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 t₄₉₁: n_l1___15→l3
Cut unsatisfiable transition t₄₄₈: 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 t₄₄₆: 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 t₄₅₂: 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 t₄₅₃: 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+1-X₃ ]
n_l4___12 [X₂+1-X₃ ]
n_l1___15 [X₂+2-X₃ ]
MPRF for transition t₄₆₂: 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 t₄₆₄: 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 t₄₄₉: 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⋅X₁+4 {O(n)}
MPRF:
n_l2___6 [X₁-X₃ ]
n_l4___3 [X₁-X₃ ]
n_l4___4 [X₁-X₃ ]
n_l1___7 [X₁+1-X₃ ]
MPRF for transition t₄₅₈: 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 t₄₅₉: 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 t₄₇₀: 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 t₄₇₁: 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:
34⋅X₁+48⋅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
t₄₄₇: 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
t₄₉₀: 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
t₄₄₅: 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
t₄₄₆: 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
t₄₉₂: 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
t₄₄₉: 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
t₄₉₃: 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
t₄₅₀: 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
t₄₅₁: 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
t₄₉₄: 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
t₄₅₂: 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
t₄₅₃: 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
t₄₉₅: 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
t₄₅₄: 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
t₄₅₅: 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
t₄₉₇: 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
t₄₅₈: 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
t₄₅₉: 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
t₄₆₁: 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
t₄₆₂: 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
t₄₆₃: 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
t₄₆₄: 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
t₄₆₅: 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
t₄₆₆: 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
t₄₆₇: 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
t₄₆₈: 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
t₄₇₀: 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
t₄₇₁: 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
t₄₇₂: 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
t₄₇₃: 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:34⋅X₁+48⋅X₂+71 {O(n)}
t₂: 1 {O(1)}
t₄₄₇: 1 {O(1)}
t₄₄₅: 1 {O(1)}
t₄₉₀: 1 {O(1)}
t₄₄₆: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₄₉: 12⋅X₁+4 {O(n)}
t₄₉₂: 1 {O(1)}
t₄₅₀: 1 {O(1)}
t₄₅₁: 1 {O(1)}
t₄₉₃: 1 {O(1)}
t₄₅₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₅₃: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₉₄: 1 {O(1)}
t₄₅₄: 1 {O(1)}
t₄₅₅: 1 {O(1)}
t₄₉₅: 1 {O(1)}
t₄₅₈: 12⋅X₂+2 {O(n)}
t₄₅₉: 12⋅X₂+2 {O(n)}
t₄₉₇: 1 {O(1)}
t₄₆₁: 1 {O(1)}
