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 < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, 1, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 100 < X₀
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 100
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-10, X₁-1, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀+11, X₁+1, X₂, X₃)

Preprocessing

Eliminate variables {X₂} that do not contribute to the problem

Found invariant 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location l6

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location l7

Found invariant 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location l5

Found invariant 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location l4

Found invariant 1 ≤ X₁ 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 < X₁ ∧ 0 ≤ X₁
t₂₀: l1(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₁: l2(X₀, X₁, X₃) → l1(X₃, 1, X₃)
t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₀ ∧ 1 ≤ X₁
t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₀ ≤ 100 ∧ 1 ≤ X₁
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₅: l5(X₀, X₁, X₃) → l1(X₀-10, X₁-1, X₃) :|: 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₂₆: l6(X₀, X₁, X₃) → l1(X₀+11, X₁+1, X₃) :|: 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100

MPRF for transition t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+101 {O(n)}

MPRF:

l3 [10⋅X₁+91-X₀ ]
l5 [10⋅X₁+91-X₀ ]
l6 [10⋅X₁+90-X₀ ]
l1 [10⋅X₁+91-X₀ ]

MPRF for transition t₂₆: l6(X₀, X₁, X₃) → l1(X₀+11, X₁+1, X₃) :|: 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₃+101 {O(n)}

MPRF:

l3 [10⋅X₁+91-X₀ ]
l5 [10⋅X₁+91-X₀ ]
l6 [10⋅X₁+91-X₀ ]
l1 [10⋅X₁+91-X₀ ]

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 X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location l6

Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l7

Found invariant 101 ≤ X₃ ∧ 102 ≤ X₁+X₃ ∧ 100+X₁ ≤ X₃ ∧ 202 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 100+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 0 ≤ X₁ for location l1

Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l4

Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location l3

MPRF for transition t₁₉: l1(X₀, X₁, X₃) → l3(X₀, X₁, X₃) :|: 0 < X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+204⋅X₃+10405 {O(n^2)}

MPRF:

l3 [X₁ ]
l6 [X₁ ]
l5 [X₁ ]
l1 [X₁+1 ]

MPRF for transition t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+294⋅X₃+19585 {O(n^2)}

MPRF:

l3 [X₁+91 ]
l6 [X₁+91 ]
l5 [X₁+90 ]
l1 [X₁+91 ]

MPRF for transition t₂₅: l5(X₀, X₁, X₃) → l1(X₀-10, X₁-1, X₃) :|: 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+294⋅X₃+19585 {O(n^2)}

MPRF:

l3 [X₁+91 ]
l6 [X₁+91 ]
l5 [X₁+91 ]
l1 [X₁+91 ]

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 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location n_l1___6

Found invariant X₃ ≤ 89 ∧ X₃ ≤ 87+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100 for location n_l6___1

Found invariant 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ for location n_l1___9

Found invariant 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location n_l5___11

Found invariant X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 for location n_l1___4

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ for location n_l6___10

Found invariant X₃ ≤ 100 ∧ X₃ ≤ 99+X₁ ∧ X₁+X₃ ≤ 101 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 200 ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location n_l6___14

Found invariant X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 for location n_l3___3

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location n_l3___5

Found invariant 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location n_l1___13

Found invariant X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 101 ≤ X₀ for location n_l5___2

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location n_l3___12

Found invariant X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location l7

Found invariant 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ for location n_l3___8

Found invariant X₃ ≤ X₀ ∧ 101 ≤ X₃ ∧ 102 ≤ X₁+X₃ ∧ 100+X₁ ≤ X₃ ∧ 202 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 100+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location n_l5___15

Found invariant 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ for location n_l5___7

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location l1

Found invariant X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location l4

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location n_l3___16

MPRF for transition t₁₀₄: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 of depth 1:

new bound:

X₃+123 {O(n)}

MPRF:

n_l3___3 [101-X₀ ]
n_l6___1 [101-X₀ ]
n_l1___4 [112-X₀ ]

MPRF for transition t₁₁₂: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 of depth 1:

new bound:

X₃+112 {O(n)}

MPRF:

n_l3___3 [101-X₀ ]
n_l6___1 [90-X₀ ]
n_l1___4 [101-X₀ ]

MPRF for transition t₁₂₀: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+11, X₁+1, X₃) :|: X₀ ≤ 100 ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ 89 ∧ X₃ ≤ 87+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₃+112 {O(n)}

MPRF:

n_l3___3 [101-X₀ ]
n_l6___1 [101-X₀ ]
n_l1___4 [101-X₀ ]

MPRF for transition t₁₀₂: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₃+115 {O(n)}

MPRF:

n_l3___12 [X₁+1 ]
n_l3___5 [X₁+1 ]
n_l3___8 [X₁ ]
n_l5___11 [X₁+1 ]
n_l1___13 [X₁+2 ]
n_l5___7 [X₁ ]
n_l1___6 [X₁+1 ]
n_l6___10 [X₁+1 ]
n_l1___9 [X₁ ]

