Initial Problem

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

Preprocessing

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l6

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

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l8

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l1

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁) → l7(X₀, X₁)
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₂: l1(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₇: l2(X₀, X₁) → l3(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l4(X₀, X₁) → l1(X₀-X₁, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁) → l2(X₀, X₁) :|: C+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l5(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁: l6(X₀, X₁) → l8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁: l7(X₀, X₁) → l1(X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁

Chain transitions t₁: l7→l1 and t₂: l1→l6 to t₁₄₆: l7→l6

Chain transitions t₁₀: l4→l1 and t₂: l1→l6 to t₁₄₇: l4→l6

Chain transitions t₁₀: l4→l1 and t₃: l1→l5 to t₁₄₈: l4→l5

Chain transitions t₁: l7→l1 and t₃: l1→l5 to t₁₄₉: l7→l5

Chain transitions t₉: l3→l1 and t₃: l1→l5 to t₁₅₀: l3→l5

Chain transitions t₉: l3→l1 and t₂: l1→l6 to t₁₅₁: l3→l6

Chain transitions t₅: l5→l2 and t₈: l2→l4 to t₁₅₂: l5→l4

Chain transitions t₄: l5→l2 and t₈: l2→l4 to t₁₅₃: l5→l4

Chain transitions t₄: l5→l2 and t₇: l2→l3 to t₁₅₄: l5→l3

Chain transitions t₅: l5→l2 and t₇: l2→l3 to t₁₅₅: l5→l3

Chain transitions t₁₅₅: l5→l3 and t₁₅₁: l3→l6 to t₁₅₆: l5→l6

Chain transitions t₁₅₄: l5→l3 and t₁₅₁: l3→l6 to t₁₅₇: l5→l6

Chain transitions t₁₅₄: l5→l3 and t₁₅₀: l3→l5 to t₁₅₈: l5→l5

Chain transitions t₁₅₅: l5→l3 and t₁₅₀: l3→l5 to t₁₅₉: l5→l5

Chain transitions t₁₅₄: l5→l3 and t₉: l3→l1 to t₁₆₀: l5→l1

Chain transitions t₁₅₅: l5→l3 and t₉: l3→l1 to t₁₆₁: l5→l1

Chain transitions t₁₅₃: l5→l4 and t₁₄₇: l4→l6 to t₁₆₂: l5→l6

Chain transitions t₁₅₂: l5→l4 and t₁₄₇: l4→l6 to t₁₆₃: l5→l6

Chain transitions t₁₅₂: l5→l4 and t₁₄₈: l4→l5 to t₁₆₄: l5→l5

Chain transitions t₁₅₃: l5→l4 and t₁₄₈: l4→l5 to t₁₆₅: l5→l5

Chain transitions t₁₅₂: l5→l4 and t₁₀: l4→l1 to t₁₆₆: l5→l1

Chain transitions t₁₅₃: l5→l4 and t₁₀: l4→l1 to t₁₆₇: l5→l1

Analysing control-flow refined program

Cut unsatisfiable transition t₁₄₆: l7→l6

Cut unsatisfiable transition t₁₅₆: l5→l6

Cut unsatisfiable transition t₁₅₇: l5→l6

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l6

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

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l8

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l1

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₁₆₄: l5(X₀, X₁) -{4}> l5(X₀-X₁, X₁) :|: 1 ≤ C ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₆₅: l5(X₀, X₁) -{4}> l5(X₀-X₁, X₁) :|: C+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₁₅₈: l5→l5

cycle: [t₁₅₈: l5→l5; t₁₅₉: l5→l5]
loop: (X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ 0 ≤ X₀,(X₀,X₁) -> (1+X₀,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
loop: (X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ 0 ≤ X₀,(X₀,X₁) -> (1+X₀,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
loop: (X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ 0 ≤ X₀,(X₀,X₁) -> (1+X₀,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
loop: (X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∨ X₀+1 ≤ X₁ ∧ 0 ≤ X₀,(X₀,X₁) -> (1+X₀,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

