Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₇: l4→l1

Cut unsatisfiable transition t₈: l4→l1

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₂: l0(X₀, X₁, X₄, X₅) → l3(X₀, X₁, X₄, X₅)
t₂₄: l1(X₀, X₁, X₄, X₅) → l2(X₀, X₁, X₄, X₅) :|: X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₃: l1(X₀, X₁, X₄, X₅) → l4(X₀, X₁, X₄, X₅) :|: X₀ < X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁, X₄, X₅) → l5(X₀, X₁, X₄, X₅)
t₂₆: l3(X₀, X₁, X₄, X₅) → l1(0, 0, X₄, X₅) :|: 0 < X₄ ∧ X₄ < X₅
t₂₇: l3(X₀, X₁, X₄, X₅) → l2(X₀, X₁, X₄, X₅) :|: X₄ ≤ 0
t₂₈: l3(X₀, X₁, X₄, X₅) → l2(X₀, X₁, X₄, X₅) :|: X₅ ≤ X₄
t₂₉: l4(X₀, X₁, X₄, X₅) → l1(X₀, X₁+1, X₄, X₅) :|: X₁ < X₄ ∧ X₁ < X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₃₀: l4(X₀, X₁, X₄, X₅) → l1(X₀+1, 0, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₃₀: l4(X₀, X₁, X₄, X₅) → l1(X₀+1, 0, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l4 [X₅-X₀ ]
l1 [X₅-X₀ ]

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃ 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}

TWN-Loops:

entry: t₃₀: l4(X₀, X₁, X₄, X₅) → l1(X₀+1, 0, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₄,X₅) -> (X₀,X₁+1,X₄,X₅) :|: X₀ < X₅ ∧ X₁ < X₄ ∧ X₁ < X₄
entry: t₂₆: l3(X₀, X₁, X₄, X₅) → l1(0, 0, X₄, X₅) :|: 0 < X₄ ∧ X₄ < X₅
results in twn-loop: twn:Inv: [2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₄,X₅) -> (X₀,X₁+1,X₄,X₅) :|: X₀ < X₅ ∧ X₁ < X₄ ∧ X₁ < X₄
order: [X₀; X₁; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0 ∧ X₀ < X₅
∨ X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < X₅

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

relevant size-bounds w.r.t. t₃₀:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₅ {O(n)}
Results in: 2⋅X₄⋅X₅+5⋅X₅ {O(n^2)}

order: [X₀; X₁; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0 ∧ X₀ < X₅
∨ X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < X₅

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

relevant size-bounds w.r.t. t₂₆:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₄+5 {O(n)}

2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₉ 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}

relevant size-bounds w.r.t. t₃₀:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₅ {O(n)}
Results in: 2⋅X₄⋅X₅+5⋅X₅ {O(n^2)}

relevant size-bounds w.r.t. t₂₆:
X₁: 0 {O(1)}
X₄: X₄ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₄+5 {O(n)}

2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₂₄: l1→l2

Cut unsatisfiable transition t₉₆: n_l1___1→l2

Cut unsatisfiable transition t₉₈: n_l1___5→l2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l4___4

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___1

MPRF for transition t₈₂: n_l1___1(X₀, X₁, X₄, X₅) → n_l4___4(X₀, X₁, X₄, X₅) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₅ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

n_l4___2 [X₅-X₀ ]
n_l1___1 [X₅-X₀ ]
n_l1___3 [X₅-X₀ ]
n_l4___4 [X₅-X₀-1 ]
n_l1___5 [X₅-X₀-1 ]

MPRF for transition t₈₃: n_l1___3(X₀, X₁, X₄, X₅) → n_l4___2(X₀, X₁, X₄, X₅) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ X₁ < X₄ ∧ 1+X₁ ≤ X₅ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

n_l4___2 [X₅-X₀ ]
n_l1___1 [X₅-X₀ ]
n_l1___3 [X₅+1-X₀ ]
n_l4___4 [X₅-X₀ ]
n_l1___5 [X₅-X₀ ]

MPRF for transition t₈₆: n_l4___2(X₀, X₁, X₄, X₅) → n_l1___1(X₀, X₁+1, X₄, X₅) :|: X₀ < X₅ ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₄ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 0 ≤ X₁ ∧ X₁ < X₄ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

n_l4___2 [X₅+1-X₀ ]
n_l1___1 [X₅-X₀ ]
n_l1___3 [X₅+1-X₀ ]
n_l4___4 [X₅-X₀ ]
n_l1___5 [X₅-X₀ ]

MPRF for transition t₈₇: n_l4___4(X₀, X₁, X₄, X₅) → n_l1___3(X₀+1, 0, X₁, X₅) :|: 1+X₀ ≤ X₅ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₀ ≤ X₅ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

n_l4___2 [X₅-X₀ ]
n_l1___1 [X₅-X₀ ]
n_l1___3 [X₅-X₀ ]
n_l4___4 [X₅-X₀ ]
n_l1___5 [X₅-X₀ ]

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___4

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___5

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6

Found invariant 1 ≤ 0 for location n_l4___2

Found invariant 1 ≤ 0 for location n_l4___4

Found invariant 1 ≤ 0 for location n_l1___3

Found invariant 1 ≤ 0 for location n_l1___5

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ 0 for location n_l1___1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6

Found invariant 1 ≤ 0 for location n_l4___2

Found invariant 1 ≤ 0 for location n_l4___4

Found invariant 1 ≤ 0 for location n_l1___3

Found invariant 1 ≤ 0 for location n_l1___5

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ 0 for location n_l1___1

MPRF for transition t₈₄: n_l1___5(X₀, X₁, X₄, X₅) → n_l4___4(X₀, X₁, X₄, X₅) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₅ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ < X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₅⋅X₅+X₄+2 {O(n^2)}

MPRF:

n_l1___3 [X₅ ]
n_l4___2 [X₄ ]
n_l1___1 [X₄ ]
n_l4___4 [X₄-X₁ ]
n_l1___5 [X₄+1-X₁ ]

MPRF for transition t₈₈: n_l4___4(X₀, X₁, X₄, X₅) → n_l1___5(X₀, X₁+1, X₄, X₅) :|: 1+X₀ ≤ X₅ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₅ ∧ 0 ≤ X₁ ∧ X₁ < X₄ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₅⋅X₅+X₄+2 {O(n^2)}

MPRF:

n_l1___3 [X₅ ]
n_l4___2 [X₅ ]
n_l1___1 [X₄+1 ]
n_l4___4 [X₄+1-X₁ ]
n_l1___5 [X₄+1-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₄⋅X₅+11⋅X₅+4⋅X₄+16 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₃₀: X₅ {O(n)}

Costbounds

Overall costbound: 4⋅X₄⋅X₅+11⋅X₅+4⋅X₄+16 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₃₀: X₅ {O(n)}

Sizebounds

t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: X₅ {O(n)}
t₂₃, X₁: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: X₅ {O(n)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₅, X₀: 2⋅X₀+X₅ {O(n)}
t₂₅, X₁: 2⋅X₁ {O(n)}
t₂₅, X₄: 3⋅X₄ {O(n)}
t₂₅, X₅: 3⋅X₅ {O(n)}
t₂₆, X₀: 0 {O(1)}
t₂₆, X₁: 0 {O(1)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₉, X₀: X₅ {O(n)}
t₂₉, X₁: 2⋅X₄⋅X₅+2⋅X₄+5⋅X₅+5 {O(n^2)}
t₂₉, X₄: X₄ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₃₀, X₀: X₅ {O(n)}
t₃₀, X₁: 0 {O(1)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₅: X₅ {O(n)}