Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₁: l10(X₀, X₁, X₂) → l9(X₀, X₁+1, X₂+1)
t₁₂: l11(X₀, X₁, X₂) → l12(X₀, X₁, X₂) :|: 0 < X₂
t₁₃: l11(X₀, X₁, X₂) → l13(X₀, X₁, X₂) :|: X₂ ≤ 0
t₁₄: l12(X₀, X₁, X₂) → l9(X₀, X₁, X₂-1)
t₁₅: l13(X₀, X₁, X₂) → l14(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l8(X₀, X₁, X₂) → l9(X₀, 0, 0)
t₉: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₀
t₁₀: l9(X₀, X₁, X₂) → l11(X₀, X₁, X₂) :|: X₀ ≤ X₁

Preprocessing

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l12

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l13

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l9

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₁: l10(X₀, X₁, X₂) → l9(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l11(X₀, X₁, X₂) → l12(X₀, X₁, X₂) :|: 0 < X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₁₃: l11(X₀, X₁, X₂) → l13(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₁₄: l12(X₀, X₁, X₂) → l9(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₁₅: l13(X₀, X₁, X₂) → l14(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l8(X₀, X₁, X₂) → l9(X₀, 0, 0)
t₉: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₀: l9(X₀, X₁, X₂) → l11(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

MPRF for transition t₁₁: l10(X₀, X₁, X₂) → l9(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l12 [X₀-X₁ ]
l10 [X₀-X₁ ]
l9 [X₀-X₁ ]
l11 [X₀-X₁ ]

MPRF for transition t₉: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l12 [X₀-X₁ ]
l10 [X₀-X₁-1 ]
l9 [X₀-X₁ ]
l11 [X₀-X₁ ]

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l11

Found invariant 1 ≤ 0 for location l12

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l13

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l9

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l14

Found invariant 1 ≤ 0 for location l11

Found invariant 1 ≤ 0 for location l12

Found invariant 1 ≤ 0 for location l13

Found invariant 1 ≤ 0 for location l10

Found invariant 1 ≤ 0 for location l9

Found invariant 1 ≤ 0 for location l14

MPRF for transition t₁₂: l11(X₀, X₁, X₂) → l12(X₀, X₁, X₂) :|: 0 < X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀⋅X₀+2⋅X₀+1 {O(n^2)}

MPRF:

l10 [X₂+2 ]
l12 [X₂ ]
l9 [X₂+1 ]
l11 [X₂+1 ]

MPRF for transition t₁₄: l12(X₀, X₁, X₂) → l9(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀⋅X₀+X₀ {O(n^2)}

MPRF:

l10 [X₂+1 ]
l12 [X₂ ]
l9 [X₂ ]
l11 [X₂ ]

MPRF for transition t₁₀: l9(X₀, X₁, X₂) → l11(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀⋅X₀+2⋅X₀+1 {O(n^2)}

MPRF:

l10 [X₂+2 ]
l12 [X₂ ]
l9 [X₂+1 ]
l11 [X₂ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃₇: n_l11___5→l13

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l11___2

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l11___5

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l9___3

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l11___6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l12___1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l13

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l9

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l12___4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l14

MPRF for transition t₁₂₄: n_l11___2(X₀, X₁, X₂) → n_l12___1(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l12___1 [X₂ ]
n_l9___3 [X₂+1 ]
n_l11___2 [X₂+1 ]

MPRF for transition t₁₂₆: n_l12___1(X₀, X₁, X₂) → n_l9___3(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

n_l12___1 [X₂ ]
n_l9___3 [X₂ ]
n_l11___2 [X₂ ]

MPRF for transition t₁₂₈: n_l9___3(X₀, X₁, X₂) → n_l11___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l12___1 [X₂ ]
n_l9___3 [X₂+1 ]
n_l11___2 [X₂ ]

CFR: Improvement to new bound with the following program:

new bound:

5⋅X₀+2 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9, n_l11___2, n_l11___5, n_l11___6, n_l12___1, n_l12___4, n_l9___3
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₁: l10(X₀, X₁, X₂) → l9(X₀, X₁+1, X₂+1) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₅: l13(X₀, X₁, X₂) → l14(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l8(X₀, X₁, X₂) → l9(X₀, 0, 0)
t₉: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₂₉: l9(X₀, X₁, X₂) → n_l11___5(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₀: l9(X₀, X₁, X₂) → n_l11___6(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₆: n_l11___2(X₀, X₁, X₂) → l13(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₂₄: n_l11___2(X₀, X₁, X₂) → n_l12___1(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₂₅: n_l11___5(X₀, X₁, X₂) → n_l12___4(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₃₈: n_l11___6(X₀, X₁, X₂) → l13(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₂₆: n_l12___1(X₀, X₁, X₂) → n_l9___3(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₂₇: n_l12___4(X₀, X₁, X₂) → n_l9___3(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₂₈: n_l9___3(X₀, X₁, X₂) → n_l11___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:5⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₂₉: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₁₂₄: X₀+1 {O(n)}
t₁₃₆: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₃₈: 1 {O(1)}
t₁₂₆: X₀ {O(n)}
t₁₂₇: 1 {O(1)}
t₁₂₈: X₀+1 {O(n)}

Costbounds

Overall costbound: 5⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₂₉: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₁₂₄: X₀+1 {O(n)}
t₁₃₆: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₃₈: 1 {O(1)}
t₁₂₆: X₀ {O(n)}
t₁₂₇: 1 {O(1)}
t₁₂₈: X₀+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀ {O(n)}
t₁₁, X₂: X₀ {O(n)}
t₁₅, X₀: 2⋅X₀ {O(n)}
t₁₅, X₁: X₀ {O(n)}
t₁₅, X₂: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 0 {O(1)}
t₈, X₂: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀ {O(n)}
t₉, X₂: X₀ {O(n)}
t₁₂₉, X₀: X₀ {O(n)}
t₁₂₉, X₁: X₀ {O(n)}
t₁₂₉, X₂: X₀ {O(n)}
t₁₃₀, X₀: X₀ {O(n)}
t₁₃₀, X₁: 0 {O(1)}
t₁₃₀, X₂: 0 {O(1)}
t₁₂₄, X₀: X₀ {O(n)}
t₁₂₄, X₁: X₀ {O(n)}
t₁₂₄, X₂: X₀ {O(n)}
t₁₃₆, X₀: X₀ {O(n)}
t₁₃₆, X₁: X₀ {O(n)}
t₁₃₆, X₂: 0 {O(1)}
t₁₂₅, X₀: X₀ {O(n)}
t₁₂₅, X₁: X₀ {O(n)}
t₁₂₅, X₂: X₀ {O(n)}
t₁₃₈, X₀: X₀ {O(n)}
t₁₃₈, X₁: 0 {O(1)}
t₁₃₈, X₂: 0 {O(1)}
t₁₂₆, X₀: X₀ {O(n)}
t₁₂₆, X₁: X₀ {O(n)}
t₁₂₆, X₂: X₀ {O(n)}
t₁₂₇, X₀: X₀ {O(n)}
t₁₂₇, X₁: X₀ {O(n)}
t₁₂₇, X₂: X₀ {O(n)}
t₁₂₈, X₀: X₀ {O(n)}
t₁₂₈, X₁: X₀ {O(n)}
t₁₂₈, X₂: X₀ {O(n)}