Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(1, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 100 < X₁
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-10, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+11, X₂, X₃)
Preprocessing
Eliminate variables {X₂} that do not contribute to the problem
Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ for location l6
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₃) → l2(X₀, X₁, X₃)
t₁₉: l1(X₀, X₁, X₃) → l3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 0 ≤ X₀
t₂₀: l1(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁, X₃) → l1(1, X₃, X₃)
t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀
t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅: l5(X₀, X₁, X₃) → l1(X₀-1, X₁-10, X₃) :|: 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₆: l6(X₀, X₁, X₃) → l1(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀
MPRF for transition t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+101 {O(n)}
MPRF:
l3 [10⋅X₀+91-X₁ ]
l5 [10⋅X₀+91-X₁ ]
l6 [10⋅X₀+90-X₁ ]
l1 [10⋅X₀+91-X₁ ]
MPRF for transition t₂₆: l6(X₀, X₁, X₃) → l1(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+101 {O(n)}
MPRF:
l3 [10⋅X₀+91-X₁ ]
l5 [10⋅X₀+91-X₁ ]
l6 [10⋅X₀+91-X₁ ]
l1 [10⋅X₀+91-X₁ ]
Found invariant 1 ≤ 0 for location l6
Found invariant 1 ≤ 0 for location l7
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant X₁ ≤ X₃ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l6
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 102 ≤ X₀+X₃ ∧ 100+X₀ ≤ X₃ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l5
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l1
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l3
MPRF for transition t₁₉: l1(X₀, X₁, X₃) → l3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+204⋅X₃+10405 {O(n^2)}
MPRF:
l3 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
l1 [X₀+1 ]
MPRF for transition t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+294⋅X₃+19585 {O(n^2)}
MPRF:
l3 [X₀+91 ]
l6 [X₀+91 ]
l5 [X₀+90 ]
l1 [X₀+91 ]
MPRF for transition t₂₅: l5(X₀, X₁, X₃) → l1(X₀-1, X₁-10, X₃) :|: 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+203⋅X₃+10303 {O(n^2)}
MPRF:
l3 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
l1 [X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₂₀: l1→l4
Cut unsatisfiable transition t₁₃₂: n_l1___4→l4
Cut unsatisfiable transition t₁₃₃: n_l1___6→l4
Cut unsatisfiable transition t₁₃₄: n_l1___9→l4
Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀ for location n_l6___1
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___9
Found invariant 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___11
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___10
Found invariant X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 200 ∧ X₃ ≤ 99+X₀ ∧ X₀+X₃ ≤ 101 ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l6___14
