Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, 20, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₇: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₈: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₉: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁₉: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₁₀: l5(X₀, X₁, X₂, X₃) → l1(0, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < X₁
t₁₂: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ < X₀
t₁₃: l5(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₄: l5(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₅: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁
t₁₆: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₁ < X₀
t₁₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₀ < X₁
t₁₈: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀
Preprocessing
Cut unsatisfiable transition t₇: l3→l5
Cut unsatisfiable transition t₉: l3→l5
Cut unsatisfiable transition t₁₁: l5→l1
Cut unsatisfiable transition t₁₂: l5→l1
Cut unsatisfiable transition t₁₃: l5→l1
Cut unsatisfiable transition t₁₄: l5→l1
Cut unsatisfiable transition t₁₆: l5→l1
Cut unsatisfiable transition t₁₇: l5→l1
Eliminate variables {X₃} that do not contribute to the problem
Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l6
Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l5
Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l1
Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l4
Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l3
Cut unsatisfiable transition t₇₅: l5→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₆₄: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₆₅: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < 0 ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₇: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₈: l2(X₀, X₁, X₂) → l1(X₂, 20, X₂)
t₆₉: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₀: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₂: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ 20 ∧ 0 ≤ X₁
t₇₃: l5(X₀, X₁, X₂) → l1(0, X₁-1, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₄: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
MPRF for transition t₇₀: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:
new bound:
20⋅X₂+8801 {O(n)}
MPRF:
l3 [420⋅X₁+401-20⋅X₀ ]
l5 [420⋅X₁+401-21⋅X₀ ]
l1 [420⋅X₁+401-20⋅X₀ ]
MPRF for transition t₇₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+421 {O(n)}
MPRF:
l3 [21⋅X₁+1-X₀ ]
l5 [21⋅X₁-X₀ ]
l1 [21⋅X₁+1-X₀ ]
MPRF for transition t₇₃: l5(X₀, X₁, X₂) → l1(0, X₁-1, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:
new bound:
19⋅X₂+8000 {O(n)}
MPRF:
l3 [400⋅X₁-19⋅X₀ ]
l5 [399⋅X₁+1-19⋅X₀ ]
l1 [400⋅X₁-19⋅X₀ ]
MPRF for transition t₇₄: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+420 {O(n)}
MPRF:
l3 [20⋅X₁+20-X₀ ]
l5 [20⋅X₁+20-X₀ ]
l1 [20⋅X₁+20-X₀ ]
Found invariant 1 ≤ 0 for location l6
Found invariant 1 ≤ 0 for location l5
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 l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ 20 ≤ X₁ for location l6
Found invariant X₂ ≤ 20 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 20 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l5
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ 20 ≤ X₁ for location l1
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ 20 ≤ X₁ for location l4
Found invariant X₂ ≤ 20 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 20 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₆₅ 120⋅X₂+50526 {O(n)}
TWN-Loops:
entry: t₇₄: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁,X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
entry: t₇₃: l5(X₀, X₁, X₂) → l1(0, X₁-1, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁,X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
entry: t₆₈: l2(X₀, X₁, X₂) → l1(X₂, 20, X₂)
results in twn-loop: twn:Inv: [X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁,X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁
Termination: true
Formula:
X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
relevant size-bounds w.r.t. t₇₄:
Runtime-bound of t₇₄: X₂+420 {O(n)}
Results in: 6⋅X₂+2520 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁
Termination: true
Formula:
X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
relevant size-bounds w.r.t. t₇₃:
Runtime-bound of t₇₃: 19⋅X₂+8000 {O(n)}
Results in: 114⋅X₂+48000 {O(n)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
Termination: true
Formula:
X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
relevant size-bounds w.r.t. t₆₈:
Runtime-bound of t₆₈: 1 {O(1)}
Results in: 6 {O(1)}
120⋅X₂+50526 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₆₉ 120⋅X₂+50526 {O(n)}
relevant size-bounds w.r.t. t₇₄:
Runtime-bound of t₇₄: X₂+420 {O(n)}
Results in: 6⋅X₂+2520 {O(n)}
relevant size-bounds w.r.t. t₇₃:
Runtime-bound of t₇₃: 19⋅X₂+8000 {O(n)}
Results in: 114⋅X₂+48000 {O(n)}
relevant size-bounds w.r.t. t₆₈:
Runtime-bound of t₆₈: 1 {O(1)}
Results in: 6 {O(1)}
120⋅X₂+50526 {O(n)}
All Bounds
Timebounds
Overall timebound:281⋅X₂+118699 {O(n)}
t₆₄: 1 {O(1)}
t₆₅: 120⋅X₂+50526 {O(n)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 120⋅X₂+50526 {O(n)}
t₇₀: 20⋅X₂+8801 {O(n)}
t₇₁: X₂+421 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 19⋅X₂+8000 {O(n)}
t₇₄: X₂+420 {O(n)}
Costbounds
Overall costbound: 281⋅X₂+118699 {O(n)}
t₆₄: 1 {O(1)}
t₆₅: 120⋅X₂+50526 {O(n)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 120⋅X₂+50526 {O(n)}
t₇₀: 20⋅X₂+8801 {O(n)}
t₇₁: X₂+421 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 19⋅X₂+8000 {O(n)}
t₇₄: X₂+420 {O(n)}
Sizebounds
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: X₁ {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₅, X₀: 20 {O(1)}
t₆₅, X₁: 20 {O(1)}
t₆₅, X₂: X₂ {O(n)}
t₆₆, X₀: X₂ {O(n)}
t₆₆, X₁: 20 {O(1)}
t₆₆, X₂: X₂ {O(n)}
t₆₇, X₀: X₂ {O(n)}
t₆₇, X₁: 20 {O(1)}
t₆₇, X₂: X₂ {O(n)}
t₆₈, X₀: X₂ {O(n)}
t₆₈, X₁: 20 {O(1)}
t₆₈, X₂: X₂ {O(n)}
t₆₉, X₀: 0 {O(1)}
t₆₉, X₁: 0 {O(1)}
t₆₉, X₂: X₂ {O(n)}
t₇₀, X₀: 20 {O(1)}
t₇₀, X₁: 20 {O(1)}
t₇₀, X₂: X₂ {O(n)}
t₇₁, X₀: 19 {O(1)}
t₇₁, X₁: 20 {O(1)}
t₇₁, X₂: X₂ {O(n)}
t₇₂, X₀: 2⋅X₂ {O(n)}
t₇₂, X₁: 20 {O(1)}
t₇₂, X₂: 2⋅X₂ {O(n)}
t₇₃, X₀: 0 {O(1)}
t₇₃, X₁: 19 {O(1)}
t₇₃, X₂: X₂ {O(n)}
t₇₄, X₀: 20 {O(1)}
t₇₄, X₁: 20 {O(1)}
t₇₄, X₂: X₂ {O(n)}