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 t₅₁₃: n_l5___11→l2

Cut unsatisfiable transition t₄₈₉: 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 t₄₇₁: 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 t₄₇₂: 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 t₄₈₅: 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+5 {O(n)}

MPRF:

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

MPRF for transition t₄₈₇: 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 t₄₇₇: 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⋅X₁+2 {O(n)}

MPRF:

n_l3___2 [X₁-X₂-2 ]
n_l5___5 [X₁-X₂-1 ]
n_l1___4 [X₁-X₂-1 ]

MPRF for transition t₄₇₈: 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⋅X₁+2 {O(n)}

MPRF:

n_l3___2 [X₁-X₂-2 ]
n_l5___5 [X₁-X₂-1 ]
n_l1___4 [X₁-X₂-1 ]

MPRF for transition t₄₈₃: 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 t₄₉₀: 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+2 {O(n)}

MPRF:

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

CFR: Improvement to new bound with the following program:

new bound:

24⋅X₀+24⋅X₁+30 {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
t₄₈₈: 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
t₅₀₈: 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
t₄₇₁: 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
t₄₇₂: 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
t₅₀₉: 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
t₄₇₃: 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
t₄₇₄: 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
t₅₁₁: 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
t₄₇₇: 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
t₄₇₈: 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
t₅₁₂: 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
t₄₇₉: 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
t₄₈₀: 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
t₄₈₂: 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
t₄₈₃: 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
t₄₈₄: 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
t₄₈₅: 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
t₄₈₆: 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
t₄₈₇: 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
t₅₁₄: 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
t₄₉₀: 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
t₅₁₅: 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
t₄₉₁: 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:24⋅X₀+24⋅X₁+48 {O(n)}
t₀: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄₈₈: 1 {O(1)}
t₄₇₁: 2⋅X₀+2⋅X₁+6 {O(n)}
