Initial Problem

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

Preprocessing

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

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

Analysing control-flow refined program

Cut unsatisfiable transition t₂: l5→l2

Cut unsatisfiable transition t₁₄₁: n_l5___11→l2

Cut unsatisfiable transition t₁₁₇: n_l5___5→n_l1___3

Cut unreachable locations [n_l1___3; n_l3___1] from the program graph

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l5___11

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___4

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___5

Found invariant X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___7

Found invariant X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___6

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___13

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l5___8

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___12

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___9

MPRF for transition t₉₉: n_l1___10(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

n_l3___9 [X₁+1-X₂ ]
n_l5___11 [X₁+2-X₂ ]
n_l1___10 [X₁+2-X₂ ]

MPRF for transition t₁₀₀: n_l1___10(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

n_l3___9 [X₁+1-X₂ ]
n_l5___11 [X₁+2-X₂ ]
n_l1___10 [X₁+2-X₂ ]

MPRF for transition t₁₁₃: n_l3___9(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

n_l3___9 [X₁+2-X₂ ]
n_l5___11 [X₁+2-X₂ ]
n_l1___10 [X₁+2-X₂ ]

MPRF for transition t₁₁₅: n_l5___11(X₀, X₁, X₂) → n_l1___10(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+6 {O(n)}

MPRF:

n_l3___9 [X₁+1-X₂ ]
n_l5___11 [X₁+2-X₂ ]
n_l1___10 [X₁+1-X₂ ]

MPRF for transition t₁₀₅: n_l1___4(X₀, X₁, X₂) → n_l3___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+1 {O(n)}

MPRF:

n_l3___2 [X₀-X₂-1 ]
n_l5___5 [X₀-X₂ ]
n_l1___4 [X₀-X₂ ]

MPRF for transition t₁₀₆: n_l1___4(X₀, X₁, X₂) → n_l3___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+1 {O(n)}

MPRF:

n_l3___2 [X₀-X₂-1 ]
n_l5___5 [X₀-X₂ ]
n_l1___4 [X₀-X₂ ]

MPRF for transition t₁₁₁: n_l3___2(X₀, X₁, X₂) → n_l5___5(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+1 {O(n)}

MPRF:

n_l3___2 [X₀-X₂ ]
n_l5___5 [X₀-X₂ ]
n_l1___4 [X₀-X₂ ]

MPRF for transition t₁₁₈: n_l5___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

8⋅X₀+1 {O(n)}

MPRF:

n_l3___2 [X₀-X₂-1 ]
n_l5___5 [X₀-X₂ ]
n_l1___4 [X₀-X₂-1 ]

CFR: Improvement to new bound with the following program:

new bound:

40⋅X₀+8⋅X₁+28 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2, l4, l5, l6, n_l1___10, n_l1___13, n_l1___4, n_l1___7, n_l3___12, n_l3___2, n_l3___6, n_l3___9, n_l5___11, n_l5___5, n_l5___8
Transitions:
t₀: l0(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₀: l2(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₀+1) :|: 0 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁₁₆: l5(X₀, X₁, X₂) → n_l1___13(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₃₆: n_l1___10(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉₉: n_l1___10(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀₀: n_l1___10(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₃₇: n_l1___13(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀₁: n_l1___13(X₀, X₁, X₂) → n_l3___12(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀₂: n_l1___13(X₀, X₁, X₂) → n_l3___12(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₃₉: n_l1___4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₀₅: n_l1___4(X₀, X₁, X₂) → n_l3___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₀₆: n_l1___4(X₀, X₁, X₂) → n_l3___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₄₀: n_l1___7(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀₇: n_l1___7(X₀, X₁, X₂) → n_l3___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀₈: n_l1___7(X₀, X₁, X₂) → n_l3___6(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁₀: n_l3___12(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂+1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁₁: n_l3___2(X₀, X₁, X₂) → n_l5___5(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₁₂: n_l3___6(X₀, X₁, X₂) → n_l5___5(X₀, X₁, X₂+1) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁₃: n_l3___9(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁₄: n_l3___9(X₀, X₁, X₂) → n_l5___8(X₀, X₁, 0) :|: X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁₅: n_l5___11(X₀, X₁, X₂) → n_l1___10(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₄₂: n_l5___5(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁₈: n_l5___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₄₃: n_l5___8(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁₉: n_l5___8(X₀, X₁, X₂) → n_l1___7(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:40⋅X₀+8⋅X₁+46 {O(n)}
t₀: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁₆: 1 {O(1)}
t₉₉: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₀₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₃₆: 1 {O(1)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₃₇: 1 {O(1)}
t₁₀₅: 8⋅X₀+1 {O(n)}
t₁₀₆: 8⋅X₀+1 {O(n)}
t₁₃₉: 1 {O(1)}
t₁₀₇: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₁₄₀: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₁₁: 8⋅X₀+1 {O(n)}
t₁₁₂: 1 {O(1)}
t₁₁₃: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁₄: 1 {O(1)}
t₁₁₅: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁₈: 8⋅X₀+1 {O(n)}
t₁₄₂: 1 {O(1)}
t₁₁₉: 1 {O(1)}
t₁₄₃: 1 {O(1)}

