Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-1)
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁-1, X₁-1)
t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂
t₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₁: l5(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₀, 2⋅X₀)
t₂: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₁: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 ≤ X₀

Preprocessing

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

Found invariant 0 ≤ X₀ for location l6

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

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l4

Found invariant 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, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁-1, X₁-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₀, 2⋅X₀) :|: 0 ≤ X₀
t₂: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₁: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l3→l5

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___6

Found invariant 0 ≤ X₀ for location l6

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___11

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___4

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

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___5

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___12

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___2

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

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___10

Found invariant X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ for location n_l3___1

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___8

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

Cut unsatisfiable transition t₃₃₃: n_l3___5→l5

MPRF for transition t₃₀₄: n_l1___3(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₂+1 ]
n_l3___5 [X₂+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂+1 ]
n_l4___4 [X₁+1 ]
n_l2___2 [X₁ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₀₇: n_l2___2(X₀, X₁, X₂) → n_l3___1(X₀, X₁-1, X₁-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₂+1 ]
n_l3___5 [X₁+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₂+1 ]
n_l2___2 [X₂+1 ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₀₈: n_l2___6(X₀, X₁, X₂) → n_l3___5(X₀, X₁-1, X₁-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+1 {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___5 [X₁ ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₁ ]
n_l2___2 [X₂ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₀₉: n_l3___1(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₁+1 ]
n_l3___5 [X₁ ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₂ ]
n_l2___2 [X₂ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₁₁: n_l3___5(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+1 {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___5 [X₂+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₁ ]
n_l2___2 [X₁ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₁₆: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₂+1 ]
n_l3___5 [X₂+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₁+1 ]
n_l2___2 [X₁ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₁₇: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₂+1 ]
n_l3___5 [X₂+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₁+1 ]
n_l2___2 [X₁ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₁₈: n_l4___4(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+2 {O(n)}

MPRF:

n_l3___1 [X₂+1 ]
n_l3___5 [X₁+1 ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₂+1 ]
n_l2___2 [X₁ ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]

MPRF for transition t₃₂₁: n_l4___8(X₀, X₁, X₂) → n_l2___6(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

6⋅X₀+1 {O(n)}

MPRF:

n_l3___1 [X₂ ]
n_l3___5 [X₂ ]
n_l3___9 [X₁ ]
n_l1___3 [X₂ ]
n_l4___4 [X₁ ]
n_l2___2 [X₁-1 ]
n_l1___7 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁-1 ]

MPRF for transition t₃₀₅: n_l1___7(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}

MPRF:

n_l2___6 [X₁ ]
n_l3___1 [2⋅X₂-X₁ ]
n_l3___5 [X₂ ]
n_l3___9 [X₂+1 ]
n_l1___3 [X₂ ]
n_l4___4 [X₂ ]
n_l2___2 [X₁ ]
n_l4___8 [X₂+1 ]
n_l1___7 [X₂+1 ]

MPRF for transition t₃₁₂: n_l3___9(X₀, X₁, X₂) → n_l4___8(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

36⋅X₀⋅X₀+24⋅X₀+8 {O(n^2)}

MPRF:

n_l2___6 [X₁ ]
n_l3___1 [X₂+1 ]
n_l3___5 [X₂+1 ]
n_l3___9 [X₂+2 ]
n_l1___3 [X₂+1 ]
n_l4___4 [X₁+1 ]
n_l2___2 [X₁ ]
n_l4___8 [X₂+1 ]
n_l1___7 [X₂+1 ]

MPRF for transition t₃₁₉: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}

MPRF:

n_l2___6 [X₁ ]
n_l3___1 [2⋅X₂-X₁ ]
n_l3___5 [X₂ ]
n_l3___9 [X₂+1 ]
n_l1___3 [X₂ ]
n_l4___4 [X₂ ]
n_l2___2 [X₁ ]
n_l4___8 [X₂+1 ]
n_l1___7 [X₂ ]

MPRF for transition t₃₂₀: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}

MPRF:

n_l2___6 [X₁ ]
n_l3___1 [2⋅X₂-X₁ ]
n_l3___5 [X₂ ]
n_l3___9 [X₂+1 ]
n_l1___3 [X₂ ]
n_l4___4 [X₂ ]
n_l2___2 [X₁ ]
n_l4___8 [X₂+1 ]
n_l1___7 [X₂ ]

CFR: Improvement to new bound with the following program:

new bound:

