Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E
t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂
t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1)
t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃)
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1)
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁: l8(X₀, X₁, X₂, X₃) → l6(1, X₁, X₂, X₃)
Preprocessing
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l6
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁: l8(X₀, X₁, X₂, X₃) → l6(1, X₁, X₂, X₃)
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀-1 ]
l1 [X₁-X₀ ]
l6 [X₁-X₀ ]
l5 [X₁-X₀ ]
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀-1 ]
l1 [X₁-X₀ ]
l6 [X₁-X₀ ]
l5 [X₁-X₀ ]
MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l1 [X₁-X₀ ]
l6 [X₁-X₀ ]
l5 [X₁-X₀ ]
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l2 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l1 [X₁-X₀ ]
l6 [X₁+1-X₀ ]
l5 [X₁+1-X₀ ]
MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₁-X₀-1 ]
l3 [X₁-X₀-1 ]
l4 [X₁-X₀-1 ]
l1 [X₁-X₀-1 ]
l6 [X₁-X₀ ]
l5 [X₁-X₀-1 ]
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+2 {O(n^2)}
MPRF:
l2 [X₃ ]
l3 [X₃ ]
l4 [X₃ ]
l6 [-1 ]
l5 [X₀ ]
l1 [X₃+1 ]
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+2 {O(n^2)}
MPRF:
l2 [X₃+1 ]
l3 [X₃ ]
l4 [X₃ ]
l6 [-1 ]
l5 [X₀ ]
l1 [X₃+1 ]
MPRF for transition t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+2 {O(n^2)}
MPRF:
l2 [X₃+1 ]
l3 [X₃+1 ]
l4 [X₃+1 ]
l6 [0 ]
l5 [X₀ ]
l1 [X₃+1 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₁₈₉: n_l1___10→l4
Eliminate variables {NoDet0,X₂} that do not contribute to the problem
Found invariant 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l6___3
Found invariant 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___1
Found invariant 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___4
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location l6
Found invariant 1+X₃ ≤ 0 ∧ 4+X₃ ≤ X₁ ∧ 3+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___11
Found invariant 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l2___5
Found invariant 1+X₃ ≤ 0 ∧ 3+X₃ ≤ X₁ ∧ 3+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l6___12
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___10
Found invariant 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___2
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___8
Found invariant 1+X₃ ≤ 0 ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___7
MPRF for transition t₂₁₇: l4(X₀, X₁, X₃) → n_l6___12(X₀+1, X₁, X₃) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ 0 ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ 0 ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀ ]
n_l2___5 [X₁-X₀ ]
n_l2___9 [X₁-X₀ ]
n_l3___4 [X₁-X₀ ]
n_l3___8 [X₀+X₁-2⋅X₃-2 ]
n_l1___6 [X₁-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₂: n_l1___10(X₀, X₁, X₃) → n_l2___9(X₀, X₁, X₃) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀-1 ]
n_l2___5 [X₁-X₀-1 ]
n_l2___9 [X₁-X₃-2 ]
n_l3___4 [X₁-X₀-1 ]
n_l3___8 [X₁-X₀-1 ]