TWN - Lifting for t₁₅₈: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₅:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₈: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₄:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₄: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₈: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₅:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₈: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₄:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₄: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN: t₁₅₉: l5→l5

TWN - Lifting for t₁₅₉: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₅:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₉: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₄:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₄: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₉: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₅:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

TWN - Lifting for t₁₅₉: l5→l5 of 2⋅X₁+4⋅X₀+8 {O(n)}

relevant size-bounds w.r.t. t₁₆₄:
X₀: X₁ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁₆₄: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₁ {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₂: l1→l6

Cut unsatisfiable transition t₃₇₅: n_l1___4→n_l5___3

Cut unsatisfiable transition t₄₁₀: n_l1___14→l6

Cut unsatisfiable transition t₄₁₂: n_l1___9→l6

Cut unreachable locations [n_l2___2; n_l5___3] from the program graph

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___17

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l2___7

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l6

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___9

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___15

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ for location n_l1___4

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___16

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___6

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___12

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___8

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___11

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___13

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l8

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ for location n_l1___14

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location n_l1___1

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___10

MPRF for transition t₃₇₂: n_l1___1(X₀, X₁) → n_l5___13(X₀, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₃₇₈: n_l2___12(X₀, X₁) → n_l4___10(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+1 {O(n)}

MPRF for transition t₃₈₅: n_l4___10(X₀, X₁) → n_l1___1(X₀-X₁, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₃₈₈: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₃₈₉: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₃₇₆: n_l1___9(X₀, X₁) → n_l5___8(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀+4⋅X₁+2 {O(n)}

MPRF for transition t₃₈₁: n_l2___7(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀+4⋅X₁+2 {O(n)}

MPRF for transition t₃₈₄: n_l3___6(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀+4⋅X₁+1 {O(n)}

MPRF for transition t₃₉₄: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀+4⋅X₁+2 {O(n)}

MPRF for transition t₃₉₅: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀+4⋅X₁+2 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l6, l7, l8, n_l1___1, n_l1___14, n_l1___4, n_l1___9, n_l2___12, n_l2___16, n_l2___7, n_l3___11, n_l3___6, n_l4___10, n_l4___15, n_l4___5, n_l5___13, n_l5___17, n_l5___8
Transitions:
t₀: l0(X₀, X₁) → l7(X₀, X₁)
t₃₇₄: l1(X₀, X₁) → n_l5___17(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁: l6(X₀, X₁) → l8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁: l7(X₀, X₁) → l1(X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₄₀₉: n_l1___1(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₃₇₂: n_l1___1(X₀, X₁) → n_l5___13(X₀, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₃₇₃: n_l1___14(X₀, X₁) → n_l5___13(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₄₁₁: n_l1___4(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁
t₃₇₆: n_l1___9(X₀, X₁) → n_l5___8(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₇₇: n_l2___12(X₀, X₁) → n_l3___11(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₇₈: n_l2___12(X₀, X₁) → n_l4___10(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₇₉: n_l2___16(X₀, X₁) → n_l4___15(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₈₁: n_l2___7(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₂: n_l2___7(X₀, X₁) → n_l4___5(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₃: n_l3___11(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₈₄: n_l3___6(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₅: n_l4___10(X₀, X₁) → n_l1___1(X₀-X₁, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₆: n_l4___15(X₀, X₁) → n_l1___14(X₀-X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₈₇: n_l4___5(X₀, X₁) → n_l1___4(X₀-X₁, X₁) :|: 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₄₁₃: n_l5___13(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₈: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₉: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄₁₄: n_l5___17(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₉₀: n_l5___17(X₀, X₁) → n_l2___16(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₉₁: n_l5___17(X₀, X₁) → n_l2___16(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₁₆: n_l5___8(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₉₄: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₉₅: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