t₄₇₂: 2⋅X₀+2⋅X₁+6 {O(n)}
t₅₀₈: 1 {O(1)}
t₄₇₃: 1 {O(1)}
t₄₇₄: 1 {O(1)}
t₅₀₉: 1 {O(1)}
t₄₇₇: 8⋅X₁+2 {O(n)}
t₄₇₈: 8⋅X₁+2 {O(n)}
t₅₁₁: 1 {O(1)}
t₄₇₉: 1 {O(1)}
t₄₈₀: 1 {O(1)}
t₅₁₂: 1 {O(1)}
t₄₈₂: 1 {O(1)}
t₄₈₃: 8⋅X₀+1 {O(n)}
t₄₈₄: 1 {O(1)}
t₄₈₅: 2⋅X₀+2⋅X₁+5 {O(n)}
t₄₈₆: 1 {O(1)}
t₄₈₇: 2⋅X₀+2⋅X₁+6 {O(n)}
t₄₉₀: 8⋅X₀+2 {O(n)}
t₅₁₄: 1 {O(1)}
t₄₉₁: 1 {O(1)}
t₅₁₅: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₀+24⋅X₁+48 {O(n)}
t₀: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄₈₈: 1 {O(1)}
t₄₇₁: 2⋅X₀+2⋅X₁+6 {O(n)}
t₄₇₂: 2⋅X₀+2⋅X₁+6 {O(n)}
t₅₀₈: 1 {O(1)}
t₄₇₃: 1 {O(1)}
t₄₇₄: 1 {O(1)}
t₅₀₉: 1 {O(1)}
t₄₇₇: 8⋅X₁+2 {O(n)}
t₄₇₈: 8⋅X₁+2 {O(n)}
t₅₁₁: 1 {O(1)}
t₄₇₉: 1 {O(1)}
t₄₈₀: 1 {O(1)}
t₅₁₂: 1 {O(1)}
t₄₈₂: 1 {O(1)}
t₄₈₃: 8⋅X₀+1 {O(n)}
t₄₈₄: 1 {O(1)}
t₄₈₅: 2⋅X₀+2⋅X₁+5 {O(n)}
t₄₈₆: 1 {O(1)}
t₄₈₇: 2⋅X₀+2⋅X₁+6 {O(n)}
t₄₉₀: 8⋅X₀+2 {O(n)}
t₅₁₄: 1 {O(1)}
t₄₉₁: 1 {O(1)}
t₅₁₅: 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+15 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀+1 {O(n)}
t₄₈₈, X₀: X₀ {O(n)}
t₄₈₈, X₁: X₁ {O(n)}
t₄₈₈, X₂: X₀+1 {O(n)}
t₄₇₁, X₀: 2⋅X₀ {O(n)}
t₄₇₁, X₁: 2⋅X₁ {O(n)}
t₄₇₁, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₄₇₂, X₀: 2⋅X₀ {O(n)}
t₄₇₂, X₁: 2⋅X₁ {O(n)}
t₄₇₂, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₅₀₈, X₀: 2⋅X₀ {O(n)}
t₅₀₈, X₁: 2⋅X₁ {O(n)}
t₅₀₈, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₄₇₃, X₀: X₀ {O(n)}
t₄₇₃, X₁: X₁ {O(n)}
t₄₇₃, X₂: X₀+1 {O(n)}
t₄₇₄, X₀: X₀ {O(n)}
t₄₇₄, X₁: X₁ {O(n)}
t₄₇₄, X₂: X₀+1 {O(n)}
t₅₀₉, X₀: X₀ {O(n)}
t₅₀₉, X₁: X₁ {O(n)}
t₅₀₉, X₂: X₀+1 {O(n)}
t₄₇₇, X₀: 8⋅X₀ {O(n)}
t₄₇₇, X₁: 8⋅X₁ {O(n)}
t₄₇₇, X₂: 8⋅X₀+2 {O(n)}
t₄₇₈, X₀: 8⋅X₀ {O(n)}
t₄₇₈, X₁: 8⋅X₁ {O(n)}
t₄₇₈, X₂: 8⋅X₀+2 {O(n)}
t₅₁₁, X₀: 8⋅X₀ {O(n)}
t₅₁₁, X₁: 8⋅X₁ {O(n)}
t₅₁₁, X₂: 8⋅X₀+2 {O(n)}
t₄₇₉, X₀: 4⋅X₀ {O(n)}
t₄₇₉, X₁: 4⋅X₁ {O(n)}
t₄₇₉, X₂: 0 {O(1)}
t₄₈₀, X₀: 4⋅X₀ {O(n)}
t₄₈₀, X₁: 4⋅X₁ {O(n)}
t₄₈₀, X₂: 0 {O(1)}
t₅₁₂, X₀: 4⋅X₀ {O(n)}
t₅₁₂, X₁: 4⋅X₁ {O(n)}
t₅₁₂, X₂: 0 {O(1)}
t₄₈₂, X₀: 2⋅X₀ {O(n)}
t₄₈₂, X₁: 2⋅X₁ {O(n)}
t₄₈₂, X₂: 2⋅X₀+4 {O(n)}
t₄₈₃, X₀: 8⋅X₀ {O(n)}
t₄₈₃, X₁: 8⋅X₁ {O(n)}
t₄₈₃, X₂: 8⋅X₀+2 {O(n)}
t₄₈₄, X₀: 8⋅X₀ {O(n)}
t₄₈₄, X₁: 8⋅X₁ {O(n)}
t₄₈₄, X₂: 1 {O(1)}
t₄₈₅, X₀: 2⋅X₀ {O(n)}
t₄₈₅, X₁: 2⋅X₁ {O(n)}
t₄₈₅, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₄₈₆, X₀: 4⋅X₀ {O(n)}
t₄₈₆, X₁: 4⋅X₁ {O(n)}
t₄₈₆, X₂: 0 {O(1)}
t₄₈₇, X₀: 2⋅X₀ {O(n)}
t₄₈₇, X₁: 2⋅X₁ {O(n)}
t₄₈₇, X₂: 2⋅X₁+4⋅X₀+9 {O(n)}
t₄₉₀, X₀: 8⋅X₀ {O(n)}
t₄₉₀, X₁: 8⋅X₁ {O(n)}
t₄₉₀, X₂: 8⋅X₀+2 {O(n)}
t₅₁₄, X₀: 16⋅X₀ {O(n)}
t₅₁₄, X₁: 16⋅X₁ {O(n)}
t₅₁₄, X₂: 8⋅X₀+3 {O(n)}
t₄₉₁, X₀: 4⋅X₀ {O(n)}
t₄₉₁, X₁: 4⋅X₁ {O(n)}
t₄₉₁, X₂: 0 {O(1)}
t₅₁₅, X₀: 0 {O(1)}
t₅₁₅, X₁: 4⋅X₁ {O(n)}
t₅₁₅, X₂: 0 {O(1)}