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 t₅₂₃: n_l1___14→l6
Cut unsatisfiable transition t₄₈₈: n_l1___4→n_l5___3
Cut unsatisfiable transition t₅₂₅: 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 t₄₈₅: 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 t₄₉₁: 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 t₄₉₈: 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+1-X₁ ]
MPRF for transition t₅₀₁: 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 t₅₀₂: 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 t₄₈₉: 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 t₄₉₄: 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 t₄₉₇: 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 t₅₀₇: 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 t₅₀₈: 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)
t₄₈₇: 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
t₅₂₂: n_l1___1(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₄₈₅: 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
t₄₈₆: 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
t₅₂₄: n_l1___4(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁
t₄₈₉: 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
t₄₉₀: 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
t₄₉₁: 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
t₄₉₂: 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
t₄₉₄: 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
t₄₉₅: 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
t₄₉₆: 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
t₄₉₇: 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
t₄₉₈: 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
t₄₉₉: 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
t₅₀₀: 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
t₅₂₆: n_l5___13(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅₀₁: 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
t₅₀₂: 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
t₅₂₇: 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
t₅₀₃: 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
t₅₀₄: 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
t₅₂₉: n_l5___8(X₀, X₁) → l6(X₀, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₀₇: 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
t₅₀₈: 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)}
t₄₈₇: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₄₈₅: 2⋅X₁ {O(n)}
t₅₂₂: 1 {O(1)}
t₄₈₆: 1 {O(1)}
t₅₂₄: 1 {O(1)}
t₄₈₉: 8⋅X₀+8⋅X₁+2 {O(n)}
t₄₉₀: 1 {O(1)}
t₄₉₁: 2⋅X₀+2⋅X₁+1 {O(n)}
t₄₉₂: 1 {O(1)}
t₄₉₄: 8⋅X₀+8⋅X₁+2 {O(n)}
t₄₉₅: 1 {O(1)}
t₄₉₆: 1 {O(1)}
t₄₉₇: 8⋅X₀+8⋅X₁+1 {O(n)}
t₄₉₈: 2⋅X₁ {O(n)}
t₄₉₉: 1 {O(1)}
t₅₀₀: 1 {O(1)}
t₅₀₁: 2⋅X₁ {O(n)}
t₅₀₂: 2⋅X₁ {O(n)}
t₅₂₆: 1 {O(1)}
t₅₀₃: 1 {O(1)}
t₅₀₄: 1 {O(1)}
t₅₂₇: 1 {O(1)}
t₅₀₇: 8⋅X₀+8⋅X₁+2 {O(n)}
t₅₀₈: 8⋅X₀+8⋅X₁+2 {O(n)}
t₅₂₉: 1 {O(1)}
Costbounds
Overall costbound: 42⋅X₀+50⋅X₁+28 {O(n)}
t₀: 1 {O(1)}
t₄₈₇: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₄₈₅: 2⋅X₁ {O(n)}
t₅₂₂: 1 {O(1)}
t₄₈₆: 1 {O(1)}
t₅₂₄: 1 {O(1)}
t₄₈₉: 8⋅X₀+8⋅X₁+2 {O(n)}
t₄₉₀: 1 {O(1)}
t₄₉₁: 2⋅X₀+2⋅X₁+1 {O(n)}
t₄₉₂: 1 {O(1)}
t₄₉₄: 8⋅X₀+8⋅X₁+2 {O(n)}
t₄₉₅: 1 {O(1)}
t₄₉₆: 1 {O(1)}
t₄₉₇: 8⋅X₀+8⋅X₁+1 {O(n)}
t₄₉₈: 2⋅X₁ {O(n)}
t₄₉₉: 1 {O(1)}
t₅₀₀: 1 {O(1)}
t₅₀₁: 2⋅X₁ {O(n)}
t₅₀₂: 2⋅X₁ {O(n)}
t₅₂₆: 1 {O(1)}
t₅₀₃: 1 {O(1)}
t₅₀₄: 1 {O(1)}
t₅₂₇: 1 {O(1)}
t₅₀₇: 8⋅X₀+8⋅X₁+2 {O(n)}
t₅₀₈: 8⋅X₀+8⋅X₁+2 {O(n)}
t₅₂₉: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₄₈₇, X₀: X₁ {O(n)}
t₄₈₇, 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)}
t₄₈₅, X₀: 4⋅X₁ {O(n)}
t₄₈₅, X₁: 4⋅X₀ {O(n)}
t₅₂₂, X₀: 4⋅X₁ {O(n)}
t₅₂₂, X₁: 4⋅X₀ {O(n)}
t₄₈₆, X₀: 2⋅X₁ {O(n)}
t₄₈₆, X₁: 2⋅X₀ {O(n)}
t₅₂₄, X₀: 0 {O(1)}
t₅₂₄, X₁: 16⋅X₀ {O(n)}
t₄₈₉, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₄₈₉, X₁: 8⋅X₀ {O(n)}
t₄₉₀, X₀: 8⋅X₁ {O(n)}
t₄₉₀, X₁: 8⋅X₀ {O(n)}
t₄₉₁, X₀: 4⋅X₁ {O(n)}
t₄₉₁, X₁: 4⋅X₀ {O(n)}
t₄₉₂, X₀: 2⋅X₁ {O(n)}
t₄₉₂, X₁: 2⋅X₀ {O(n)}
t₄₉₄, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₄₉₄, X₁: 8⋅X₀ {O(n)}
t₄₉₅, X₀: 16⋅X₀+32⋅X₁+4 {O(n)}
t₄₉₅, X₁: 16⋅X₀ {O(n)}
t₄₉₆, X₀: 8⋅X₁+1 {O(n)}
t₄₉₆, X₁: 8⋅X₀ {O(n)}
t₄₉₇, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₄₉₇, X₁: 8⋅X₀ {O(n)}
t₄₉₈, X₀: 4⋅X₁ {O(n)}
t₄₉₈, X₁: 4⋅X₀ {O(n)}
t₄₉₉, X₀: 2⋅X₁ {O(n)}
t₄₉₉, X₁: 2⋅X₀ {O(n)}
t₅₀₀, X₀: 0 {O(1)}
t₅₀₀, X₁: 16⋅X₀ {O(n)}
t₅₀₁, X₀: 4⋅X₁ {O(n)}
t₅₀₁, X₁: 4⋅X₀ {O(n)}
t₅₀₂, X₀: 4⋅X₁ {O(n)}
t₅₀₂, X₁: 4⋅X₀ {O(n)}
t₅₂₆, X₀: 6⋅X₁ {O(n)}
t₅₂₆, X₁: 6⋅X₀ {O(n)}
t₅₀₃, X₀: X₁ {O(n)}
t₅₀₃, X₁: X₀ {O(n)}
t₅₀₄, X₀: X₁ {O(n)}
t₅₀₄, X₁: X₀ {O(n)}
t₅₂₇, X₀: X₁ {O(n)}
t₅₂₇, X₁: X₀ {O(n)}
t₅₀₇, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₅₀₇, X₁: 8⋅X₀ {O(n)}
t₅₀₈, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₅₀₈, X₁: 8⋅X₀ {O(n)}
t₅₂₉, X₀: 16⋅X₁+8⋅X₀+2 {O(n)}
t₅₂₉, X₁: 8⋅X₀ {O(n)}