Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₂: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: 0 ≤ X₁ ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l2(E, X₁, X₂, X₃) :|: X₃+1 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l2(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₁) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁
t₇: l2(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₀: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃

Preprocessing

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l2

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l1

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l4

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₂: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: 0 ≤ X₁ ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l2(E, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l2(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₁) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₇: l2(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₀: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l1→l3

Cut unsatisfiable transition t₁₃₁: n_l1___15→l3

Cut unsatisfiable transition t₈₈: n_l1___7→n_l2___5

Cut unreachable locations [n_l2___5; n_l4___1; n_l4___2] from the program graph

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁ for location n_l2___6

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l4___17

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l4___9

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l4___4

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l1___7

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l4___12

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___16

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location n_l2___18

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location n_l1___15

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l1

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location n_l1___14

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l2___10

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___8

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l3

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location n_l2___13

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___11

MPRF for transition t₈₆: n_l1___15(X₀, X₁, X₂, X₃) → n_l2___13(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ Arg3_P ≤ 1+Arg2_P ∧ 1+Arg1_P ≤ Arg3_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

n_l2___13 [X₂+1-X₃ ]
n_l4___11 [X₂+1-X₃ ]
n_l4___12 [X₂+1-X₃ ]
n_l1___15 [X₂+2-X₃ ]

MPRF for transition t₉₂: n_l2___13(X₀, X₁, X₂, X₃) → n_l4___11(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

n_l2___13 [X₂+2-X₃ ]
n_l4___11 [X₂+1-X₃ ]
n_l4___12 [X₂+1-X₃ ]
n_l1___15 [X₂+2-X₃ ]

MPRF for transition t₉₃: n_l2___13(X₀, X₁, X₂, X₃) → n_l4___12(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

n_l2___13 [X₂+2-X₃ ]
n_l4___11 [X₂+2-X₃ ]
n_l4___12 [X₂+1-X₃ ]
n_l1___15 [X₂+2-X₃ ]

MPRF for transition t₁₀₂: n_l4___11(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

n_l2___13 [X₂+2-X₃ ]
n_l4___11 [X₂+2-X₃ ]
n_l4___12 [X₂+1-X₃ ]
n_l1___15 [X₂+2-X₃ ]

MPRF for transition t₁₀₄: n_l4___12(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

2⋅X₁+4⋅X₂+4 {O(n)}

MPRF:

n_l2___13 [2⋅X₂-X₃ ]
n_l4___11 [2⋅X₂-X₃ ]
n_l4___12 [2⋅X₂-X₃ ]
n_l1___15 [2⋅X₂-X₃ ]

MPRF for transition t₈₉: n_l1___7(X₀, X₁, X₂, X₃) → n_l2___6(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+Arg3_P ≤ Arg1_P ∧ Arg1_P ≤ Arg2_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

12⋅X₂+4 {O(n)}

MPRF:

n_l2___6 [X₂-X₃ ]
n_l4___3 [X₂-X₃ ]
n_l4___4 [X₂-X₃ ]
n_l1___7 [X₂+1-X₃ ]

MPRF for transition t₉₈: n_l2___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁ of depth 1:

new bound:

12⋅X₂+2 {O(n)}

MPRF:

n_l2___6 [X₂-X₃ ]
n_l4___3 [X₂-X₃-1 ]
n_l4___4 [X₂-X₃ ]
n_l1___7 [X₂-X₃ ]

MPRF for transition t₉₉: n_l2___6(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁ of depth 1:

new bound:

12⋅X₂+2 {O(n)}

MPRF:

n_l2___6 [X₂-X₃ ]
n_l4___3 [X₂-X₃ ]
n_l4___4 [X₂-X₃-1 ]
n_l1___7 [X₂-X₃ ]

MPRF for transition t₁₁₀: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

12⋅X₂+4 {O(n)}

MPRF:

n_l2___6 [X₂+1-X₃ ]
n_l4___3 [X₂+1-X₃ ]
n_l4___4 [X₂-X₃ ]
n_l1___7 [X₂+1-X₃ ]

MPRF for transition t₁₁₁: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

12⋅X₁+2 {O(n)}

MPRF:

n_l2___6 [X₁-X₃ ]
n_l4___3 [X₁-X₃ ]
n_l4___4 [X₁-X₃ ]
n_l1___7 [X₁-X₃ ]

CFR: Improvement to new bound with the following program:

new bound:

