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

Analysing control-flow refined program

Cut unsatisfiable transition t₂: l1→l6

Cut unsatisfiable transition t₁₂₉: n_l1___14→l6

Cut unsatisfiable transition t₉₄: n_l1___4→n_l5___3

Cut unsatisfiable transition t₁₃₁: 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 t₉₁: n_l1___1(X₀, X₁) → n_l5___13(X₀, X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF:

n_l4___10 [X₀ ]
n_l1___1 [X₀+1 ]
n_l5___13 [X₀ ]
n_l2___12 [X₀ ]

MPRF for transition t₉₇: n_l2___12(X₀, X₁) → n_l4___10(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2⋅X₁+1 {O(n)}

MPRF:

n_l4___10 [X₀-1 ]
n_l1___1 [X₀+X₁-1 ]
n_l5___13 [X₀+X₁-1 ]
n_l2___12 [X₀ ]

MPRF for transition t₁₀₄: 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:

n_l4___10 [X₀+1-X₁ ]
n_l1___1 [X₀ ]
n_l5___13 [X₀ ]
n_l2___12 [X₀ ]

MPRF for transition t₁₀₇: 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:

n_l4___10 [X₀-1 ]
n_l1___1 [X₀+X₁-1 ]
n_l5___13 [X₀ ]
n_l2___12 [X₀-1 ]

MPRF for transition t₁₀₈: 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:

n_l4___10 [X₀-1 ]
n_l1___1 [X₀+X₁-1 ]
n_l5___13 [X₀ ]
n_l2___12 [X₀-1 ]

MPRF for transition t₉₅: n_l1___9(X₀, X₁) → n_l5___8(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+8⋅X₁+2 {O(n)}

MPRF:

n_l3___6 [X₁-X₀ ]
n_l1___9 [X₁+1-X₀ ]
n_l5___8 [X₁-X₀ ]
n_l2___7 [X₁-X₀ ]

MPRF for transition t₁₀₀: n_l2___7(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+8⋅X₁+2 {O(n)}

MPRF:

n_l3___6 [X₁-X₀ ]
n_l1___9 [X₁+1-X₀ ]
n_l5___8 [X₁+1-X₀ ]
n_l2___7 [X₁+1-X₀ ]

MPRF for transition t₁₀₃: n_l3___6(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

8⋅X₀+8⋅X₁+1 {O(n)}

MPRF:

n_l3___6 [X₁-X₀ ]
n_l1___9 [X₁-X₀ ]
n_l5___8 [X₁-X₀ ]
n_l2___7 [X₁-X₀ ]

MPRF for transition t₁₁₃: 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:

8⋅X₀+8⋅X₁+2 {O(n)}

MPRF:

n_l3___6 [X₁-X₀ ]
n_l1___9 [X₁+1-X₀ ]
n_l5___8 [X₁+1-X₀ ]
n_l2___7 [X₁-X₀ ]

MPRF for transition t₁₁₄: 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:

8⋅X₀+8⋅X₁+2 {O(n)}

MPRF:

n_l3___6 [X₁-X₀ ]
n_l1___9 [X₁+1-X₀ ]
n_l5___8 [X₁+1-X₀ ]
n_l2___7 [X₁-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

42⋅X₀+50⋅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)
t₉₃: l1(X₀, X₁) → n_l5___17(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 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
t₁₂₈: n_l1___1(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₉₁: n_l1___1(X₀, X₁) → n_l5___13(X₀, X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₉₂: n_l1___14(X₀, X₁) → n_l5___13(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₁₃₀: n_l1___4(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁
t₉₅: n_l1___9(X₀, X₁) → n_l5___8(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₉₆: n_l2___12(X₀, X₁) → n_l3___11(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₇: n_l2___12(X₀, X₁) → n_l4___10(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₈: n_l2___16(X₀, X₁) → n_l4___15(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀₀: n_l2___7(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₀₁: 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
t₁₀₂: 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
t₁₀₃: n_l3___6(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₀₄: 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
t₁₀₅: 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
t₁₀₆: 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
t₁₃₂: n_l5___13(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₇: 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
t₁₀₈: 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
t₁₃₃: 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
t₁₀₉: 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
t₁₁₀: 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
t₁₃₅: n_l5___8(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁₁₃: 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
t₁₁₄: 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:42⋅X₀+50⋅X₁+28 {O(n)}
t₀: 1 {O(1)}
t₉₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₉₁: 2⋅X₁ {O(n)}
t₁₂₈: 1 {O(1)}
t₉₂: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₉₅: 8⋅X₀+8⋅X₁+2 {O(n)}
t₉₆: 1 {O(1)}
t₉₇: 2⋅X₀+2⋅X₁+1 {O(n)}
t₉₈: 1 {O(1)}
t₁₀₀: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₀₃: 8⋅X₀+8⋅X₁+1 {O(n)}
t₁₀₄: 2⋅X₁ {O(n)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 2⋅X₁ {O(n)}
t₁₀₈: 2⋅X₁ {O(n)}
t₁₃₂: 1 {O(1)}
t₁₀₉: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₃₃: 1 {O(1)}
t₁₁₃: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₁₄: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₃₅: 1 {O(1)}