n_l1___6 [X₁-X₀-1 ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₃-1 ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₄: n_l1___6(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₃+1 ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀-1 ]
n_l2___5 [X₁-X₀ ]
n_l2___9 [X₁-X₃-1 ]
n_l3___4 [X₁-X₀ ]
n_l3___8 [X₀+X₁-2⋅X₃-2 ]
n_l1___6 [X₁-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₆: n_l2___5(X₀, X₁, X₃) → n_l4___7(X₀, X₁, Arg3_P) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀ ]
n_l2___5 [X₁-X₀ ]
n_l2___9 [X₁-X₀ ]
n_l3___4 [X₁-X₀ ]
n_l3___8 [X₁-X₀ ]
n_l1___6 [X₁-X₀ ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁+1-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₇: n_l2___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, Arg3_P) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀-1 ]
n_l2___5 [X₁-X₀-1 ]
n_l2___9 [X₁-X₀ ]
n_l3___4 [X₁-X₀-1 ]
n_l3___8 [X₁-X₀-1 ]
n_l1___6 [X₁-X₀-1 ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₈: n_l2___9(X₀, X₁, X₃) → n_l4___7(X₀, X₁, Arg3_P) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l4 [X₁+1-X₀ ]
n_l2___5 [X₁+1-X₀ ]
n_l2___9 [X₁-X₃ ]
n_l3___4 [X₁+1-X₀ ]
n_l3___8 [X₁-X₃ ]
n_l1___6 [X₁+1-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l1___10 [X₁-X₃ ]
n_l6___12 [X₁+2-X₀ ]
n_l5___11 [X₁+1-X₀ ]
n_l6___3 [X₁+1-X₀ ]
n_l5___2 [X₁+1-X₀ ]
MPRF for transition t₂₃₀: n_l3___8(X₀, X₁, X₃) → n_l1___6(X₀, X₁, X₃-1) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁+X₃-X₀ ]
n_l2___5 [X₁-X₀-1 ]
n_l2___9 [X₁-X₀ ]
n_l3___4 [X₁-X₀-1 ]
n_l3___8 [X₁-X₃-1 ]
n_l1___6 [X₁-X₀-1 ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁+X₃+1-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₃₁: n_l4___7(X₀, X₁, X₃) → n_l6___3(X₀+1, X₁, X₃) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l4 [X₁-X₀-2⋅X₃-1 ]
n_l2___5 [X₁+1-X₀ ]
n_l2___9 [X₁-X₃ ]
n_l3___4 [X₁+1-X₀ ]
n_l3___8 [X₁-X₃ ]
n_l1___6 [X₁+1-X₀ ]
n_l4___7 [X₁+1-X₀ ]
n_l1___10 [X₁-X₃ ]
n_l6___12 [X₁-X₀-2⋅X₃ ]
n_l5___11 [X₁-X₀-2⋅X₃ ]
n_l6___3 [X₁+1-X₀ ]
n_l5___2 [X₁+1-X₀ ]
MPRF for transition t₂₃₃: n_l5___11(X₀, X₁, X₃) → n_l1___10(X₀, X₁, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ 0 ∧ 4+X₃ ≤ X₁ ∧ 3+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l4 [X₁-X₀-1 ]
n_l2___5 [X₁-X₀-1 ]
n_l2___9 [X₁-X₃-2 ]
n_l3___4 [X₁-X₀-1 ]
n_l3___8 [X₁-X₀-1 ]
n_l1___6 [X₁-X₀-1 ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₀-1 ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₃₄: n_l5___2(X₀, X₁, X₃) → n_l1___10(X₀, X₁, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l4 [X₁-X₀-1 ]
n_l2___5 [X₁-X₀-1 ]
n_l2___9 [X₁-X₀-1 ]
n_l3___4 [X₁-X₀-1 ]
n_l3___8 [X₁-X₃-2 ]
n_l1___6 [X₁-X₀-1 ]
n_l4___7 [X₁-X₀-1 ]
n_l1___10 [X₁-X₃-2 ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₃₅: n_l6___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ 0 ∧ 3+X₃ ≤ X₁ ∧ 3+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀ ]
n_l2___5 [X₁-X₀ ]
n_l2___9 [X₁-X₃-1 ]
n_l3___4 [X₁-X₀ ]
n_l3___8 [X₀+X₁-2⋅X₃-2 ]