MPRF for transition t₁₀₅: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

910⋅X₃+122213 {O(n)}

MPRF:

n_l3___12 [10⋅X₀+910⋅X₁ ]
n_l3___5 [910⋅X₁+9191-91⋅X₀ ]
n_l3___8 [910⋅X₁+9282-91⋅X₀ ]
n_l5___11 [10⋅X₀+910⋅X₁-1010 ]
n_l1___13 [10⋅X₀+910⋅X₁ ]
n_l5___7 [910⋅X₁+9282-91⋅X₀ ]
n_l1___6 [910⋅X₁+9282-91⋅X₀ ]
n_l6___10 [910⋅X₁+9191-91⋅X₀ ]
n_l1___9 [910⋅X₁+9282-91⋅X₀ ]

MPRF for transition t₁₀₆: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ of depth 1:

new bound:

10⋅X₃+1342 {O(n)}

MPRF:

n_l3___12 [10⋅X₁+101-X₀ ]
n_l3___5 [10⋅X₁+101-X₀ ]
n_l3___8 [10⋅X₁+101-X₀ ]
n_l5___11 [10⋅X₁+101-X₀ ]
n_l1___13 [10⋅X₁+101-X₀ ]
n_l5___7 [10⋅X₁+101-X₀ ]
n_l1___6 [10⋅X₁+101-X₀ ]
n_l6___10 [10⋅X₁+101-X₀ ]
n_l1___9 [10⋅X₁+102-X₀ ]

MPRF for transition t₁₀₇: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₃+114 {O(n)}

MPRF:

n_l3___12 [X₁ ]
n_l3___5 [X₁ ]
n_l3___8 [X₁-1 ]
n_l5___11 [X₁-1 ]
n_l1___13 [X₁ ]
n_l5___7 [X₁-1 ]
n_l1___6 [X₁ ]
n_l6___10 [X₁ ]
n_l1___9 [X₁-1 ]

MPRF for transition t₁₀₈: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₃+115 {O(n)}

MPRF:

n_l3___12 [X₁ ]
n_l3___5 [X₁-1 ]
n_l3___8 [X₁-2 ]
n_l5___11 [X₁-1 ]
n_l1___13 [X₁ ]
n_l5___7 [X₁-2 ]
n_l1___6 [X₁-1 ]
n_l6___10 [X₁-1 ]
n_l1___9 [X₁-2 ]

MPRF for transition t₁₁₃: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

X₃+114 {O(n)}

MPRF:

n_l3___12 [X₁ ]
n_l3___5 [X₁ ]
n_l3___8 [X₁-1 ]
n_l5___11 [X₁-1 ]
n_l1___13 [X₁ ]
n_l5___7 [X₁-1 ]
n_l1___6 [X₁ ]
n_l6___10 [X₁ ]
n_l1___9 [X₁-1 ]

MPRF for transition t₁₁₄: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

9⋅X₃+1219 {O(n)}

MPRF:

n_l3___12 [9⋅X₁ ]
n_l3___5 [9⋅X₁+92-X₀ ]
n_l3___8 [9⋅X₁+93-X₀ ]
n_l5___11 [9⋅X₁-9 ]
n_l1___13 [9⋅X₁ ]
n_l5___7 [9⋅X₁+93-X₀ ]
n_l1___6 [9⋅X₁+92-X₀ ]
n_l6___10 [9⋅X₁+91-X₀ ]
n_l1___9 [9⋅X₁+93-X₀ ]

MPRF for transition t₁₁₅: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₀ ≤ 111 ∧ 101 ≤ X₀ ∧ 2 ≤ X₁ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ of depth 1:

new bound:

10⋅X₃+1332 {O(n)}

MPRF:

n_l3___12 [10⋅X₁ ]
n_l3___5 [10⋅X₁+91-X₀ ]
n_l3___8 [10⋅X₁+92-X₀ ]
n_l5___11 [10⋅X₁-10 ]
n_l1___13 [10⋅X₁ ]
n_l5___7 [10⋅X₁+91-X₀ ]
n_l1___6 [10⋅X₁+91-X₀ ]
n_l6___10 [10⋅X₁+91-X₀ ]
n_l1___9 [10⋅X₁+92-X₀ ]

MPRF for transition t₁₁₆: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-10, X₁-1, X₃) :|: 1 ≤ X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

X₃+114 {O(n)}

MPRF:

n_l3___12 [X₁ ]
n_l3___5 [X₁ ]
n_l3___8 [X₁-1 ]
n_l5___11 [X₁ ]
n_l1___13 [X₁ ]
n_l5___7 [X₁-1 ]
n_l1___6 [X₁ ]
n_l6___10 [X₁ ]
n_l1___9 [X₁-1 ]