22⋅X₀+30⋅X₁+10 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l6, l7, l8, n_l1___1, n_l1___14, n_l1___4, n_l1___9, n_l2___12, n_l2___16, n_l2___7, n_l3___11, n_l3___6, n_l4___10, n_l4___15, n_l4___5, n_l5___13, n_l5___17, n_l5___8
Transitions:
t₀: l0(X₀, X₁) → l7(X₀, X₁)
t₃₇₄: l1(X₀, X₁) → n_l5___17(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁: l6(X₀, X₁) → l8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁: l7(X₀, X₁) → l1(X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₄₀₉: n_l1___1(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₃₇₂: n_l1___1(X₀, X₁) → n_l5___13(X₀, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₃₇₃: n_l1___14(X₀, X₁) → n_l5___13(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₄₁₁: n_l1___4(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁
t₃₇₆: n_l1___9(X₀, X₁) → n_l5___8(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₇₇: n_l2___12(X₀, X₁) → n_l3___11(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₇₈: n_l2___12(X₀, X₁) → n_l4___10(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₇₉: n_l2___16(X₀, X₁) → n_l4___15(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₈₁: n_l2___7(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₂: n_l2___7(X₀, X₁) → n_l4___5(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₃: n_l3___11(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₈₄: n_l3___6(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₈₅: n_l4___10(X₀, X₁) → n_l1___1(X₀-X₁, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₆: n_l4___15(X₀, X₁) → n_l1___14(X₀-X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₈₇: n_l4___5(X₀, X₁) → n_l1___4(X₀-X₁, X₁) :|: 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₄₁₃: n_l5___13(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₈: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₈₉: n_l5___13(X₀, X₁) → n_l2___12(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄₁₄: n_l5___17(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₉₀: n_l5___17(X₀, X₁) → n_l2___16(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₉₁: n_l5___17(X₀, X₁) → n_l2___16(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₁₆: n_l5___8(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₉₄: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₃₉₅: n_l5___8(X₀, X₁) → n_l2___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:22⋅X₀+30⋅X₁+28 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃₇₂: 2⋅X₁ {O(n)}
t₃₇₃: 1 {O(1)}
t₃₇₄: 1 {O(1)}
t₃₇₆: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₇₇: 1 {O(1)}
t₃₇₈: 2⋅X₀+2⋅X₁+1 {O(n)}
t₃₇₉: 1 {O(1)}
t₃₈₁: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₈₂: 1 {O(1)}
t₃₈₃: 1 {O(1)}
t₃₈₄: 4⋅X₀+4⋅X₁+1 {O(n)}
t₃₈₅: 2⋅X₁ {O(n)}
t₃₈₆: 1 {O(1)}
t₃₈₇: 1 {O(1)}
t₃₈₈: 2⋅X₁ {O(n)}
t₃₈₉: 2⋅X₁ {O(n)}
t₃₉₀: 1 {O(1)}
t₃₉₁: 1 {O(1)}
t₃₉₄: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₉₅: 4⋅X₀+4⋅X₁+2 {O(n)}
t₄₀₉: 1 {O(1)}
t₄₁₁: 1 {O(1)}
t₄₁₃: 1 {O(1)}
t₄₁₄: 1 {O(1)}
t₄₁₆: 1 {O(1)}