n_l1___6 [X₁-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁+1-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₃₇: n_l6___3(X₀, X₁, X₃) → n_l5___2(X₀, X₁, X₃) :|: X₀ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l4 [X₁-X₀ ]
n_l2___5 [X₁-X₀ ]
n_l2___9 [X₁-X₃-1 ]
n_l3___4 [X₁-X₀ ]
n_l3___8 [X₁-X₃-1 ]
n_l1___6 [X₁-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l1___10 [X₁-X₀ ]
n_l6___12 [X₁-X₀ ]
n_l5___11 [X₁-X₀ ]
n_l6___3 [X₁+1-X₀ ]
n_l5___2 [X₁-X₀ ]
MPRF for transition t₂₂₃: n_l1___6(X₀, X₁, X₃) → n_l2___5(X₀, X₁, X₃) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 2+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
14⋅X₁⋅X₁+27⋅X₁+15 {O(n^2)}
MPRF:
n_l6___12 [2⋅X₀+X₁+4⋅X₃ ]
l4 [2⋅X₀+X₁-2 ]
n_l2___5 [2⋅X₀+X₁+X₃ ]
n_l2___9 [3⋅X₀+X₁ ]
n_l3___4 [2⋅X₀+X₁+X₃ ]
n_l3___8 [2⋅X₀+X₁+X₃ ]
n_l1___6 [2⋅X₀+X₁+X₃+1 ]
n_l4___7 [2⋅X₀+X₁ ]
n_l6___3 [2⋅X₀+X₁-2 ]
n_l5___11 [3⋅X₀+X₁ ]
n_l5___2 [3⋅X₀+X₁ ]
n_l1___10 [3⋅X₀+X₁ ]
MPRF for transition t₂₂₅: n_l2___5(X₀, X₁, X₃) → n_l3___4(X₀, X₁, Arg3_P) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
MPRF:
n_l6___12 [X₁-X₀ ]
l4 [X₁+X₃-X₀ ]
n_l2___5 [X₁+X₃-X₀ ]
n_l2___9 [X₁ ]
n_l3___4 [X₁+X₃-X₀-1 ]
n_l3___8 [X₁+X₃-X₀ ]
n_l1___6 [X₁+X₃-X₀ ]
n_l4___7 [X₁-X₀ ]
n_l6___3 [X₁-X₀ ]
n_l5___11 [X₁ ]
n_l5___2 [X₁ ]
n_l1___10 [X₁ ]
MPRF for transition t₂₂₉: n_l3___4(X₀, X₁, X₃) → n_l1___6(X₀, X₁, X₃-1) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 3+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₁⋅X₁+8⋅X₁+5 {O(n^2)}
MPRF:
n_l6___12 [X₃ ]
l4 [X₃ ]
n_l2___5 [X₃+1 ]
n_l2___9 [X₀ ]
n_l3___4 [X₃+1 ]
n_l3___8 [X₃ ]
n_l1___6 [X₃+1 ]
n_l4___7 [0 ]
n_l6___3 [0 ]
n_l5___11 [X₀ ]
n_l5___2 [X₀ ]
n_l1___10 [X₀ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:3⋅X₁⋅X₁+14⋅X₁+16 {O(n^2)}
t₀: 1 {O(1)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₇: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₈: X₁+1 {O(n)}
t₉: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₁₀: X₁+1 {O(n)}
t₄: X₁+2 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₁⋅X₁+14⋅X₁+16 {O(n^2)}
t₀: 1 {O(1)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₇: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₈: X₁+1 {O(n)}
t₉: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₁₀: X₁+1 {O(n)}
t₄: X₁+2 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₅, X₀: X₁+2 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₃: 1 {O(1)}
t₆, X₀: X₁+2 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₃: X₁+3 {O(n)}
t₇, X₀: X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₃: X₁+3 {O(n)}
t₈, X₀: X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₃: X₁+3 {O(n)}
t₉, X₀: X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₃: X₁+3 {O(n)}
t₁₀, X₀: X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₃: X₁+4 {O(n)}
t₄, X₀: X₁+2 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₃: X₁+2 {O(n)}
t₂, X₀: X₁+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₃: X₁+X₃+4 {O(n)}
t₃, X₀: X₁+3 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₃: X₁+X₃+4 {O(n)}
t₁₁, X₀: X₁+3 {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₃: X₁+X₃+4 {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}