MPRF for transition t₁₁₉: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-10, X₁-1, X₃) :|: X₀ ≤ 111 ∧ 101 ≤ X₀ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ of depth 1:

new bound:

10⋅X₃+1332 {O(n)}

MPRF:

n_l3___12 [10⋅X₁ ]
n_l3___5 [10⋅X₁+91-X₀ ]
n_l3___8 [10⋅X₁+92-X₀ ]
n_l5___11 [10⋅X₁-10 ]
n_l1___13 [10⋅X₁ ]
n_l5___7 [10⋅X₁+92-X₀ ]
n_l1___6 [10⋅X₁+91-X₀ ]
n_l6___10 [10⋅X₁+91-X₀ ]
n_l1___9 [10⋅X₁+92-X₀ ]

MPRF for transition t₁₂₁: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+11, X₁+1, X₃) :|: X₀ ≤ 100 ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₃+1332 {O(n)}

MPRF:

n_l3___12 [10⋅X₁ ]
n_l3___5 [10⋅X₁+91-X₀ ]
n_l3___8 [10⋅X₁+91-X₀ ]
n_l5___11 [10⋅X₁-10 ]
n_l1___13 [10⋅X₁ ]
n_l5___7 [10⋅X₁+91-X₀ ]
n_l1___6 [10⋅X₁+91-X₀ ]
n_l6___10 [10⋅X₁+91-X₀ ]
n_l1___9 [10⋅X₁+91-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

967⋅X₃+129689 {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) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 < X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₂₁: l2(X₀, X₁, X₃) → l1(X₃, 1, X₃)
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₃₁: n_l1___13(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₀₂: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₀₄: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₀₅: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₀₆: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₀₇: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₀₈: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₀₉: n_l3___16(X₀, X₁, X₃) → n_l5___15(X₀, X₁, X₃) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁₁₀: n_l3___16(X₀, X₁, X₃) → n_l6___14(X₀, X₁, X₃) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁₁₁: n_l3___3(X₀, X₁, X₃) → n_l5___2(X₀, X₁, X₃) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₁₂: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₁₃: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₁₄: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₁₅: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₀ ≤ 111 ∧ 101 ≤ X₀ ∧ 2 ≤ X₁ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₁₆: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-10, X₁-1, X₃) :|: 1 ≤ X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₁₁₇: n_l5___15(X₀, X₁, X₃) → n_l1___13(X₀-10, X₁-1, X₃) :|: 100 < X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 101 ≤ X₃ ∧ 102 ≤ X₁+X₃ ∧ 100+X₁ ≤ X₃ ∧ 202 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ 100+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₁₁₈: n_l5___2(X₀, X₁, X₃) → n_l1___6(X₀-10, X₁-1, X₃) :|: X₀ ≤ 111 ∧ 100 < X₀ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ 100 ∧ X₃ ≤ 98+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 211 ∧ 2 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 101 ≤ X₀
t₁₁₉: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-10, X₁-1, X₃) :|: X₀ ≤ 111 ∧ 101 ≤ X₀ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₂₀: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+11, X₁+1, X₃) :|: X₀ ≤ 100 ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ 89 ∧ X₃ ≤ 87+X₁ ∧ 11+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100
t₁₂₁: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+11, X₁+1, X₃) :|: X₀ ≤ 100 ∧ 91 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀
t₁₂₂: n_l6___14(X₀, X₁, X₃) → n_l1___4(X₀+11, X₁+1, X₃) :|: X₀ ≤ 100 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₃ ≤ 100 ∧ X₃ ≤ 99+X₁ ∧ X₁+X₃ ≤ 101 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 200 ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100

All Bounds

Timebounds

Overall timebound:967⋅X₃+129700 {O(n)}
t₁₈: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₁₀₂: X₃+115 {O(n)}
t₁₃₁: 1 {O(1)}
t₁₀₄: X₃+123 {O(n)}
t₁₀₅: 910⋅X₃+122213 {O(n)}
t₁₀₆: 10⋅X₃+1342 {O(n)}
t₁₀₇: X₃+114 {O(n)}
t₁₀₈: X₃+115 {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: 10⋅X₃+1332 {O(n)}
t₁₁₆: X₃+114 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 1 {O(1)}
t₁₁₉: 10⋅X₃+1332 {O(n)}
t₁₂₀: X₃+112 {O(n)}
t₁₂₁: 10⋅X₃+1332 {O(n)}
t₁₂₂: 1 {O(1)}