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location n_l3___3
Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___5
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___13
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___2
Found invariant 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___12
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___8
Found invariant X₃ ≤ X₁ ∧ 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 102 ≤ X₀+X₃ ∧ 100+X₀ ≤ X₃ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___15
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___7
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___16
MPRF for transition t₁₀₄: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+123 {O(n)}
MPRF:
n_l3___3 [101-X₁ ]
n_l6___1 [101-X₁ ]
n_l1___4 [112-X₁ ]
MPRF for transition t₁₁₂: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+112 {O(n)}
MPRF:
n_l3___3 [101-X₁ ]
n_l6___1 [90-X₁ ]
n_l1___4 [101-X₁ ]
MPRF for transition t₁₂₀: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+112 {O(n)}
MPRF:
n_l3___3 [101-X₁ ]
n_l6___1 [101-X₁ ]
n_l1___4 [101-X₁ ]
MPRF for transition t₁₀₂: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀ ]
n_l1___13 [X₀+1 ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₁₀₅: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
10⋅X₃+1343 {O(n)}
MPRF:
n_l3___12 [10⋅X₀+101-X₁ ]
n_l3___5 [10⋅X₀+101-X₁ ]
n_l3___8 [10⋅X₀+102-X₁ ]
n_l5___11 [10⋅X₀+101-X₁ ]
n_l1___13 [10⋅X₀+101-X₁ ]
n_l5___7 [10⋅X₀+102-X₁ ]
n_l1___6 [10⋅X₀+102-X₁ ]
n_l6___10 [10⋅X₀+101-X₁ ]
n_l1___9 [10⋅X₀+102-X₁ ]
MPRF for transition t₁₀₆: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 101 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₃+1332 {O(n)}
MPRF:
n_l3___12 [10⋅X₀ ]
n_l3___5 [10⋅X₀+91-X₁ ]
n_l3___8 [10⋅X₀+91-X₁ ]
n_l5___11 [10⋅X₀-10 ]
n_l1___13 [10⋅X₀ ]
n_l5___7 [10⋅X₀+91-X₁ ]
n_l1___6 [10⋅X₀+91-X₁ ]
n_l6___10 [10⋅X₀+91-X₁ ]
n_l1___9 [10⋅X₀+92-X₁ ]
MPRF for transition t₁₀₇: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀-1 ]
n_l1___13 [X₀ ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₁₀₈: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀+1 ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀ ]
n_l1___13 [X₀+1 ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₁₁₃: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀-1 ]
n_l1___13 [X₀ ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₁₁₄: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
9⋅X₃+1219 {O(n)}
MPRF:
n_l3___12 [9⋅X₀ ]
n_l3___5 [9⋅X₀+92-X₁ ]
n_l3___8 [9⋅X₀+93-X₁ ]
n_l5___11 [9⋅X₀-9 ]
n_l1___13 [9⋅X₀ ]
n_l5___7 [9⋅X₀+93-X₁ ]
n_l1___6 [9⋅X₀+92-X₁ ]
n_l6___10 [9⋅X₀+91-X₁ ]
n_l1___9 [9⋅X₀+93-X₁ ]
MPRF for transition t₁₁₅: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
101⋅X₃+11615 {O(n)}
MPRF:
n_l3___12 [101⋅X₀-91 ]
n_l3___5 [101⋅X₀-X₁ ]
n_l3___8 [101⋅X₀-X₁-90 ]
n_l5___11 [101⋅X₀-101 ]
n_l1___13 [101⋅X₀ ]
n_l5___7 [101⋅X₀-X₁-91 ]
n_l1___6 [101⋅X₀-X₁ ]
n_l6___10 [101⋅X₀-X₁ ]