22⋅X₁+60⋅X₂+50 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: Arg1_P, Arg2_P, Arg3_P, NoDet0
Locations: l0, l1, l3, n_l1___14, n_l1___15, n_l1___7, n_l2___10, n_l2___13, n_l2___18, n_l2___6, n_l4___11, n_l4___12, n_l4___16, n_l4___17, n_l4___3, n_l4___4, n_l4___8, n_l4___9
Transitions:
t₂: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: 0 ≤ X₁ ∧ X₁ ≤ X₂
t₈₇: l1(X₀, X₁, X₂, X₃) → n_l2___18(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ Arg3_P ≤ 1+Arg2_P ∧ 1+Arg1_P ≤ Arg3_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₀: n_l1___14(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₁) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₈₅: n_l1___14(X₀, X₁, X₂, X₃) → n_l2___10(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+Arg3_P ≤ Arg1_P ∧ Arg1_P ≤ Arg2_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₈₆: n_l1___15(X₀, X₁, X₂, X₃) → n_l2___13(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ Arg3_P ≤ 1+Arg2_P ∧ 1+Arg1_P ≤ Arg3_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₂: n_l1___7(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₁) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₈₉: n_l1___7(X₀, X₁, X₂, X₃) → n_l2___6(NoDet0, Arg1_P, Arg2_P, Arg3_P) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+Arg3_P ≤ Arg1_P ∧ Arg1_P ≤ Arg2_P ∧ 0 ≤ Arg1_P ∧ X₁ ≤ Arg1_P ∧ Arg1_P ≤ X₁ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₃₃: n_l2___10(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉₀: n_l2___10(X₀, X₁, X₂, X₃) → n_l4___8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉₁: n_l2___10(X₀, X₁, X₂, X₃) → n_l4___9(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₁₃₄: n_l2___13(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₂: n_l2___13(X₀, X₁, X₂, X₃) → n_l4___11(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₃: n_l2___13(X₀, X₁, X₂, X₃) → n_l4___12(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₅: n_l2___18(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₄: n_l2___18(X₀, X₁, X₂, X₃) → n_l4___16(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1 ≤ X₃ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₉₅: n_l2___18(X₀, X₁, X₂, X₃) → n_l4___17(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ 1 ≤ X₃ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₃₇: n_l2___6(X₀, X₁, X₂, X₃) → l3(0, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁
t₉₈: n_l2___6(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁
t₉₉: n_l2___6(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁
t₁₀₁: n_l4___11(X₀, X₁, X₂, X₃) → n_l1___14(X₀, X₁, X₂, 0) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂+1 ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₂: n_l4___11(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₃: n_l4___12(X₀, X₁, X₂, X₃) → n_l1___14(X₀, X₁, X₂, 0) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂+1 ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₀₄: n_l4___12(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₀₅: n_l4___16(X₀, X₁, X₂, X₃) → n_l1___14(X₀, X₁, X₂, 0) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂+1 ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₆: n_l4___16(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₇: n_l4___17(X₀, X₁, X₂, X₃) → n_l1___14(X₀, X₁, X₂, 0) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₃ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂+1 ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₀₈: n_l4___17(X₀, X₁, X₂, X₃) → n_l1___15(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₃ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₁₀: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁₁: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₁₂: n_l4___8(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁₃: n_l4___9(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₃+1) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0

All Bounds

Timebounds

Overall timebound:22⋅X₁+60⋅X₂+71 {O(n)}
t₂: 1 {O(1)}
t₈₇: 1 {O(1)}
t₈₅: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₈₆: 2⋅X₁+2⋅X₂+8 {O(n)}
t₈₉: 12⋅X₂+4 {O(n)}
t₁₃₂: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₁₃₃: 1 {O(1)}
t₉₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₉₃: 2⋅X₁+2⋅X₂+8 {O(n)}
t₁₃₄: 1 {O(1)}
t₉₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₁₃₅: 1 {O(1)}
t₉₈: 12⋅X₂+2 {O(n)}
t₉₉: 12⋅X₂+2 {O(n)}
t₁₃₇: 1 {O(1)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₁₀₃: 1 {O(1)}
t₁₀₄: 2⋅X₁+4⋅X₂+4 {O(n)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₁₁₀: 12⋅X₂+4 {O(n)}
t₁₁₁: 12⋅X₁+2 {O(n)}
t₁₁₂: 1 {O(1)}
t₁₁₃: 1 {O(1)}

Costbounds

Overall costbound: 22⋅X₁+60⋅X₂+71 {O(n)}
t₂: 1 {O(1)}
t₈₇: 1 {O(1)}
t₈₅: 1 {O(1)}
t₁₃₀: 1 {O(1)}
t₈₆: 2⋅X₁+2⋅X₂+8 {O(n)}
t₈₉: 12⋅X₂+4 {O(n)}
t₁₃₂: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₁₃₃: 1 {O(1)}
t₉₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₉₃: 2⋅X₁+2⋅X₂+8 {O(n)}
t₁₃₄: 1 {O(1)}
t₉₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₁₃₅: 1 {O(1)}
t₉₈: 12⋅X₂+2 {O(n)}
t₉₉: 12⋅X₂+2 {O(n)}
t₁₃₇: 1 {O(1)}
t₁₀₁: 1 {O(1)}
t₁₀₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₁₀₃: 1 {O(1)}
t₁₀₄: 2⋅X₁+4⋅X₂+4 {O(n)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₁₁₀: 12⋅X₂+4 {O(n)}
t₁₁₁: 12⋅X₁+2 {O(n)}
t₁₁₂: 1 {O(1)}
t₁₁₃: 1 {O(1)}