Costbounds

Overall costbound: 967⋅X₃+129700 {O(n)}
t₁₈: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₁₀₂: X₃+115 {O(n)}
t₁₃₁: 1 {O(1)}
t₁₀₄: X₃+123 {O(n)}
t₁₀₅: 910⋅X₃+122213 {O(n)}
t₁₀₆: 10⋅X₃+1342 {O(n)}
t₁₀₇: X₃+114 {O(n)}
t₁₀₈: X₃+115 {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: 10⋅X₃+1332 {O(n)}
t₁₁₆: X₃+114 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 1 {O(1)}
t₁₁₉: 10⋅X₃+1332 {O(n)}
t₁₂₀: X₃+112 {O(n)}
t₁₂₁: 10⋅X₃+1332 {O(n)}
t₁₂₂: 1 {O(1)}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₀₃, X₀: X₃ {O(n)}
t₁₀₃, X₁: 1 {O(1)}
t₁₀₃, X₃: X₃ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₁: 1 {O(1)}
t₂₁, X₃: X₃ {O(n)}
t₂₄, X₀: X₃+101 {O(n)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₃: X₃ {O(n)}
t₁₀₂, X₀: 101 {O(1)}
t₁₀₂, X₁: 11⋅X₃+1446 {O(n)}
t₁₀₂, X₃: X₃ {O(n)}
t₁₃₁, X₀: X₃+101 {O(n)}
t₁₃₁, X₁: 0 {O(1)}
t₁₃₁, X₃: 2⋅X₃ {O(n)}
t₁₀₄, X₀: 12⋅X₃+1243 {O(n)}
t₁₀₄, X₁: X₃+114 {O(n)}
t₁₀₄, X₃: X₃ {O(n)}
t₁₀₅, X₀: 101 {O(1)}
t₁₀₅, X₁: 11⋅X₃+1446 {O(n)}
t₁₀₅, X₃: X₃ {O(n)}
t₁₀₆, X₀: 111 {O(1)}
t₁₀₆, X₁: 11⋅X₃+1446 {O(n)}
t₁₀₆, X₃: X₃ {O(n)}
t₁₀₇, X₀: 101 {O(1)}
t₁₀₇, X₁: 11⋅X₃+1446 {O(n)}
t₁₀₇, X₃: X₃ {O(n)}
t₁₀₈, X₀: 100 {O(1)}
t₁₀₈, X₁: 11⋅X₃+1446 {O(n)}
t₁₀₈, X₃: X₃ {O(n)}
t₁₀₉, X₀: X₃ {O(n)}
t₁₀₉, X₁: 1 {O(1)}
t₁₀₉, X₃: X₃ {O(n)}
t₁₁₀, X₀: X₃ {O(n)}
t₁₁₀, X₁: 1 {O(1)}
t₁₁₀, X₃: X₃ {O(n)}
t₁₁₁, X₀: 111 {O(1)}
t₁₁₁, X₁: X₃+114 {O(n)}
t₁₁₁, X₃: X₃ {O(n)}
t₁₁₂, X₀: 12⋅X₃+1243 {O(n)}
t₁₁₂, X₁: X₃+114 {O(n)}
t₁₁₂, X₃: X₃ {O(n)}
t₁₁₃, X₀: 101 {O(1)}
t₁₁₃, X₁: 11⋅X₃+1446 {O(n)}
t₁₁₃, X₃: X₃ {O(n)}
t₁₁₄, X₀: 100 {O(1)}
t₁₁₄, X₁: 11⋅X₃+1446 {O(n)}
t₁₁₄, X₃: X₃ {O(n)}
t₁₁₅, X₀: 111 {O(1)}
t₁₁₅, X₁: 11⋅X₃+1446 {O(n)}
t₁₁₅, X₃: X₃ {O(n)}
t₁₁₆, X₀: 101 {O(1)}
t₁₁₆, X₁: 11⋅X₃+1446 {O(n)}
t₁₁₆, X₃: X₃ {O(n)}
t₁₁₇, X₀: X₃ {O(n)}
t₁₁₇, X₁: 0 {O(1)}
t₁₁₇, X₃: X₃ {O(n)}
t₁₁₈, X₀: 101 {O(1)}
t₁₁₈, X₁: X₃+114 {O(n)}
t₁₁₈, X₃: X₃ {O(n)}
t₁₁₉, X₀: 101 {O(1)}
t₁₁₉, X₁: 11⋅X₃+1446 {O(n)}
t₁₁₉, X₃: X₃ {O(n)}
t₁₂₀, X₀: 12⋅X₃+1243 {O(n)}
t₁₂₀, X₁: X₃+114 {O(n)}
t₁₂₀, X₃: X₃ {O(n)}
t₁₂₁, X₀: 111 {O(1)}
t₁₂₁, X₁: 11⋅X₃+1446 {O(n)}
t₁₂₁, X₃: X₃ {O(n)}
t₁₂₂, X₀: X₃+11 {O(n)}
t₁₂₂, X₁: 2 {O(1)}
t₁₂₂, X₃: X₃ {O(n)}