Costbounds

Overall costbound: 40⋅X₀+8⋅X₁+46 {O(n)}
t₀: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁₆: 1 {O(1)}
t₉₉: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₀₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₃₆: 1 {O(1)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₃₇: 1 {O(1)}
t₁₀₅: 8⋅X₀+1 {O(n)}
t₁₀₆: 8⋅X₀+1 {O(n)}
t₁₃₉: 1 {O(1)}
t₁₀₇: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₁₄₀: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₁₁: 8⋅X₀+1 {O(n)}
t₁₁₂: 1 {O(1)}
t₁₁₃: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁₄: 1 {O(1)}
t₁₁₅: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁₈: 8⋅X₀+1 {O(n)}
t₁₄₂: 1 {O(1)}
t₁₁₉: 1 {O(1)}
t₁₄₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁₀, X₀: 4⋅X₀ {O(n)}
t₁₀, X₁: 4⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+21⋅X₀+16 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀+1 {O(n)}
t₁₁₆, X₀: X₀ {O(n)}
t₁₁₆, X₁: X₁ {O(n)}
t₁₁₆, X₂: X₀+1 {O(n)}
t₉₉, X₀: 2⋅X₀ {O(n)}
t₉₉, X₁: 2⋅X₁ {O(n)}
t₉₉, X₂: 2⋅X₁+4⋅X₀+10 {O(n)}
t₁₀₀, X₀: 2⋅X₀ {O(n)}
t₁₀₀, X₁: 2⋅X₁ {O(n)}
t₁₀₀, X₂: 2⋅X₁+4⋅X₀+10 {O(n)}
t₁₃₆, X₀: 2⋅X₀ {O(n)}
t₁₃₆, X₁: 2⋅X₁ {O(n)}
t₁₃₆, X₂: 2⋅X₁+4⋅X₀+10 {O(n)}
t₁₀₁, X₀: X₀ {O(n)}
t₁₀₁, X₁: X₁ {O(n)}
t₁₀₁, X₂: X₀+1 {O(n)}
t₁₀₂, X₀: X₀ {O(n)}
t₁₀₂, X₁: X₁ {O(n)}
t₁₀₂, X₂: X₀+1 {O(n)}
t₁₃₇, X₀: X₀ {O(n)}
t₁₃₇, X₁: X₁ {O(n)}
t₁₃₇, X₂: X₀+1 {O(n)}
t₁₀₅, X₀: 8⋅X₀ {O(n)}
t₁₀₅, X₁: 8⋅X₁ {O(n)}
t₁₀₅, X₂: 8⋅X₀+2 {O(n)}
t₁₀₆, X₀: 8⋅X₀ {O(n)}
t₁₀₆, X₁: 8⋅X₁ {O(n)}
t₁₀₆, X₂: 8⋅X₀+2 {O(n)}
t₁₃₉, X₀: 8⋅X₀ {O(n)}
t₁₃₉, X₁: 8⋅X₁ {O(n)}
t₁₃₉, X₂: 8⋅X₀+2 {O(n)}
t₁₀₇, X₀: 4⋅X₀ {O(n)}
t₁₀₇, X₁: 4⋅X₁ {O(n)}
t₁₀₇, X₂: 0 {O(1)}
t₁₀₈, X₀: 4⋅X₀ {O(n)}
t₁₀₈, X₁: 4⋅X₁ {O(n)}
t₁₀₈, X₂: 0 {O(1)}
t₁₄₀, X₀: 4⋅X₀ {O(n)}
t₁₄₀, X₁: 4⋅X₁ {O(n)}
t₁₄₀, X₂: 0 {O(1)}
t₁₁₀, X₀: 2⋅X₀ {O(n)}
t₁₁₀, X₁: 2⋅X₁ {O(n)}
t₁₁₀, X₂: 2⋅X₀+4 {O(n)}
t₁₁₁, X₀: 8⋅X₀ {O(n)}
t₁₁₁, X₁: 8⋅X₁ {O(n)}
t₁₁₁, X₂: 8⋅X₀+2 {O(n)}
t₁₁₂, X₀: 8⋅X₀ {O(n)}
t₁₁₂, X₁: 8⋅X₁ {O(n)}
t₁₁₂, X₂: 1 {O(1)}
t₁₁₃, X₀: 2⋅X₀ {O(n)}
t₁₁₃, X₁: 2⋅X₁ {O(n)}
t₁₁₃, X₂: 2⋅X₁+4⋅X₀+10 {O(n)}
t₁₁₄, X₀: 4⋅X₀ {O(n)}
t₁₁₄, X₁: 4⋅X₁ {O(n)}
t₁₁₄, X₂: 0 {O(1)}
t₁₁₅, X₀: 2⋅X₀ {O(n)}
t₁₁₅, X₁: 2⋅X₁ {O(n)}
t₁₁₅, X₂: 2⋅X₁+4⋅X₀+10 {O(n)}
t₁₁₈, X₀: 8⋅X₀ {O(n)}
t₁₁₈, X₁: 8⋅X₁ {O(n)}
t₁₁₈, X₂: 8⋅X₀+2 {O(n)}
t₁₄₂, X₀: 16⋅X₀ {O(n)}
t₁₄₂, X₁: 16⋅X₁ {O(n)}
t₁₄₂, X₂: 8⋅X₀+3 {O(n)}
t₁₁₉, X₀: 4⋅X₀ {O(n)}
t₁₁₉, X₁: 4⋅X₁ {O(n)}
t₁₁₉, X₂: 0 {O(1)}
t₁₄₃, X₀: 0 {O(1)}
t₁₄₃, X₁: 4⋅X₁ {O(n)}
t₁₄₃, X₂: 0 {O(1)}