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₁+1 {O(n)}
t₈₇, X₁: X₁ {O(n)}
t₈₇, X₂: X₂ {O(n)}
t₈₇, X₃: X₁+1 {O(n)}
t₈₅, X₁: 6⋅X₁ {O(n)}
t₈₅, X₂: 6⋅X₂ {O(n)}
t₈₅, X₃: 0 {O(1)}
t₁₃₀, X₁: 0 {O(1)}
t₁₃₀, X₂: 6⋅X₂ {O(n)}
t₁₃₀, X₃: 0 {O(1)}
t₈₆, X₁: 2⋅X₁ {O(n)}
t₈₆, X₂: 2⋅X₂ {O(n)}
t₈₆, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₈₉, X₁: 12⋅X₁ {O(n)}
t₈₉, X₂: 12⋅X₂ {O(n)}
t₈₉, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₁₃₂, X₁: 36⋅X₁ {O(n)}
t₁₃₂, X₂: 36⋅X₂ {O(n)}
t₁₃₂, X₃: 36⋅X₁ {O(n)}
t₉₀, X₁: 6⋅X₁ {O(n)}
t₉₀, X₂: 6⋅X₂ {O(n)}
t₉₀, X₃: 0 {O(1)}
t₉₁, X₁: 6⋅X₁ {O(n)}
t₉₁, X₂: 6⋅X₂ {O(n)}
t₉₁, X₃: 0 {O(1)}
t₁₃₃, X₀: 0 {O(1)}
t₁₃₃, X₁: 6⋅X₁ {O(n)}
t₁₃₃, X₂: 6⋅X₂ {O(n)}
t₁₃₃, X₃: 0 {O(1)}
t₉₂, X₁: 2⋅X₁ {O(n)}
t₉₂, X₂: 2⋅X₂ {O(n)}
t₉₂, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₉₃, X₁: 2⋅X₁ {O(n)}
t₉₃, X₂: 2⋅X₂ {O(n)}
t₉₃, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₃₄, X₀: 0 {O(1)}
t₁₃₄, X₁: 2⋅X₁ {O(n)}
t₁₃₄, X₂: 2⋅X₂ {O(n)}
t₁₃₄, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₉₄, X₁: X₁ {O(n)}
t₉₄, X₂: X₂ {O(n)}
t₉₄, X₃: X₁+1 {O(n)}
t₉₅, X₁: X₁ {O(n)}
t₉₅, X₂: X₂ {O(n)}
t₉₅, X₃: X₁+1 {O(n)}
t₁₃₅, X₀: 0 {O(1)}
t₁₃₅, X₁: X₁ {O(n)}
t₁₃₅, X₂: X₂ {O(n)}
t₁₃₅, X₃: X₁+1 {O(n)}
t₉₈, X₁: 12⋅X₁ {O(n)}
t₉₈, X₂: 12⋅X₂ {O(n)}
t₉₈, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₉₉, X₁: 12⋅X₁ {O(n)}
t₉₉, X₂: 12⋅X₂ {O(n)}
t₉₉, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₁₃₇, X₀: 0 {O(1)}
t₁₃₇, X₁: 12⋅X₁ {O(n)}
t₁₃₇, X₂: 12⋅X₂ {O(n)}
t₁₃₇, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₁₀₁, X₁: 2⋅X₁ {O(n)}
t₁₀₁, X₂: 2⋅X₂ {O(n)}
t₁₀₁, X₃: 0 {O(1)}
t₁₀₂, X₁: 2⋅X₁ {O(n)}
t₁₀₂, X₂: 2⋅X₂ {O(n)}
t₁₀₂, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₀₃, X₁: 2⋅X₁ {O(n)}
t₁₀₃, X₂: 2⋅X₂ {O(n)}
t₁₀₃, X₃: 0 {O(1)}
t₁₀₄, X₁: 2⋅X₁ {O(n)}
t₁₀₄, X₂: 2⋅X₂ {O(n)}
t₁₀₄, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₀₅, X₁: X₁ {O(n)}
t₁₀₅, X₂: X₂ {O(n)}
t₁₀₅, X₃: 0 {O(1)}
t₁₀₆, X₁: X₁ {O(n)}
t₁₀₆, X₂: X₂ {O(n)}
t₁₀₆, X₃: X₁+2 {O(n)}
t₁₀₇, X₁: X₁ {O(n)}
t₁₀₇, X₂: X₂ {O(n)}
t₁₀₇, X₃: 0 {O(1)}
t₁₀₈, X₁: X₁ {O(n)}
t₁₀₈, X₂: X₂ {O(n)}
t₁₀₈, X₃: X₁+2 {O(n)}
t₁₁₀, X₁: 12⋅X₁ {O(n)}
t₁₁₀, X₂: 12⋅X₂ {O(n)}
t₁₁₀, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₁₁₁, X₁: 12⋅X₁ {O(n)}
t₁₁₁, X₂: 12⋅X₂ {O(n)}
t₁₁₁, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₁₁₂, X₁: 6⋅X₁ {O(n)}
t₁₁₂, X₂: 6⋅X₂ {O(n)}
t₁₁₂, X₃: 1 {O(1)}
t₁₁₃, X₁: 6⋅X₁ {O(n)}
t₁₁₃, X₂: 6⋅X₂ {O(n)}
t₁₁₃, X₃: 1 {O(1)}