→l4 to t₈₀: l5→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₈₁: l2→l3

Chain transitions t₉: l5→l1 and t₂: l1→l3 to t₈₂: l5→l3

Chain transitions t₈: l6→l3 and t₅: l3→l6 to t₈₃: l6→l6

Chain transitions t₈₂: l5→l3 and t₅: l3→l6 to t₈₄: l5→l6

Chain transitions t₈₂: l5→l3 and t₆: l3→l5 to t₈₅: l5→l5

Chain transitions t₈: l6→l3 and t₆: l3→l5 to t₈₆: l6→l5

Chain transitions t₈₁: l2→l3 and t₆: l3→l5 to t₈₇: l2→l5

Chain transitions t₈₁: l2→l3 and t₅: l3→l6 to t₈₈: l2→l6

Analysing control-flow refined program

Cut unsatisfiable transition t₇₇: l5→l4

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₀ ≤ X₃ for location l7

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ for location l4

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

MPRF for transition t₈₄: l5(X₀, X₁, X₂, X₃, X₄) -{3}> l6(X₀-1, X₂, 1, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 < X₂ ∧ 2 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF for transition t₈₅: l5(X₀, X₁, X₂, X₃, X₄) -{3}> l5(X₀-1, X₂, 1, X₃, X₄) :|: 1 ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ 2 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF for transition t₈₆: l6(X₀, X₁, X₂, X₃, X₄) -{2}> l5(X₀, X₁, 2⋅X₂, X₃, X₄) :|: X₀ ≤ 2⋅X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ 2⋅X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ 2⋅X₂ ∧ 2 ≤ X₁+2⋅X₂ ∧ 1 ≤ X₀+2⋅X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃+4 {O(n)}

TWN: t₈₃: l6→l6

cycle: [t₈₃: l6→l6]
loop: (2⋅X₂ < X₀ ∧ 0 < 2⋅X₂,(X₀,X₂) -> (X₀,2⋅X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ * 2^n

Termination: true
Formula:

0 < 2⋅X₂ ∧ 2⋅X₂ < 0
∨ 0 < 2⋅X₂ ∧ 0 < X₀ ∧ 2⋅X₂ ≤ 0 ∧ 0 ≤ 2⋅X₂

Stabilization-Threshold for: 2⋅X₂ < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
loop: (2⋅X₂ < X₀ ∧ 0 < 2⋅X₂,(X₀,X₂) -> (X₀,2⋅X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ * 2^n

Termination: true
Formula:

0 < 2⋅X₂ ∧ 2⋅X₂ < 0
∨ 0 < 2⋅X₂ ∧ 0 < X₀ ∧ 2⋅X₂ ≤ 0 ∧ 0 ≤ 2⋅X₂

Stabilization-Threshold for: 2⋅X₂ < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}

TWN - Lifting for t₈₃: l6→l6 of 2⋅X₀+5 {O(n)}

relevant size-bounds w.r.t. t₈₄:
X₀: X₃ {O(n)}
Runtime-bound of t₈₄: X₃+3 {O(n)}
Results in: 2⋅X₃⋅X₃+11⋅X₃+15 {O(n^2)}

TWN - Lifting for t₈₃: l6→l6 of 2⋅X₀+5 {O(n)}

relevant size-bounds w.r.t. t₈₈:
X₀: X₃ {O(n)}
Runtime-bound of t₈₈: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___3

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l6___1

Found invariant X₀ ≤ X₃ for location l7

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

Found invariant 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ for location l4

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₈₀: l3(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₈₂: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(X₀, X₁, 2⋅X₂, X₃, X₄) :|: X₂ < X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₇₉: n_l3___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₂ ∧ 2+X₂ ≤ 2⋅X₀ ∧ X₂ < X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃ {O(n^2)}

MPRF for transition t₁₈₁: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l3___2(X₀, X₁, 2⋅X₂, X₃, X₄) :|: X₂ < X₀ ∧ 2 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+2⋅X₃ {O(n^2)}

MPRF for transition t₁₈₆: n_l3___2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃+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⋅X₃⋅X₃+21⋅X₃+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₆: X₃+1 {O(n)}
t₈: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₉: X₃+1 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₃⋅X₃+21⋅X₃+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₆: X₃+1 {O(n)}
t₈: 2⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₉: X₃+1 {O(n)}
t₁₀: 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: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₃+1 {O(n)}
t₂, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+X₄+1 {O(EXP)}
t₂, X₂: 1 {O(1)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅X₃+1 {O(n)}
t₃, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+X₄+1 {O(EXP)}
t₃, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+X₂+1 {O(EXP)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: X₄ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₃+1 {O(n)}
t₅, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+X₄+1 {O(EXP)}
t₅, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7) {O(EXP)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₃+1 {O(n)}
t₆, X₁: 2⋅2^(2⋅X₃⋅X₃+9⋅X₃+7)+2⋅X₄+2 {O(EXP)}
t₆, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+1 {O(EXP)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₀: X₃+1 {O(n)}
t₈, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+X₄+1 {O(EXP)}
t₈, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7) {O(EXP)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: X₃+1 {O(n)}
t₉, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+1 {O(EXP)}
t₉, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+1 {O(EXP)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: 3⋅X₃+1 {O(n)}
t₁₀, X₁: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+2⋅X₄+1 {O(EXP)}
t₁₀, X₂: 2^(2⋅X₃⋅X₃+9⋅X₃+7)+2⋅X₂+1 {O(EXP)}
t₁₀, X₃: 3⋅X₃ {O(n)}
t₁₀, X₄: 3⋅X₄ {O(n)}