Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₆, X₇, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₅, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₆
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: (X₂)² ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ < (X₂)² ∧ 0 < X₁
t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, 5⋅X₁+(X₀)², 2⋅X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables {X₃,X₄} that do not contribute to the problem

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

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

Found invariant 1 ≤ X₄ ∧ X₀ ≤ X₃ for location l1

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₄, X₅, X₃, X₄, X₅) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃
t₂₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₄
t₂₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0
t₂₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: (X₂)² ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < (X₂)² ∧ 0 < X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, 5⋅X₁+(X₀)², 2⋅X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₄, X₅, X₃, X₄, X₅) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: (X₂)² ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

1 {O(1)}

MPRF for transition t₃₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

TWN: t₂₉: l4→l6

cycle: [t₂₉: l4→l6; t₃₁: l6→l4]
loop: (X₁ < (X₂)² ∧ 0 < X₁,(X₀,X₁,X₂) -> (X₀,5⋅X₁+(X₀)²,2⋅X₂)
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ * 5^n + [[n != 0]] * 1/4⋅(X₀)² * 5^n + [[n != 0]] * -1/4⋅(X₀)²
X₂: X₂ * 2^n

Termination: true
Formula:

0 < 4⋅X₁+(X₀)² ∧ 4⋅X₁+(X₀)² < 0
∨ 0 < 4⋅X₁+(X₀)² ∧ 0 < 4⋅(X₂)² ∧ 4⋅X₁+(X₀)² ≤ 0 ∧ 0 ≤ 4⋅X₁+(X₀)²
∨ 0 < 4⋅X₁+(X₀)² ∧ 0 < (X₀)² ∧ 4⋅X₁+(X₀)² ≤ 0 ∧ 0 ≤ 4⋅X₁+(X₀)² ∧ 0 ≤ 4⋅(X₂)² ∧ 4⋅(X₂)² ≤ 0
∨ (X₀)² < 0 ∧ 0 ≤ 4⋅X₁+(X₀)² ∧ 4⋅X₁+(X₀)² ≤ 0 ∧ 4⋅X₁+(X₀)² < 0
∨ (X₀)² < 0 ∧ 0 < 4⋅(X₂)² ∧ 4⋅X₁+(X₀)² ≤ 0 ∧ 0 ≤ 4⋅X₁+(X₀)²
∨ (X₀)² < 0 ∧ 0 < (X₀)² ∧ 4⋅X₁+(X₀)² ≤ 0 ∧ 0 ≤ 4⋅X₁+(X₀)² ∧ 0 ≤ 4⋅(X₂)² ∧ 4⋅(X₂)² ≤ 0

Stabilization-Threshold for: 0 < X₁
alphas_abs: (X₀)²
M: 0
N: 1
Bound: 2⋅X₀⋅X₀+2 {O(n^2)}
Stabilization-Threshold for: X₁ < (X₂)²
alphas_abs: (X₀)²+4⋅(X₂)²
M: 11
N: 1
Bound: 2⋅X₀⋅X₀+8⋅X₂⋅X₂+12 {O(n^2)}

TWN - Lifting for t₂₉: l4→l6 of 4⋅X₀⋅X₀+8⋅X₂⋅X₂+16 {O(n^2)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₃ {O(n)}
X₂: 2⋅X₅ {O(n)}
Runtime-bound of t₂₃: X₃ {O(n)}
Results in: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}

TWN: t₃₁: l6→l4

TWN - Lifting for t₃₁: l6→l4 of 4⋅X₀⋅X₀+8⋅X₂⋅X₂+16 {O(n^2)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₃ {O(n)}
X₂: 2⋅X₅ {O(n)}
Runtime-bound of t₂₃: X₃ {O(n)}
Results in: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}