Costbounds

Overall costbound: 42⋅X₀+50⋅X₁+28 {O(n)}
t₀: 1 {O(1)}
t₉₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₉₁: 2⋅X₁ {O(n)}
t₁₂₈: 1 {O(1)}
t₉₂: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₉₅: 8⋅X₀+8⋅X₁+2 {O(n)}
t₉₆: 1 {O(1)}
t₉₇: 2⋅X₀+2⋅X₁+1 {O(n)}
t₉₈: 1 {O(1)}
t₁₀₀: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₀₃: 8⋅X₀+8⋅X₁+1 {O(n)}
t₁₀₄: 2⋅X₁ {O(n)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 2⋅X₁ {O(n)}
t₁₀₈: 2⋅X₁ {O(n)}
t₁₃₂: 1 {O(1)}
t₁₀₉: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₃₃: 1 {O(1)}
t₁₁₃: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₁₄: 8⋅X₀+8⋅X₁+2 {O(n)}
t₁₃₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₉₃, X₀: X₁ {O(n)}
t₉₃, X₁: X₀ {O(n)}
t₁₁, X₀: 27⋅X₁+8⋅X₀+2 {O(n)}
t₁₁, X₁: 2⋅X₀ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₉₁, X₀: 4⋅X₁ {O(n)}
t₉₁, X₁: 4⋅X₀ {O(n)}
t₁₂₈, X₀: 4⋅X₁ {O(n)}
t₁₂₈, X₁: 4⋅X₀ {O(n)}
t₉₂, X₀: 2⋅X₁ {O(n)}
t₉₂, X₁: 2⋅X₀ {O(n)}
t₁₃₀, X₀: 0 {O(1)}
t₁₃₀, X₁: 16⋅X₀ {O(n)}
t₉₅, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₉₅, X₁: 8⋅X₀ {O(n)}
t₉₆, X₀: 8⋅X₁ {O(n)}
t₉₆, X₁: 8⋅X₀ {O(n)}
t₉₇, X₀: 4⋅X₁ {O(n)}
t₉₇, X₁: 4⋅X₀ {O(n)}
t₉₈, X₀: 2⋅X₁ {O(n)}
t₉₈, X₁: 2⋅X₀ {O(n)}
t₁₀₀, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₁₀₀, X₁: 8⋅X₀ {O(n)}
t₁₀₁, X₀: 16⋅X₀+32⋅X₁+4 {O(n)}
t₁₀₁, X₁: 16⋅X₀ {O(n)}
t₁₀₂, X₀: 8⋅X₁+1 {O(n)}
t₁₀₂, X₁: 8⋅X₀ {O(n)}
t₁₀₃, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₁₀₃, X₁: 8⋅X₀ {O(n)}
t₁₀₄, X₀: 4⋅X₁ {O(n)}
t₁₀₄, X₁: 4⋅X₀ {O(n)}
t₁₀₅, X₀: 2⋅X₁ {O(n)}
t₁₀₅, X₁: 2⋅X₀ {O(n)}
t₁₀₆, X₀: 0 {O(1)}
t₁₀₆, X₁: 16⋅X₀ {O(n)}
t₁₀₇, X₀: 4⋅X₁ {O(n)}
t₁₀₇, X₁: 4⋅X₀ {O(n)}
t₁₀₈, X₀: 4⋅X₁ {O(n)}
t₁₀₈, X₁: 4⋅X₀ {O(n)}
t₁₃₂, X₀: 6⋅X₁ {O(n)}
t₁₃₂, X₁: 6⋅X₀ {O(n)}
t₁₀₉, X₀: X₁ {O(n)}
t₁₀₉, X₁: X₀ {O(n)}
t₁₁₀, X₀: X₁ {O(n)}
t₁₁₀, X₁: X₀ {O(n)}
t₁₃₃, X₀: X₁ {O(n)}
t₁₃₃, X₁: X₀ {O(n)}
t₁₁₃, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₁₁₃, X₁: 8⋅X₀ {O(n)}
t₁₁₄, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₁₁₄, X₁: 8⋅X₀ {O(n)}
t₁₃₅, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₁₃₅, X₁: 8⋅X₀ {O(n)}