t₄₆₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₆₃: 1 {O(1)}
t₄₆₄: 2⋅X₁+4⋅X₂+4 {O(n)}
t₄₆₅: 1 {O(1)}
t₄₆₆: 1 {O(1)}
t₄₆₇: 1 {O(1)}
t₄₆₈: 1 {O(1)}
t₄₇₀: 12⋅X₂+4 {O(n)}
t₄₇₁: 12⋅X₁+2 {O(n)}
t₄₇₂: 1 {O(1)}
t₄₇₃: 1 {O(1)}
Costbounds
Overall costbound: 34⋅X₁+48⋅X₂+71 {O(n)}
t₂: 1 {O(1)}
t₄₄₇: 1 {O(1)}
t₄₄₅: 1 {O(1)}
t₄₉₀: 1 {O(1)}
t₄₄₆: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₄₉: 12⋅X₁+4 {O(n)}
t₄₉₂: 1 {O(1)}
t₄₅₀: 1 {O(1)}
t₄₅₁: 1 {O(1)}
t₄₉₃: 1 {O(1)}
t₄₅₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₅₃: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₉₄: 1 {O(1)}
t₄₅₄: 1 {O(1)}
t₄₅₅: 1 {O(1)}
t₄₉₅: 1 {O(1)}
t₄₅₈: 12⋅X₂+2 {O(n)}
t₄₅₉: 12⋅X₂+2 {O(n)}
t₄₉₇: 1 {O(1)}
t₄₆₁: 1 {O(1)}
t₄₆₂: 2⋅X₁+2⋅X₂+8 {O(n)}
t₄₆₃: 1 {O(1)}
t₄₆₄: 2⋅X₁+4⋅X₂+4 {O(n)}
t₄₆₅: 1 {O(1)}
t₄₆₆: 1 {O(1)}
t₄₆₇: 1 {O(1)}
t₄₆₈: 1 {O(1)}
t₄₇₀: 12⋅X₂+4 {O(n)}
t₄₇₁: 12⋅X₁+2 {O(n)}
t₄₇₂: 1 {O(1)}
t₄₇₃: 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)}
t₄₄₇, X₁: X₁ {O(n)}
t₄₄₇, X₂: X₂ {O(n)}
t₄₄₇, X₃: X₁+1 {O(n)}
t₄₄₅, X₁: 6⋅X₁ {O(n)}
t₄₄₅, X₂: 6⋅X₂ {O(n)}
t₄₄₅, X₃: 0 {O(1)}
t₄₉₀, X₁: 0 {O(1)}
t₄₉₀, X₂: 6⋅X₂ {O(n)}
t₄₉₀, X₃: 0 {O(1)}
t₄₄₆, X₁: 2⋅X₁ {O(n)}
t₄₄₆, X₂: 2⋅X₂ {O(n)}
t₄₄₆, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₄₉, X₁: 12⋅X₁ {O(n)}
t₄₄₉, X₂: 12⋅X₂ {O(n)}
t₄₄₉, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₉₂, X₁: 36⋅X₁ {O(n)}
t₄₉₂, X₂: 36⋅X₂ {O(n)}
t₄₉₂, X₃: 36⋅X₁ {O(n)}
t₄₅₀, X₁: 6⋅X₁ {O(n)}
t₄₅₀, X₂: 6⋅X₂ {O(n)}
t₄₅₀, X₃: 0 {O(1)}
t₄₅₁, X₁: 6⋅X₁ {O(n)}
t₄₅₁, X₂: 6⋅X₂ {O(n)}
t₄₅₁, X₃: 0 {O(1)}
t₄₉₃, X₀: 0 {O(1)}
t₄₉₃, X₁: 6⋅X₁ {O(n)}
t₄₉₃, X₂: 6⋅X₂ {O(n)}
t₄₉₃, X₃: 0 {O(1)}
t₄₅₂, X₁: 2⋅X₁ {O(n)}
t₄₅₂, X₂: 2⋅X₂ {O(n)}
t₄₅₂, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₅₃, X₁: 2⋅X₁ {O(n)}
t₄₅₃, X₂: 2⋅X₂ {O(n)}
t₄₅₃, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₉₄, X₀: 0 {O(1)}
t₄₉₄, X₁: 2⋅X₁ {O(n)}
t₄₉₄, X₂: 2⋅X₂ {O(n)}
t₄₉₄, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₅₄, X₁: X₁ {O(n)}
t₄₅₄, X₂: X₂ {O(n)}
t₄₅₄, X₃: X₁+1 {O(n)}
t₄₅₅, X₁: X₁ {O(n)}
t₄₅₅, X₂: X₂ {O(n)}
t₄₅₅, X₃: X₁+1 {O(n)}
t₄₉₅, X₀: 0 {O(1)}
t₄₉₅, X₁: X₁ {O(n)}
t₄₉₅, X₂: X₂ {O(n)}
t₄₉₅, X₃: X₁+1 {O(n)}
t₄₅₈, X₁: 12⋅X₁ {O(n)}
t₄₅₈, X₂: 12⋅X₂ {O(n)}
t₄₅₈, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₅₉, X₁: 12⋅X₁ {O(n)}
t₄₅₉, X₂: 12⋅X₂ {O(n)}
t₄₅₉, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₉₇, X₀: 0 {O(1)}
t₄₉₇, X₁: 12⋅X₁ {O(n)}
t₄₉₇, X₂: 12⋅X₂ {O(n)}
t₄₉₇, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₆₁, X₁: 2⋅X₁ {O(n)}
t₄₆₁, X₂: 2⋅X₂ {O(n)}
t₄₆₁, X₃: 0 {O(1)}
t₄₆₂, X₁: 2⋅X₁ {O(n)}
t₄₆₂, X₂: 2⋅X₂ {O(n)}
t₄₆₂, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₆₃, X₁: 2⋅X₁ {O(n)}
t₄₆₃, X₂: 2⋅X₂ {O(n)}
t₄₆₃, X₃: 0 {O(1)}
t₄₆₄, X₁: 2⋅X₁ {O(n)}
t₄₆₄, X₂: 2⋅X₂ {O(n)}
t₄₆₄, X₃: 6⋅X₁+6⋅X₂+16 {O(n)}
t₄₆₅, X₁: X₁ {O(n)}
t₄₆₅, X₂: X₂ {O(n)}
t₄₆₅, X₃: 0 {O(1)}
t₄₆₆, X₁: X₁ {O(n)}
t₄₆₆, X₂: X₂ {O(n)}
t₄₆₆, X₃: X₁+2 {O(n)}
t₄₆₇, X₁: X₁ {O(n)}
t₄₆₇, X₂: X₂ {O(n)}
t₄₆₇, X₃: 0 {O(1)}
t₄₆₈, X₁: X₁ {O(n)}
t₄₆₈, X₂: X₂ {O(n)}
t₄₆₈, X₃: X₁+2 {O(n)}
t₄₇₀, X₁: 12⋅X₁ {O(n)}
t₄₇₀, X₂: 12⋅X₂ {O(n)}
t₄₇₀, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₇₁, X₁: 12⋅X₁ {O(n)}
t₄₇₁, X₂: 12⋅X₂ {O(n)}
t₄₇₁, X₃: 12⋅X₁+12⋅X₂+8 {O(n)}
t₄₇₂, X₁: 6⋅X₁ {O(n)}
t₄₇₂, X₂: 6⋅X₂ {O(n)}
t₄₇₂, X₃: 1 {O(1)}
t₄₇₃, X₁: 6⋅X₁ {O(n)}
t₄₇₃, X₂: 6⋅X₂ {O(n)}
t₄₇₃, X₃: 1 {O(1)}