Chain transitions t₃₀: l5→l1 and t₂₃: l1→l4 to t₆₉: l5→l4

Chain transitions t₂₅: l3→l1 and t₂₃: l1→l4 to t₇₀: l3→l4

Chain transitions t₂₅: l3→l1 and t₂₂: l1→l2 to t₇₁: l3→l2

Chain transitions t₃₀: l5→l1 and t₂₂: l1→l2 to t₇₂: l5→l2

Chain transitions t₃₁: l6→l4 and t₂₉: l4→l6 to t₇₃: l6→l6

Chain transitions t₆₉: l5→l4 and t₂₉: l4→l6 to t₇₄: l5→l6

Chain transitions t₆₉: l5→l4 and t₂₈: l4→l5 to t₇₅: l5→l5

Chain transitions t₃₁: l6→l4 and t₂₈: l4→l5 to t₇₆: l6→l5

Chain transitions t₇₀: l3→l4 and t₂₈: l4→l5 to t₇₇: l3→l5

Chain transitions t₇₀: l3→l4 and t₂₉: l4→l6 to t₇₈: l3→l6

Chain transitions t₇₀: l3→l4 and t₂₇: l4→l5 to t₇₉: l3→l5

Chain transitions t₆₉: l5→l4 and t₂₇: l4→l5 to t₈₀: l5→l5

Chain transitions t₃₁: l6→l4 and t₂₇: l4→l5 to t₈₁: l6→l5

Analysing control-flow refined program

Cut unsatisfiable transition t₇₅: l5→l5

Cut unsatisfiable transition t₇₇: l3→l5

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

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

Found invariant 1 ≤ X₄ ∧ X₀ ≤ X₃ for location l1

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

MPRF for transition t₇₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l6(X₀-1, X₄, X₅, X₃, X₄, X₅) :|: 1 < X₀ ∧ X₄ < (X₅)² ∧ 0 < X₄ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ 2⋅X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₄+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 2 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃+2 {O(n)}

MPRF for transition t₇₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l5(X₀, 5⋅X₁+Temp_Int₉₃₃, 2⋅X₂, X₃, X₄, X₅) :|: 5⋅X₁+(X₀)² ≤ 0 ∧ 0 < Temp_Int₉₃₃ ∧ X₀ ≤ Temp_Int₉₃₃ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ 5⋅X₁+(X₀)² ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ 5⋅X₁+(X₀)²+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ 5⋅X₁+(X₀)²+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ 5⋅X₁+(X₀)² ∧ 2 ≤ X₀+5⋅X₁+(X₀)² ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF for transition t₈₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l5(X₀-1, X₄, X₅, X₃, X₄, X₅) :|: 1 < X₀ ∧ (X₅)² ≤ X₄ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ 0 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ 2⋅X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₄+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 2 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃ {O(n)}

MPRF for transition t₈₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l5(X₀, 5⋅X₁+Temp_Int₉₃₄, 2⋅X₂, X₃, X₄, X₅) :|: 4⋅(X₂)² ≤ 5⋅X₁+(X₀)² ∧ 0 < Temp_Int₉₃₄ ∧ X₀ ≤ Temp_Int₉₃₄ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ 5⋅X₁+(X₀)² ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ 5⋅X₁+(X₀)²+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ 5⋅X₁+(X₀)²+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ 5⋅X₁+(X₀)² ∧ 2 ≤ X₀+5⋅X₁+(X₀)² ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

TWN: t₇₃: l6→l6

cycle: [t₇₃: l6→l6]
loop: (5⋅X₁+(X₀)² < 4⋅(X₂)² ∧ 0 < 5⋅X₁+(X₀)²,(X₀,X₁,X₂) -> (X₀,5⋅X₁+(X₀)²,2⋅X₂)
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ * 5^n + [[n != 0]] * 1/4⋅(X₀)² * 5^n + [[n != 0]] * -1/4⋅(X₀)²
X₂: X₂ * 2^n

Termination: true
Formula:

0 < 20⋅X₁+5⋅(X₀)² ∧ 20⋅X₁+5⋅(X₀)² < 0
∨ 0 < 20⋅X₁+5⋅(X₀)² ∧ 0 < 16⋅(X₂)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)²
∨ 0 < 20⋅X₁+5⋅(X₀)² ∧ 0 < (X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 0 ≤ 16⋅(X₂)² ∧ 16⋅(X₂)² ≤ 0
∨ (X₀)² < 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 20⋅X₁+5⋅(X₀)² < 0
∨ (X₀)² < 0 ∧ 0 < 16⋅(X₂)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)²
∨ (X₀)² < 0 ∧ 0 < (X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 0 ≤ 16⋅(X₂)² ∧ 16⋅(X₂)² ≤ 0

Stabilization-Threshold for: 0 < 5⋅X₁+(X₀)²
alphas_abs: (X₀)²
M: 0
N: 1
Bound: 2⋅X₀⋅X₀+2 {O(n^2)}
Stabilization-Threshold for: 5⋅X₁+(X₀)² < 4⋅(X₂)²
alphas_abs: (X₀)²+16⋅(X₂)²
M: 11
N: 1
Bound: 2⋅X₀⋅X₀+32⋅X₂⋅X₂+12 {O(n^2)}
loop: (5⋅X₁+(X₀)² < 4⋅(X₂)² ∧ 0 < 5⋅X₁+(X₀)²,(X₀,X₁,X₂) -> (X₀,5⋅X₁+(X₀)²,2⋅X₂)
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ * 5^n + [[n != 0]] * 1/4⋅(X₀)² * 5^n + [[n != 0]] * -1/4⋅(X₀)²
X₂: X₂ * 2^n

Termination: true
Formula:

