Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆)
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: 0 < X₁
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ 0

Preprocessing

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

Found invariant X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l7

Found invariant X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂ for location l5

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l8

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l4

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₄: l0(X₀, X₁, X₂, X₃, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₅, X₆)
t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₆: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₇: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₈: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₅, X₆)
t₂₉: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₀: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₁: l4(X₀, X₁, X₂, X₃, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0
t₃₂: l5(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂
t₃₃: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₃₄: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0
t₃₅: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₅, X₆) :|: X₁ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0

MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]
l6 [X₀-1 ]
l7 [X₀ ]
l5 [X₂ ]

MPRF for transition t₃₃: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l5 [X₂ ]

MPRF for transition t₃₄: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₆ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l6 [X₁ ]
l7 [X₁ ]
l5 [X₃ ]

Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6

Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l7

Found invariant X₆ ≤ 0 ∧ X₅+X₆ ≤ 0 ∧ X₆ ≤ X₃ ∧ X₃+X₆ ≤ 0 ∧ X₂+X₆ ≤ 0 ∧ X₆ ≤ X₁ ∧ X₁+X₆ ≤ 0 ∧ X₀+X₆ ≤ 0 ∧ X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₃+X₅ ≤ 0 ∧ X₅ ≤ X₂ ∧ X₂+X₅ ≤ 0 ∧ X₁+X₅ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l5

Found invariant X₆ ≤ 0 ∧ X₅+X₆ ≤ 0 ∧ X₆ ≤ X₁ ∧ X₁+X₆ ≤ 0 ∧ X₀+X₆ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₁+X₅ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l8

Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l1

Found invariant X₆ ≤ 0 ∧ X₅+X₆ ≤ 0 ∧ X₆ ≤ X₁ ∧ X₁+X₆ ≤ 0 ∧ X₀+X₆ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₅ ≤ 0 ∧ X₁+X₅ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l4

Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l3

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l5

Found invariant 1 ≤ 0 for location l8

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l5

Found invariant 1 ≤ 0 for location l8

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₆ 5⋅X₅+5⋅X₆+5 {O(n)}

TWN-Loops:

entry: t₂₈: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₅, X₆)
results in twn-loop: twn:Inv: [X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 0 ∧ 0 ≤ 1] , (X₀,X₁,X₂,X₃,X₅,X₆) -> (X₀,X₁,X₀,X₁,X₅,X₆) :|: 0 < X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
entry: t₃₄: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0
results in twn-loop: twn:Inv: [X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0] , (X₀,X₁,X₂,X₃,X₅,X₆) -> (X₂,X₃,X₂,X₃,X₅,X₆) :|: 0 < X₃ ∧ X₂ ≤ 0 ∧ X₃ ≤ 0
entry: t₃₃: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0] , (X₀,X₁,X₂,X₃,X₅,X₆) -> (X₂,X₃,X₂,X₃,X₅,X₆) :|: 0 < X₃ ∧ X₂ ≤ 0 ∧ X₃ ≤ 0
order: [X₀; X₁; X₅; X₆]
closed-form:
X₀: X₀
X₁: X₁
X₅: X₅
X₆: X₆

Termination: true
Formula:

X₁ < 0 ∧ X₀ < 0 ∧ 0 < X₁
∨ X₁ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₁
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ < 0 ∧ 0 < X₁
∨ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₁

relevant size-bounds w.r.t. t₂₈:
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 5 {O(1)}

order: [X₂; X₀; X₃; X₁; X₅; X₆]
closed-form:
X₂: X₂
X₀: [[n == 0]] * X₀ + [[n != 0]] * X₂
X₃: X₃
X₁: [[n == 0]] * X₁ + [[n != 0]] * X₃
X₅: X₅
X₆: X₆

Termination: true
Formula:

X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃

relevant size-bounds w.r.t. t₃₄:
Runtime-bound of t₃₄: X₆ {O(n)}
Results in: 5⋅X₆ {O(n)}

order: [X₂; X₀; X₃; X₁; X₅; X₆]
closed-form:
X₂: X₂
X₀: [[n == 0]] * X₀ + [[n != 0]] * X₂
X₃: X₃
X₁: [[n == 0]] * X₁ + [[n != 0]] * X₃
X₅: X₅
X₆: X₆

Termination: true
Formula:

X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ < 0 ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ < X₅ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ < X₆
∨ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₃

relevant size-bounds w.r.t. t₃₃:
Runtime-bound of t₃₃: X₅ {O(n)}
Results in: 5⋅X₅ {O(n)}

5⋅X₅+5⋅X₆+5 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₀ 5⋅X₅+5⋅X₆+5 {O(n)}

relevant size-bounds w.r.t. t₂₈:
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 5 {O(1)}

relevant size-bounds w.r.t. t₃₄:
Runtime-bound of t₃₄: X₆ {O(n)}
Results in: 5⋅X₆ {O(n)}

relevant size-bounds w.r.t. t₃₃:
Runtime-bound of t₃₃: X₅ {O(n)}
Results in: 5⋅X₅ {O(n)}

5⋅X₅+5⋅X₆+5 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₂ 5⋅X₅+5⋅X₆+5 {O(n)}

relevant size-bounds w.r.t. t₂₈:
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 5 {O(1)}

relevant size-bounds w.r.t. t₃₄:
Runtime-bound of t₃₄: X₆ {O(n)}
Results in: 5⋅X₆ {O(n)}

relevant size-bounds w.r.t. t₃₃:
Runtime-bound of t₃₃: X₅ {O(n)}
Results in: 5⋅X₅ {O(n)}

