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) → l6(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₄
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₂, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃
t₇: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₁
t₃: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀+1, 0, X₄)
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l3(0, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l7

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₀ for location l3

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) → l6(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₂, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀+1, 0, X₄) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l3(0, X₁, X₂, X₃, X₄)

MPRF for transition t₂: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₄: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀+1, 0, X₄) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₂, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₅: l1→l2

cycle: [t₅: l1→l2; t₇: l2→l1]
loop: (X₃+1 ≤ X₄,(X₃,X₄) -> (X₃+1,X₄)
order: [X₃; X₄]
closed-form:
X₃: X₃ + [[n != 0]] * n^1
X₄: X₄

Termination: true
Formula:

1 < 0
∨ X₃+1 < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ X₃+1

Stabilization-Threshold for: X₃+1 ≤ X₄
alphas_abs: X₃+1+X₄
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₄+4 {O(n)}

TWN - Lifting for t₅: l1→l2 of 2⋅X₃+2⋅X₄+6 {O(n)}

relevant size-bounds w.r.t. t₄:
X₃: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₄: X₁ {O(n)}
Results in: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}

TWN: t₇: l2→l1

TWN - Lifting for t₇: l2→l1 of 2⋅X₃+2⋅X₄+6 {O(n)}

relevant size-bounds w.r.t. t₄:
X₃: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₄: X₁ {O(n)}
Results in: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}

Chain transitions t₄: l4→l1 and t₆: l1→l3 to t₅₃: l4→l3

Chain transitions t₇: l2→l1 and t₆: l1→l3 to t₅₄: l2→l3

Chain transitions t₇: l2→l1 and t₅: l1→l2 to t₅₅: l2→l2

Chain transitions t₄: l4→l1 and t₅: l1→l2 to t₅₆: l4→l2

Chain transitions t₁: l6→l3 and t₃: l3→l5 to t₅₇: l6→l5

Chain transitions t₅₃: l4→l3 and t₃: l3→l5 to t₅₈: l4→l5

Chain transitions t₅₃: l4→l3 and t₂: l3→l4 to t₅₉: l4→l4

Chain transitions t₁: l6→l3 and t₂: l3→l4 to t₆₀: l6→l4

Chain transitions t₅₄: l2→l3 and t₂: l3→l4 to t₆₁: l2→l4

Chain transitions t₅₄: l2→l3 and t₃: l3→l5 to t₆₂: l2→l5

Analysing control-flow refined program

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l7

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₀ for location l3

MPRF for transition t₅₆: l4(X₀, X₁, X₂, X₃, X₄) -{2}> l2(X₀, X₁, 1+X₀, 0, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁+X₀ ∧ 0 ≤ 2⋅X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₅₉: l4(X₀, X₁, X₂, X₃, X₄) -{3}> l4(1+X₀, X₁, 1+X₀, 0, X₄) :|: X₄ ≤ 0 ∧ 2+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁+X₀ ∧ 0 ≤ 2⋅X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆₁: l2(X₀, X₁, X₂, X₃, X₄) -{3}> l4(X₂, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ X₃+1 ∧ X₂+1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃+1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₅₅: l2→l2

cycle: [t₅₅: l2→l2]
loop: (2+X₃ ≤ X₄,(X₃,X₄) -> (1+X₃,X₄)
order: [X₃; X₄]
closed-form:
X₃: X₃ + [[n != 0]] * n^1
X₄: X₄

Termination: true
Formula:

1 < 0
∨ 2+X₃ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₃ ≤ X₄ ∧ X₄ ≤ 2+X₃

Stabilization-Threshold for: 2+X₃ ≤ X₄
alphas_abs: 2+X₃+X₄
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₄+6 {O(n)}

TWN - Lifting for t₅₅: l2→l2 of 2⋅X₃+2⋅X₄+8 {O(n)}

relevant size-bounds w.r.t. t₅₆:
X₃: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₅₆: X₁ {O(n)}
Results in: 2⋅X₁⋅X₄+8⋅X₁ {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 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2

Found invariant 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___1

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___3

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l7

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₁ {O(n)} for transition t₁₄₁: l1(X₀, X₁, X₂, X₃, X₄) → n_l2___3(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₁ {O(n)} for transition t₁₄₃: n_l2___3(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀, X₁, X₀+1, X₃+1, X₄) :|: X₀+1 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₀+1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₁₄₀: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l2___1(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₄ ∧ X₀+1 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁⋅X₄+2⋅X₁ {O(n^2)}

MPRF for transition t₁₄₂: n_l2___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀, X₁, X₀+1, X₃+1, X₄) :|: 1 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀ ∧ 1+X₃ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁⋅X₄+X₁ {O(n^2)}

MPRF for transition t₁₄₇: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l3(X₂, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {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+15⋅X₁+4 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₆: X₁ {O(n)}
t₇: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁⋅X₄+15⋅X₁+4 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₆: X₁ {O(n)}
t₇: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₈: 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: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₁+X₂+2 {O(n)}
t₂, X₃: 2⋅X₁⋅X₄+6⋅X₁+X₃ {O(n^2)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₁+X₂+2 {O(n)}
t₃, X₃: 2⋅X₁⋅X₄+6⋅X₁+X₃ {O(n^2)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁+1 {O(n)}
t₄, X₃: 0 {O(1)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₁+1 {O(n)}
t₅, X₃: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 2⋅X₁+2 {O(n)}
t₆, X₃: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁+1 {O(n)}
t₇, X₃: 2⋅X₁⋅X₄+6⋅X₁ {O(n^2)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₁+X₂+2 {O(n)}
t₈, X₃: 2⋅X₁⋅X₄+6⋅X₁+X₃ {O(n^2)}
t₈, X₄: 2⋅X₄ {O(n)}