0 < 20⋅X₁+5⋅(X₀)² ∧ 20⋅X₁+5⋅(X₀)² < 0
∨ 0 < 20⋅X₁+5⋅(X₀)² ∧ 0 < 16⋅(X₂)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)²
∨ 0 < 20⋅X₁+5⋅(X₀)² ∧ 0 < (X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 0 ≤ 16⋅(X₂)² ∧ 16⋅(X₂)² ≤ 0
∨ (X₀)² < 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 20⋅X₁+5⋅(X₀)² < 0
∨ (X₀)² < 0 ∧ 0 < 16⋅(X₂)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)²
∨ (X₀)² < 0 ∧ 0 < (X₀)² ∧ 20⋅X₁+5⋅(X₀)² ≤ 0 ∧ 0 ≤ 20⋅X₁+5⋅(X₀)² ∧ 0 ≤ 16⋅(X₂)² ∧ 16⋅(X₂)² ≤ 0

Stabilization-Threshold for: 0 < 5⋅X₁+(X₀)²
alphas_abs: (X₀)²
M: 0
N: 1
Bound: 2⋅X₀⋅X₀+2 {O(n^2)}
Stabilization-Threshold for: 5⋅X₁+(X₀)² < 4⋅(X₂)²
alphas_abs: (X₀)²+16⋅(X₂)²
M: 11
N: 1
Bound: 2⋅X₀⋅X₀+32⋅X₂⋅X₂+12 {O(n^2)}

TWN - Lifting for t₇₃: l6→l6 of 32⋅X₂⋅X₂+4⋅X₀⋅X₀+16 {O(n^2)}

relevant size-bounds w.r.t. t₇₄:
X₀: 2⋅X₃ {O(n)}
X₂: 7⋅X₅ {O(n)}
Runtime-bound of t₇₄: 2⋅X₃+2 {O(n)}
Results in: 3136⋅X₃⋅X₅⋅X₅+32⋅X₃⋅X₃⋅X₃+3136⋅X₅⋅X₅+32⋅X₃⋅X₃+32⋅X₃+32 {O(n^3)}

TWN - Lifting for t₇₃: l6→l6 of 32⋅X₂⋅X₂+4⋅X₀⋅X₀+16 {O(n^2)}

relevant size-bounds w.r.t. t₇₈:
X₀: X₃ {O(n)}
X₂: X₅ {O(n)}
Runtime-bound of t₇₈: 1 {O(1)}
Results in: 32⋅X₅⋅X₅+4⋅X₃⋅X₃+16 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₂₈: l4→l5

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___2

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location n_l4___1

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

Found invariant 1 ≤ X₄ ∧ X₀ ≤ X₃ for location l1

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₂₀₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___2(X₀, X₁, X₂, X₃, Arg4_P, X₅) :|: Arg4_P ≤ X₁ ∧ 1 ≤ Arg4_P ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₁₄: n_l4___1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: (X₂)² ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:64⋅X₃⋅X₅⋅X₅+8⋅X₃⋅X₃⋅X₃+35⋅X₃+6 {O(n^3)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₃ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₃ {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}
t₃₀: X₃ {O(n)}
t₃₁: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}

Costbounds

Overall costbound: 64⋅X₃⋅X₅⋅X₅+8⋅X₃⋅X₃⋅X₃+35⋅X₃+6 {O(n^3)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₃ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₃ {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}
t₃₀: X₃ {O(n)}
t₃₁: 32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃ {O(n^3)}

Sizebounds

t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₀: 2⋅X₃ {O(n)}
t₂₂, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅+2⋅X₅+X₂ {O(EXP)}
t₂₂, X₃: 2⋅X₃ {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₂, X₅: 2⋅X₅ {O(n)}
t₂₃, X₀: X₃ {O(n)}
t₂₃, X₁: 2⋅X₄ {O(n)}
t₂₃, X₂: 2⋅X₅ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: 2⋅X₃+X₀ {O(n)}
t₂₄, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅+2⋅X₂+2⋅X₅ {O(EXP)}
t₂₄, X₃: 3⋅X₃ {O(n)}
t₂₄, X₄: 3⋅X₄ {O(n)}
t₂₄, X₅: 3⋅X₅ {O(n)}
t₂₅, X₀: X₃ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: X₃ {O(n)}
t₂₇, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅+2⋅X₅ {O(EXP)}
t₂₇, X₃: X₃ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₈, X₀: 0 {O(1)}
t₂₈, X₁: 0 {O(1)}
t₂₈, X₂: 0 {O(1)}
t₂₈, X₃: 0 {O(1)}
t₂₈, X₄: 0 {O(1)}
t₂₈, X₅: 0 {O(1)}
t₂₉, X₀: X₃ {O(n)}
t₂₉, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅ {O(EXP)}
t₂₉, X₃: X₃ {O(n)}
t₂₉, X₄: X₄ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₃₀, X₀: X₃ {O(n)}
t₃₀, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅+2⋅X₅ {O(EXP)}
t₃₀, X₃: X₃ {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₁, X₀: X₃ {O(n)}
t₃₁, X₂: 2⋅2^(32⋅X₃⋅X₅⋅X₅+4⋅X₃⋅X₃⋅X₃+16⋅X₃)⋅X₅ {O(EXP)}
t₃₁, X₃: X₃ {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₁, X₅: X₅ {O(n)}