n_l1___9 [101⋅X₀-X₁-90 ]
MPRF for transition t₁₁₆: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀ ]
n_l1___13 [X₀ ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₁₁₉: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₃+1422 {O(n)}
MPRF:
n_l3___12 [10⋅X₀+181-X₁ ]
n_l3___5 [10⋅X₀+181-X₁ ]
n_l3___8 [10⋅X₀+182-X₁ ]
n_l5___11 [10⋅X₀+181-X₁ ]
n_l1___13 [10⋅X₀+181-X₁ ]
n_l5___7 [10⋅X₀+182-X₁ ]
n_l1___6 [10⋅X₀+181-X₁ ]
n_l6___10 [10⋅X₀+181-X₁ ]
n_l1___9 [10⋅X₀+182-X₁ ]
MPRF for transition t₁₂₁: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
910⋅X₃+121212 {O(n)}
MPRF:
n_l3___12 [910⋅X₀ ]
n_l3___5 [910⋅X₀+8281-91⋅X₁ ]
n_l3___8 [910⋅X₀+8281-91⋅X₁ ]
n_l5___11 [910⋅X₀-910 ]
n_l1___13 [910⋅X₀ ]
n_l5___7 [910⋅X₀+8281-91⋅X₁ ]
n_l1___6 [910⋅X₀+8281-91⋅X₁ ]
n_l6___10 [910⋅X₀+8281-91⋅X₁ ]
n_l1___9 [910⋅X₀+8281-91⋅X₁ ]
CFR: Improvement to new bound with the following program:
new bound:
1058⋅X₃+139060 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l7, n_l1___13, n_l1___4, n_l1___6, n_l1___9, n_l3___12, n_l3___16, n_l3___3, n_l3___5, n_l3___8, n_l5___11, n_l5___15, n_l5___2, n_l5___7, n_l6___1, n_l6___10, n_l6___14
Transitions:
t₁₈: l0(X₀, X₁, X₃) → l2(X₀, X₁, X₃)
t₁₀₃: l1(X₀, X₁, X₃) → n_l3___16(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₁: l2(X₀, X₁, X₃) → l1(1, X₃, X₃)
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₃₁: n_l1___13(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₂: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀₄: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₁₀₅: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₆: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 101 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀₇: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₈: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀₉: n_l3___16(X₀, X₁, X₃) → n_l5___15(X₀, X₁, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁₁₀: n_l3___16(X₀, X₁, X₃) → n_l6___14(X₀, X₁, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁₁₁: n_l3___3(X₀, X₁, X₃) → n_l5___2(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₁₁₂: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₁₁₃: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁₄: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁₅: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁₆: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁₇: n_l5___15(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₃ ≤ X₁ ∧ 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 102 ≤ X₀+X₃ ∧ 100+X₀ ≤ X₃ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁₁₈: n_l5___2(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 100 < X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₁₉: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₂₀: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀
t₁₂₁: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂₂: n_l6___14(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 200 ∧ X₃ ≤ 99+X₀ ∧ X₀+X₃ ≤ 101 ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:1058⋅X₃+139071 {O(n)}
t₁₈: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₁₀₂: X₃+114 {O(n)}
t₁₃₁: 1 {O(1)}
t₁₀₄: X₃+123 {O(n)}
t₁₀₅: 10⋅X₃+1343 {O(n)}
t₁₀₆: 10⋅X₃+1332 {O(n)}
t₁₀₇: X₃+114 {O(n)}
t₁₀₈: X₃+114 {O(n)}
t₁₀₉: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₁₁: 1 {O(1)}
t₁₁₂: X₃+112 {O(n)}
t₁₁₃: X₃+114 {O(n)}
t₁₁₄: 9⋅X₃+1219 {O(n)}
t₁₁₅: 101⋅X₃+11615 {O(n)}
t₁₁₆: X₃+114 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 1 {O(1)}
t₁₁₉: 10⋅X₃+1422 {O(n)}
t₁₂₀: X₃+112 {O(n)}
t₁₂₁: 910⋅X₃+121212 {O(n)}
t₁₂₂: 1 {O(1)}
Costbounds
Overall costbound: 1058⋅X₃+139071 {O(n)}
t₁₈: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₁₀₂: X₃+114 {O(n)}
t₁₃₁: 1 {O(1)}
t₁₀₄: X₃+123 {O(n)}
t₁₀₅: 10⋅X₃+1343 {O(n)}
t₁₀₆: 10⋅X₃+1332 {O(n)}
t₁₀₇: X₃+114 {O(n)}
t₁₀₈: X₃+114 {O(n)}
t₁₀₉: 1 {O(1)}
t₁₁₀: 1 {O(1)}
t₁₁₁: 1 {O(1)}
t₁₁₂: X₃+112 {O(n)}
t₁₁₃: X₃+114 {O(n)}
t₁₁₄: 9⋅X₃+1219 {O(n)}
t₁₁₅: 101⋅X₃+11615 {O(n)}
t₁₁₆: X₃+114 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 1 {O(1)}
t₁₁₉: 10⋅X₃+1422 {O(n)}
t₁₂₀: X₃+112 {O(n)}
t₁₂₁: 910⋅X₃+121212 {O(n)}
t₁₂₂: 1 {O(1)}
Sizebounds
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₀₃, X₀: 1 {O(1)}
t₁₀₃, X₁: X₃ {O(n)}
t₁₀₃, X₃: X₃ {O(n)}
t₂₁, X₀: 1 {O(1)}
t₂₁, X₁: X₃ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₄, X₀: 0 {O(1)}
t₂₄, X₁: X₃+101 {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₁₀₂, X₀: 911⋅X₃+121326 {O(n)}
t₁₀₂, X₁: 101 {O(1)}
t₁₀₂, X₃: X₃ {O(n)}
t₁₃₁, X₀: 0 {O(1)}
t₁₃₁, X₁: X₃+101 {O(n)}
t₁₃₁, X₃: 2⋅X₃ {O(n)}
t₁₀₄, X₀: X₃+114 {O(n)}
t₁₀₄, X₁: 12⋅X₃+1243 {O(n)}
t₁₀₄, X₃: X₃ {O(n)}
t₁₀₅, X₀: 911⋅X₃+121326 {O(n)}
t₁₀₅, X₁: 101 {O(1)}
t₁₀₅, X₃: X₃ {O(n)}
t₁₀₆, X₀: 911⋅X₃+121326 {O(n)}
t₁₀₆, X₁: 111 {O(1)}
t₁₀₆, X₃: X₃ {O(n)}
t₁₀₇, X₀: 911⋅X₃+121326 {O(n)}
t₁₀₇, X₁: 101 {O(1)}
t₁₀₇, X₃: X₃ {O(n)}
t₁₀₈, X₀: 911⋅X₃+121326 {O(n)}
t₁₀₈, X₁: 100 {O(1)}
t₁₀₈, X₃: X₃ {O(n)}
t₁₀₉, X₀: 1 {O(1)}
t₁₀₉, X₁: X₃ {O(n)}
t₁₀₉, X₃: X₃ {O(n)}
t₁₁₀, X₀: 1 {O(1)}
t₁₁₀, X₁: X₃ {O(n)}
t₁₁₀, X₃: X₃ {O(n)}
t₁₁₁, X₀: X₃+114 {O(n)}
t₁₁₁, X₁: 111 {O(1)}
t₁₁₁, X₃: X₃ {O(n)}
t₁₁₂, X₀: X₃+114 {O(n)}
t₁₁₂, X₁: 12⋅X₃+1243 {O(n)}
t₁₁₂, X₃: X₃ {O(n)}
t₁₁₃, X₀: 911⋅X₃+121326 {O(n)}
t₁₁₃, X₁: 101 {O(1)}
t₁₁₃, X₃: X₃ {O(n)}
t₁₁₄, X₀: 911⋅X₃+121326 {O(n)}
t₁₁₄, X₁: 100 {O(1)}
t₁₁₄, X₃: X₃ {O(n)}
t₁₁₅, X₀: 911⋅X₃+121326 {O(n)}
t₁₁₅, X₁: 111 {O(1)}
t₁₁₅, X₃: X₃ {O(n)}
t₁₁₆, X₀: 911⋅X₃+121326 {O(n)}
t₁₁₆, X₁: 101 {O(1)}
t₁₁₆, X₃: X₃ {O(n)}
t₁₁₇, X₀: 0 {O(1)}
t₁₁₇, X₁: X₃ {O(n)}
t₁₁₇, X₃: X₃ {O(n)}
t₁₁₈, X₀: X₃+114 {O(n)}
t₁₁₈, X₁: 101 {O(1)}
t₁₁₈, X₃: X₃ {O(n)}
t₁₁₉, X₀: 911⋅X₃+121326 {O(n)}
t₁₁₉, X₁: 101 {O(1)}
t₁₁₉, X₃: X₃ {O(n)}
t₁₂₀, X₀: X₃+114 {O(n)}
t₁₂₀, X₁: 12⋅X₃+1243 {O(n)}
t₁₂₀, X₃: X₃ {O(n)}
t₁₂₁, X₀: 911⋅X₃+121326 {O(n)}
t₁₂₁, X₁: 111 {O(1)}
t₁₂₁, X₃: X₃ {O(n)}
t₁₂₂, X₀: 2 {O(1)}
t₁₂₂, X₁: X₃+11 {O(n)}
t₁₂₂, X₃: X₃ {O(n)}