5⋅X₅+5⋅X₆+5 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₅ 5⋅X₅+5⋅X₆+5 {O(n)}

relevant size-bounds w.r.t. t₂₈:
Runtime-bound of t₂₈: 1 {O(1)}
Results in: 5 {O(1)}

relevant size-bounds w.r.t. t₃₄:
Runtime-bound of t₃₄: X₆ {O(n)}
Results in: 5⋅X₆ {O(n)}

relevant size-bounds w.r.t. t₃₃:
Runtime-bound of t₃₃: X₅ {O(n)}
Results in: 5⋅X₅ {O(n)}

5⋅X₅+5⋅X₆+5 {O(n)}

knowledge_propagation leads to new time bound 5⋅X₅+5⋅X₆+6 {O(n)} for transition t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅

All Bounds

Timebounds

Overall timebound:26⋅X₆+27⋅X₅+30 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 5⋅X₅+5⋅X₆+6 {O(n)}
t₂₆: 5⋅X₅+5⋅X₆+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅ {O(n)}
t₃₀: 5⋅X₅+5⋅X₆+5 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 5⋅X₅+5⋅X₆+5 {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: X₆ {O(n)}
t₃₅: 5⋅X₅+5⋅X₆+5 {O(n)}

Costbounds

Overall costbound: 26⋅X₆+27⋅X₅+30 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 5⋅X₅+5⋅X₆+6 {O(n)}
t₂₆: 5⋅X₅+5⋅X₆+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅ {O(n)}
t₃₀: 5⋅X₅+5⋅X₆+5 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 5⋅X₅+5⋅X₆+5 {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: X₆ {O(n)}
t₃₅: 5⋅X₅+5⋅X₆+5 {O(n)}

Sizebounds

t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₅, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₂₅, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₂₅, X₂: 15⋅X₆+21⋅X₅+X₂+15 {O(n)}
t₂₅, X₃: 15⋅X₅+21⋅X₆+X₃+15 {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₆, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₂₆, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₂₆, X₂: 15⋅X₆+21⋅X₅+X₂+15 {O(n)}
t₂₆, X₃: 15⋅X₅+21⋅X₆+X₃+15 {O(n)}
t₂₆, X₅: 2⋅X₅ {O(n)}
t₂₆, X₆: 2⋅X₆ {O(n)}
t₂₇, X₀: 5⋅X₆+8⋅X₅+5 {O(n)}
t₂₇, X₁: 5⋅X₅+8⋅X₆+5 {O(n)}
t₂₇, X₂: 15⋅X₆+21⋅X₅+X₂+15 {O(n)}
t₂₇, X₃: 15⋅X₅+21⋅X₆+X₃+15 {O(n)}
t₂₇, X₅: 3⋅X₅ {O(n)}
t₂₇, X₆: 3⋅X₆ {O(n)}
t₂₈, X₀: X₅ {O(n)}
t₂₈, X₁: X₆ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₂₉, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₂₉, X₂: 2⋅X₂+30⋅X₆+42⋅X₅+30 {O(n)}
t₂₉, X₃: 2⋅X₃+30⋅X₅+42⋅X₆+30 {O(n)}
t₂₉, X₅: 2⋅X₅ {O(n)}
t₂₉, X₆: 2⋅X₆ {O(n)}
t₃₀, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₀, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₀, X₂: 15⋅X₆+21⋅X₅+X₂+15 {O(n)}
t₃₀, X₃: 15⋅X₅+21⋅X₆+X₃+15 {O(n)}
t₃₀, X₅: 2⋅X₅ {O(n)}
t₃₀, X₆: 2⋅X₆ {O(n)}
t₃₁, X₀: 5⋅X₆+8⋅X₅+5 {O(n)}
t₃₁, X₁: 5⋅X₅+8⋅X₆+5 {O(n)}
t₃₁, X₂: 15⋅X₆+21⋅X₅+X₂+15 {O(n)}
t₃₁, X₃: 15⋅X₅+21⋅X₆+X₃+15 {O(n)}
t₃₁, X₅: 3⋅X₅ {O(n)}
t₃₁, X₆: 3⋅X₆ {O(n)}
t₃₂, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₂, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₂, X₂: 15⋅X₆+21⋅X₅+15 {O(n)}
t₃₂, X₃: 15⋅X₅+21⋅X₆+15 {O(n)}
t₃₂, X₅: 2⋅X₅ {O(n)}
t₃₂, X₆: 2⋅X₆ {O(n)}
t₃₃, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₃, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₃, X₂: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₃, X₃: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₃, X₅: 2⋅X₅ {O(n)}
t₃₃, X₆: 2⋅X₆ {O(n)}
t₃₄, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₄, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₄, X₂: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₄, X₃: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₄, X₅: 2⋅X₅ {O(n)}
t₃₄, X₆: 2⋅X₆ {O(n)}
t₃₅, X₀: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₅, X₁: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₅, X₂: 5⋅X₆+7⋅X₅+5 {O(n)}
t₃₅, X₃: 5⋅X₅+7⋅X₆+5 {O(n)}
t₃₅, X₅: 2⋅X₅ {O(n)}
t₃₅, X₆: 2⋅X₆ {O(n)}