144⋅X₀⋅X₀+162⋅X₀+47 {O(n^2)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: Arg0_P, Arg2_P
Locations: l0, l3, l5, l6, l7, l8, n_l1___11, n_l1___3, n_l1___7, n_l2___10, n_l2___2, n_l2___6, n_l3___1, n_l3___5, n_l3___9, n_l4___12, n_l4___4, n_l4___8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₃₁₀: l3(X₀, X₁, X₂) → n_l4___12(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₀, 2⋅X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₀
t₂: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₁: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 ≤ X₀
t₃₀₃: n_l1___11(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: 0 ≤ X₂ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₀₄: n_l1___3(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₀₅: n_l1___7(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₀₆: n_l2___10(X₀, X₁, X₂) → n_l3___1(X₀, X₁-1, X₁-1) :|: 0 ≤ X₂ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₀₇: n_l2___2(X₀, X₁, X₂) → n_l3___1(X₀, X₁-1, X₁-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₀₈: n_l2___6(X₀, X₁, X₂) → n_l3___5(X₀, X₁-1, X₁-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₃₂: n_l3___1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀
t₃₀₉: n_l3___1(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀
t₃₁₁: n_l3___5(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₃₄: n_l3___9(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₂: n_l3___9(X₀, X₁, X₂) → n_l4___8(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₃: n_l4___12(X₀, X₁, X₂) → n_l1___11(Arg0_P, X₁, Arg2_P) :|: 0 ≤ X₂ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₄: n_l4___12(X₀, X₁, X₂) → n_l1___11(Arg0_P, X₁, Arg2_P) :|: 0 ≤ X₂ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₅: n_l4___12(X₀, X₁, X₂) → n_l2___10(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 2⋅X₀ ≤ X₂ ∧ X₂ ≤ 2⋅X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₆: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₇: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₈: n_l4___4(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁₉: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₂₀: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₂₁: n_l4___8(X₀, X₁, X₂) → n_l2___6(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:144⋅X₀⋅X₀+162⋅X₀+60 {O(n^2)}
t₀: 1 {O(1)}
t₃₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃₀₃: 1 {O(1)}
t₃₀₄: 6⋅X₀+2 {O(n)}
t₃₀₅: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₀₆: 1 {O(1)}
t₃₀₇: 6⋅X₀+2 {O(n)}
t₃₀₈: 6⋅X₀+1 {O(n)}
t₃₀₉: 6⋅X₀+2 {O(n)}
t₃₃₂: 1 {O(1)}
t₃₁₁: 6⋅X₀+1 {O(n)}
t₃₁₂: 36⋅X₀⋅X₀+24⋅X₀+8 {O(n^2)}
t₃₃₄: 1 {O(1)}
t₃₁₃: 1 {O(1)}
t₃₁₄: 1 {O(1)}
t₃₁₅: 1 {O(1)}
t₃₁₆: 6⋅X₀+2 {O(n)}
t₃₁₇: 6⋅X₀+2 {O(n)}
t₃₁₈: 6⋅X₀+2 {O(n)}
t₃₁₉: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₂₀: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₂₁: 6⋅X₀+1 {O(n)}