Costbounds

Overall costbound: 22⋅X₀+30⋅X₁+28 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃₇₂: 2⋅X₁ {O(n)}
t₃₇₃: 1 {O(1)}
t₃₇₄: 1 {O(1)}
t₃₇₆: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₇₇: 1 {O(1)}
t₃₇₈: 2⋅X₀+2⋅X₁+1 {O(n)}
t₃₇₉: 1 {O(1)}
t₃₈₁: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₈₂: 1 {O(1)}
t₃₈₃: 1 {O(1)}
t₃₈₄: 4⋅X₀+4⋅X₁+1 {O(n)}
t₃₈₅: 2⋅X₁ {O(n)}
t₃₈₆: 1 {O(1)}
t₃₈₇: 1 {O(1)}
t₃₈₈: 2⋅X₁ {O(n)}
t₃₈₉: 2⋅X₁ {O(n)}
t₃₉₀: 1 {O(1)}
t₃₉₁: 1 {O(1)}
t₃₉₄: 4⋅X₀+4⋅X₁+2 {O(n)}
t₃₉₅: 4⋅X₀+4⋅X₁+2 {O(n)}
t₄₀₉: 1 {O(1)}
t₄₁₁: 1 {O(1)}
t₄₁₃: 1 {O(1)}
t₄₁₄: 1 {O(1)}
t₄₁₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁₁, X₀: 15⋅X₁+4⋅X₀+2 {O(n)}
t₁₁, X₁: 2⋅X₀ {O(n)}
t₃₇₂, X₀: 2⋅X₁ {O(n)}
t₃₇₂, X₁: 2⋅X₀ {O(n)}
t₃₇₃, X₀: 2⋅X₁ {O(n)}
t₃₇₃, X₁: 2⋅X₀ {O(n)}
t₃₇₄, X₀: X₁ {O(n)}
t₃₇₄, X₁: X₀ {O(n)}
t₃₇₆, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₃₇₆, X₁: 4⋅X₀ {O(n)}
t₃₇₇, X₀: 4⋅X₁ {O(n)}
t₃₇₇, X₁: 4⋅X₀ {O(n)}
t₃₇₈, X₀: 2⋅X₁ {O(n)}
t₃₇₈, X₁: 2⋅X₀ {O(n)}
t₃₇₉, X₀: 2⋅X₁ {O(n)}
t₃₇₉, X₁: 2⋅X₀ {O(n)}
t₃₈₁, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₃₈₁, X₁: 4⋅X₀ {O(n)}
t₃₈₂, X₀: 16⋅X₁+8⋅X₀+4 {O(n)}
t₃₈₂, X₁: 8⋅X₀ {O(n)}
t₃₈₃, X₀: 4⋅X₁+1 {O(n)}
t₃₈₃, X₁: 4⋅X₀ {O(n)}
t₃₈₄, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₃₈₄, X₁: 4⋅X₀ {O(n)}
t₃₈₅, X₀: 2⋅X₁ {O(n)}
t₃₈₅, X₁: 2⋅X₀ {O(n)}
t₃₈₆, X₀: 2⋅X₁ {O(n)}
t₃₈₆, X₁: 2⋅X₀ {O(n)}
t₃₈₇, X₀: 0 {O(1)}
t₃₈₇, X₁: 8⋅X₀ {O(n)}
t₃₈₈, X₀: 2⋅X₁ {O(n)}
t₃₈₈, X₁: 2⋅X₀ {O(n)}
t₃₈₉, X₀: 2⋅X₁ {O(n)}
t₃₈₉, X₁: 2⋅X₀ {O(n)}
t₃₉₀, X₀: X₁ {O(n)}
t₃₉₀, X₁: X₀ {O(n)}
t₃₉₁, X₀: X₁ {O(n)}
t₃₉₁, X₁: X₀ {O(n)}
t₃₉₄, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₃₉₄, X₁: 4⋅X₀ {O(n)}
t₃₉₅, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₃₉₅, X₁: 4⋅X₀ {O(n)}
t₄₀₉, X₀: 2⋅X₁ {O(n)}
t₄₀₉, X₁: 2⋅X₀ {O(n)}
t₄₁₁, X₀: 0 {O(1)}
t₄₁₁, X₁: 8⋅X₀ {O(n)}
t₄₁₃, X₀: 4⋅X₁ {O(n)}
t₄₁₃, X₁: 4⋅X₀ {O(n)}
t₄₁₄, X₀: X₁ {O(n)}
t₄₁₄, X₁: X₀ {O(n)}
t₄₁₆, X₀: 4⋅X₀+8⋅X₁+2 {O(n)}
t₄₁₆, X₁: 4⋅X₀ {O(n)}