Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ < 0
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ 0 < X₂
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ < 0
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ 0 < X₂
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
t₁₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₂
t₁₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₅
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(2⋅X₅, 2⋅X₅, X₂, X₃, X₄, X₅, X₆)
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₅
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0
Preprocessing
Cut unsatisfiable transition t₁₀: l1→l4
Cut unsatisfiable transition t₁₁: l1→l4
Cut unsatisfiable transition t₁₃: l1→l4
Cut unsatisfiable transition t₁₄: l1→l4
Cut unsatisfiable transition t₁₅: l1→l4
Cut unsatisfiable transition t₁₆: l1→l4
Eliminate variables {X₃,X₄,X₆} that do not contribute to the problem
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₅ for location l5
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₅ for location l4
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₃₇: l0(X₀, X₁, X₂, X₅) → l7(X₀, X₁, X₂, X₅)
t₃₈: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: X₂ < 0 ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₃₉: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: 0 < X₂ ∧ 0 < X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₀: l1(X₀, X₁, X₂, X₅) → l4(X₁-1, X₁-1, X₂, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₁: l2(X₀, X₁, X₂, X₅) → l3(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₂: l3(X₀, X₁, X₂, X₅) → l1(X₀, X₁, nondef.0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₃: l4(X₀, X₁, X₂, X₅) → l2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅
t₄₄: l4(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₀ < X₅ ∧ 0 ≤ X₅
t₄₅: l5(X₀, X₁, X₂, X₅) → l4(2⋅X₅, 2⋅X₅, X₂, X₅) :|: 0 ≤ X₅
t₄₆: l6(X₀, X₁, X₂, X₅) → l8(X₀, X₁, X₂, X₅)
t₄₇: l7(X₀, X₁, X₂, X₅) → l5(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅
t₄₈: l7(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ < 0
MPRF for transition t₄₀: l1(X₀, X₁, X₂, X₅) → l4(X₁-1, X₁-1, X₂, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 2:
new bound:
32⋅X₅+1 {O(n)}
MPRF:
l3 [X₁ ; X₀ ]
l1 [X₁ ; X₀ ]
l4 [X₁ ; X₀ ]
l2 [X₁ ; X₀ ]
MPRF for transition t₃₈: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: X₂ < 0 ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
MPRF for transition t₃₉: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: 0 < X₂ ∧ 0 < X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
MPRF for transition t₄₁: l2(X₀, X₁, X₂, X₅) → l3(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+2 ]
l2 [X₀+2 ]
MPRF for transition t₄₂: l3(X₀, X₁, X₂, X₅) → l1(X₀, X₁, nondef.0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
MPRF:
l3 [X₀+2 ]
l1 [X₀+1 ]
l4 [X₀+2 ]
l2 [X₀+2 ]
MPRF for transition t₄₃: l4(X₀, X₁, X₂, X₅) → l2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ of depth 1:
new bound:
1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+2 ]
l2 [X₀+1 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₄₄: l4→l6
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l2___6
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___9
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l1___4
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l3___5
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___11
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___3
Found invariant 0 ≤ X₅ for location l5
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___2
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀ for location n_l4___8
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___1
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___10
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l4___7
MPRF for transition t₁₀₅: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₀+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₀₆: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₁+1 ]
n_l2___3 [X₁+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₀₇: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₁+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₁₅: n_l2___3(X₀, X₁, X₂, X₅) → n_l3___2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁ ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₁+1 ]
n_l2___3 [X₀+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₁₈: n_l3___2(X₀, X₁, X₂, X₅) → n_l1___1(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₁+1 ]
n_l2___3 [X₀+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₂₁: n_l4___7(X₀, X₁, X₂, X₅) → n_l2___3(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₀ ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₁ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₁₀₈: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
12⋅X₅+8 {O(n)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [2 ]
n_l3___2 [2 ]
n_l1___1 [2 ]
n_l3___5 [2 ]
n_l1___4 [2 ]
n_l4___8 [2 ]
n_l2___6 [2 ]
MPRF for transition t₁₀₉: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
348⋅X₅⋅X₅+342⋅X₅+78 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [2⋅X₀+1-X₁ ]
n_l3___2 [2⋅X₀+1-X₁ ]
n_l1___1 [X₁+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+1 ]
n_l2___6 [X₀+1 ]
MPRF for transition t₁₁₀: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+1 ]
n_l2___6 [X₀+1 ]
MPRF for transition t₁₁₆: n_l2___6(X₀, X₁, X₂, X₅) → n_l3___5(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [X₁+1-X₀ ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+2 ]
MPRF for transition t₁₁₉: n_l3___5(X₀, X₁, X₂, X₅) → n_l1___4(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₁+1 ]
n_l3___5 [X₀+2 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+2 ]
MPRF for transition t₁₂₂: n_l4___8(X₀, X₁, X₂, X₅) → n_l2___6(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:5440⋅X₅⋅X₅+788⋅X₅+33 {O(n^2)}
t₃₇: 1 {O(1)}
t₃₈: 1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
t₃₉: 1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
t₄₀: 32⋅X₅+1 {O(n)}
t₄₁: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₂: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₃: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
Costbounds
Overall costbound: 5440⋅X₅⋅X₅+788⋅X₅+33 {O(n^2)}
t₃₇: 1 {O(1)}
t₃₈: 1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
t₃₉: 1088⋅X₅⋅X₅+132⋅X₅+4 {O(n^2)}
t₄₀: 32⋅X₅+1 {O(n)}
t₄₁: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₂: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₃: 1088⋅X₅⋅X₅+164⋅X₅+6 {O(n^2)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
Sizebounds
t₃₇, X₀: X₀ {O(n)}
t₃₇, X₁: X₁ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₅: X₅ {O(n)}
t₃₈, X₀: 36⋅X₅+3 {O(n)}
t₃₈, X₁: 34⋅X₅+1 {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₉, X₀: 36⋅X₅+3 {O(n)}
t₃₉, X₁: 34⋅X₅+1 {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₄₀, X₀: 34⋅X₅+2 {O(n)}
t₄₀, X₁: 34⋅X₅+1 {O(n)}
t₄₀, X₂: 0 {O(1)}
t₄₀, X₅: X₅ {O(n)}
t₄₁, X₀: 36⋅X₅+3 {O(n)}
t₄₁, X₁: 34⋅X₅+1 {O(n)}
t₄₁, X₅: X₅ {O(n)}
t₄₂, X₀: 36⋅X₅+3 {O(n)}
t₄₂, X₁: 34⋅X₅+1 {O(n)}
t₄₂, X₅: X₅ {O(n)}
t₄₃, X₀: 36⋅X₅+3 {O(n)}
t₄₃, X₁: 34⋅X₅+1 {O(n)}
t₄₃, X₅: X₅ {O(n)}
t₄₄, X₀: 106⋅X₅+8 {O(n)}
t₄₄, X₁: 102⋅X₅+3 {O(n)}
t₄₄, X₅: 3⋅X₅ {O(n)}
t₄₅, X₀: 2⋅X₅ {O(n)}
t₄₅, X₁: 2⋅X₅ {O(n)}
t₄₅, X₂: X₂ {O(n)}
t₄₅, X₅: X₅ {O(n)}
t₄₆, X₀: 106⋅X₅+X₀+8 {O(n)}
t₄₆, X₁: 102⋅X₅+X₁+3 {O(n)}
t₄₆, X₅: 4⋅X₅ {O(n)}
t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₅: X₅ {O(n)}
t₄₈, X₀: X₀ {O(n)}
t₄₈, X₁: X₁ {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₈, X₅: X₅ {O(n)}