Costbounds

Overall costbound: 144⋅X₀⋅X₀+162⋅X₀+60 {O(n^2)}
t₀: 1 {O(1)}
t₃₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃₀₃: 1 {O(1)}
t₃₀₄: 6⋅X₀+2 {O(n)}
t₃₀₅: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₀₆: 1 {O(1)}
t₃₀₇: 6⋅X₀+2 {O(n)}
t₃₀₈: 6⋅X₀+1 {O(n)}
t₃₀₉: 6⋅X₀+2 {O(n)}
t₃₃₂: 1 {O(1)}
t₃₁₁: 6⋅X₀+1 {O(n)}
t₃₁₂: 36⋅X₀⋅X₀+24⋅X₀+8 {O(n^2)}
t₃₃₄: 1 {O(1)}
t₃₁₃: 1 {O(1)}
t₃₁₄: 1 {O(1)}
t₃₁₅: 1 {O(1)}
t₃₁₆: 6⋅X₀+2 {O(n)}
t₃₁₇: 6⋅X₀+2 {O(n)}
t₃₁₈: 6⋅X₀+2 {O(n)}
t₃₁₉: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₂₀: 36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
t₃₂₁: 6⋅X₀+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃₁₀, X₀: X₀ {O(n)}
t₃₁₀, X₁: 2⋅X₀ {O(n)}
t₃₁₀, X₂: 2⋅X₀ {O(n)}
t₁₁, X₀: 3⋅X₀ {O(n)}
t₁₁, X₁: 24⋅X₀+X₁+7 {O(n)}
t₁₁, X₂: 72⋅X₀+X₂+37 {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: 2⋅X₀ {O(n)}
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)}
t₃₀₃, X₀: 2⋅X₀ {O(n)}
t₃₀₃, X₁: 4⋅X₀ {O(n)}
t₃₀₃, X₂: 4⋅X₀+2 {O(n)}
t₃₀₄, X₀: 3⋅X₀ {O(n)}
t₃₀₄, X₁: 6⋅X₀+2 {O(n)}
t₃₀₄, X₂: 28⋅X₀+14 {O(n)}
t₃₀₅, X₀: 3⋅X₀ {O(n)}
t₃₀₅, X₁: 6⋅X₀+2 {O(n)}
t₃₀₅, X₂: 32⋅X₀+17 {O(n)}
t₃₀₆, X₀: X₀ {O(n)}
t₃₀₆, X₁: 2⋅X₀+1 {O(n)}
t₃₀₆, X₂: 2⋅X₀+1 {O(n)}
t₃₀₇, X₀: 3⋅X₀ {O(n)}
t₃₀₇, X₁: 6⋅X₀+2 {O(n)}
t₃₀₇, X₂: 6⋅X₀+3 {O(n)}
t₃₀₈, X₀: 3⋅X₀ {O(n)}
t₃₀₈, X₁: 6⋅X₀+2 {O(n)}
t₃₀₈, X₂: 6⋅X₀+2 {O(n)}
t₃₀₉, X₀: 3⋅X₀ {O(n)}
t₃₀₉, X₁: 6⋅X₀+2 {O(n)}
t₃₀₉, X₂: 8⋅X₀+4 {O(n)}
t₃₃₂, X₀: 4⋅X₀ {O(n)}
t₃₃₂, X₁: 8⋅X₀+3 {O(n)}
t₃₃₂, X₂: 8⋅X₀+4 {O(n)}
t₃₁₁, X₀: 3⋅X₀ {O(n)}
t₃₁₁, X₁: 6⋅X₀+2 {O(n)}
t₃₁₁, X₂: 6⋅X₀+2 {O(n)}
t₃₁₂, X₀: 3⋅X₀ {O(n)}
t₃₁₂, X₁: 6⋅X₀+2 {O(n)}
t₃₁₂, X₂: 32⋅X₀+17 {O(n)}
t₃₃₄, X₀: 8⋅X₀ {O(n)}
t₃₃₄, X₁: 16⋅X₀+4 {O(n)}
t₃₃₄, X₂: 64⋅X₀+33 {O(n)}
t₃₁₃, X₀: X₀ {O(n)}
t₃₁₃, X₁: 2⋅X₀ {O(n)}
t₃₁₃, X₂: 2⋅X₀ {O(n)}
t₃₁₄, X₀: X₀ {O(n)}
t₃₁₄, X₁: 2⋅X₀ {O(n)}
t₃₁₄, X₂: 2⋅X₀ {O(n)}
t₃₁₅, X₀: X₀ {O(n)}
t₃₁₅, X₁: 2⋅X₀ {O(n)}
t₃₁₅, X₂: 2⋅X₀ {O(n)}
t₃₁₆, X₀: 3⋅X₀ {O(n)}
t₃₁₆, X₁: 6⋅X₀+2 {O(n)}
t₃₁₆, X₂: 14⋅X₀+6 {O(n)}
t₃₁₇, X₀: 3⋅X₀ {O(n)}
t₃₁₇, X₁: 6⋅X₀+2 {O(n)}
t₃₁₇, X₂: 14⋅X₀+6 {O(n)}
t₃₁₈, X₀: 3⋅X₀ {O(n)}
t₃₁₈, X₁: 6⋅X₀+2 {O(n)}
t₃₁₈, X₂: 14⋅X₀+6 {O(n)}
t₃₁₉, X₀: 3⋅X₀ {O(n)}
t₃₁₉, X₁: 6⋅X₀+2 {O(n)}
t₃₁₉, X₂: 32⋅X₀+17 {O(n)}
t₃₂₀, X₀: 3⋅X₀ {O(n)}
t₃₂₀, X₁: 6⋅X₀+2 {O(n)}
t₃₂₀, X₂: 32⋅X₀+17 {O(n)}
t₃₂₁, X₀: 3⋅X₀ {O(n)}
t₃₂₁, X₁: 6⋅X₀+2 {O(n)}
t₃₂₁, X₂: 32⋅X₀+17 {O(n)}