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

Preprocessing

Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7

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

Found invariant 0 ≤ X₃ for location l1

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4

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

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

new bound:

X₂ {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

TWN: t₅: l5→l6

cycle: [t₅: l5→l6; t₇: l6→l5]
loop: (X₄ < X₁,(X₁,X₄) -> (X₁,X₄+1)
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₄ < X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}

TWN - Lifting for t₅: l5→l6 of 2⋅X₁+2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₄:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₄: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}

TWN: t₇: l6→l5

TWN - Lifting for t₇: l6→l5 of 2⋅X₁+2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₄:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₄: X₂ {O(n)}
Results in: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}

Chain transitions t₆: l5→l1 and t₃: l1→l4 to t₅₃: l5→l4

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₅₄: l2→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₅: l2→l3

Chain transitions t₆: l5→l1 and t₂: l1→l3 to t₅₆: l5→l3

Chain transitions t₅₆: l5→l3 and t₄: l3→l5 to t₅₇: l5→l5

Chain transitions t₅₅: l2→l3 and t₄: l3→l5 to t₅₈: l2→l5

Chain transitions t₅: l5→l6 and t₇: l6→l5 to t₅₉: l5→l5

Analysing control-flow refined program

Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7

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

Found invariant 0 ≤ X₃ for location l1

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4

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

MPRF for transition t₅₇: l5(X₀, X₁, X₂, X₃, X₄) -{3}> l5(X₀+1, X₁, X₂, X₀, 0) :|: X₁ ≤ X₄ ∧ X₀ < X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂+X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

TWN: t₅₉: l5→l5

cycle: [t₅₉: l5→l5]
loop: (X₄ < X₁,(X₁,X₄) -> (X₁,X₄+1)
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₄ < X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}
loop: (X₄ < X₁,(X₁,X₄) -> (X₁,X₄+1)
order: [X₁; X₄]
closed-form:
X₁: X₁
X₄: X₄ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₄ < X₁
alphas_abs: X₄+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}

TWN - Lifting for t₅₉: l5→l5 of 2⋅X₁+2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₅₇:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₅₇: 2⋅X₂+1 {O(n)}
Results in: 4⋅X₁⋅X₂+2⋅X₁+8⋅X₂+4 {O(n^2)}

TWN - Lifting for t₅₉: l5→l5 of 2⋅X₁+2⋅X₄+4 {O(n)}

relevant size-bounds w.r.t. t₅₈:
X₁: X₁ {O(n)}
X₄: 0 {O(1)}
Runtime-bound of t₅₈: 1 {O(1)}
Results in: 2⋅X₁+4 {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 X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3

Found invariant 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___1

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___2

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7

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

Found invariant 0 ≤ X₃ for location l1

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l4

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

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₂₆: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₃+1 ∧ X₄ ≤ 0 ∧ X₄ < X₁ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₂₈: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: 0 < X₁ ∧ X₀ ≤ X₃+1 ∧ X₄ ≤ 0 ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₂₅: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₃+1 ∧ 1 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₄ < X₁ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₂+2⋅X₂ {O(n^2)}

MPRF for transition t₁₂₇: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: X₄ < X₁ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₃+1 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₂+X₂ {O(n^2)}

MPRF for transition t₁₃₂: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {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⋅X₂+11⋅X₂+4 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆: X₂ {O(n)}
t₇: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁⋅X₂+11⋅X₂+4 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆: X₂ {O(n)}
t₇: 2⋅X₁⋅X₂+4⋅X₂ {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: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₂+X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂ {O(n)}
t₂, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₃, X₀: 2⋅X₂+X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: X₂ {O(n)}
t₃, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂ {O(n)}
t₄, X₄: 0 {O(1)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₂ {O(n)}
t₅, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₆, X₀: 2⋅X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₂ {O(n)}
t₆, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂ {O(n)}
t₇, X₄: 2⋅X₁⋅X₂+4⋅X₂ {O(n^2)}
t₈, X₀: 2⋅X₂+X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: X₂ {O(n)}
t₈, X₄: 2⋅X₁⋅X₂+4⋅X₂+X₄ {O(n^2)}