Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁
t₃: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀
t₁₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l4(X₀, X₁, X₂, X₃) → l2(X₂, X₃, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₉: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃)
t₁₀: l7(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁, X₂, X₃) :|: X₀ < X₁
t₁₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀

Preprocessing

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l2

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₃: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁: l4(X₀, X₁, X₂, X₃) → l2(X₂, X₃, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃) :|: 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀: l7(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF:

l5 [X₀+X₁-1 ]
l6 [X₀+X₁-1 ]
l7 [X₀+X₁-1 ]
l2 [X₀+X₁ ]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

l5 [X₀+X₁-2 ]
l6 [X₀+X₁-2 ]
l7 [X₀+X₁-2 ]
l2 [X₀+X₁-1 ]

MPRF for transition t₇: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l5 [X₁ ]
l6 [X₁-1 ]
l7 [X₁ ]
l2 [X₁ ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l5 [X₀ ]
l6 [X₀ ]
l7 [X₀-1 ]
l2 [X₀ ]

MPRF for transition t₉: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃) :|: 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l5 [X₁ ]
l6 [X₁ ]
l7 [X₁ ]
l2 [X₁ ]

MPRF for transition t₁₀: l7(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l5 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l2 [X₀ ]

Found invariant 1 ≤ 0 for location l2

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 l1

Found invariant 1 ≤ 0 for location l3

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l2

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l3

Found invariant 1 ≤ 0 for location l2

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 l1

Found invariant 1 ≤ 0 for location l3

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l2

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 8⋅X₂+8⋅X₃+16 {O(n)}

TWN-Loops:

entry: t₁₀: l7(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∨ 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
entry: t₁: l4(X₀, X₁, X₂, X₃) → l2(X₂, X₃, X₂, X₃)
results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∨ 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
entry: t₉: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃) :|: 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∨ 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
entry: t₁: l4(X₀, X₁, X₂, X₃) → l2(X₂, X₃, X₂, X₃)
results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∨ 0 < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

relevant size-bounds w.r.t. t₁₀:
Runtime-bound of t₁₀: X₂ {O(n)}
Results in: 8⋅X₂ {O(n)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

relevant size-bounds w.r.t. t₁:
Runtime-bound of t₁: 1 {O(1)}
Results in: 8 {O(1)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

relevant size-bounds w.r.t. t₉:
Runtime-bound of t₉: X₃ {O(n)}
Results in: 8⋅X₃ {O(n)}

order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃

Termination: true
Formula:

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

relevant size-bounds w.r.t. t₁:
Runtime-bound of t₁: 1 {O(1)}
Results in: 8 {O(1)}

8⋅X₂+8⋅X₃+16 {O(n)}

All Bounds

Timebounds

Overall timebound:12⋅X₂+12⋅X₃+23 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: X₃ {O(n)}
t₈: X₂ {O(n)}
t₉: X₃ {O(n)}
t₁₀: X₂ {O(n)}
t₁₁: 8⋅X₂+8⋅X₃+16 {O(n)}

Costbounds

Overall costbound: 12⋅X₂+12⋅X₃+23 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: X₃ {O(n)}
t₈: X₂ {O(n)}
t₉: X₃ {O(n)}
t₁₀: X₂ {O(n)}
t₁₁: 8⋅X₂+8⋅X₃+16 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₂ {O(n)}
t₂, X₁: X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 2⋅X₂ {O(n)}
t₄, X₁: 2⋅X₃ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₅, X₀: 2⋅X₂ {O(n)}
t₅, X₁: 2⋅X₃ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₆, X₀: 2⋅X₂ {O(n)}
t₆, X₁: 2⋅X₃ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}
t₁₂, X₀: 6⋅X₂ {O(n)}
t₁₂, X₁: 6⋅X₃ {O(n)}
t₁₂, X₂: 6⋅X₂ {O(n)}
t₁₂, X₃: 6⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₂ {O(n)}
t₉, X₁: X₃ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₂ {O(n)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}