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 ]

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 t₉₉: n_l1___4→l4

Cut unsatisfiable transition t₁₀₀: n_l1___6→l4

Cut unsatisfiable transition t₁₀₁: 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 t₇₁: 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 t₇₉: 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 t₈₇: 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 t₆₉: 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+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+1 ]
n_l5___7 [X₁-1 ]
n_l1___6 [X₁ ]
n_l6___10 [X₁ ]
n_l1___9 [X₁-1 ]

MPRF for transition t₇₂: 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 t₇₃: 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:

101⋅X₃+11615 {O(n)}

MPRF:

n_l3___12 [101⋅X₁+91-X₀ ]
n_l3___5 [101⋅X₁-X₀ ]
n_l3___8 [101⋅X₁-X₀-91 ]
n_l5___11 [101⋅X₁-X₀ ]
n_l1___13 [101⋅X₁+91-X₀ ]
n_l5___7 [101⋅X₁-X₀-91 ]
n_l1___6 [101⋅X₁-X₀ ]
n_l6___10 [101⋅X₁-X₀ ]
n_l1___9 [101⋅X₁-X₀-90 ]

MPRF for transition t₇₄: 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 t₇₅: 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+216 {O(n)}

MPRF:

n_l3___12 [X₁+103 ]
n_l3___5 [X₁+102 ]
n_l3___8 [X₁+101 ]
n_l5___11 [X₁+102 ]
n_l1___13 [X₁+103 ]
n_l5___7 [X₁+101 ]
n_l1___6 [X₁+102 ]
n_l6___10 [X₁+102 ]
n_l1___9 [X₁+101 ]

MPRF for transition t₈₀: 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 t₈₁: 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 t₈₂: 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 t₈₃: 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 t₈₆: 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 t₈₈: 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:

1058⋅X₃+140062 {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)
t₇₀: 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
t₉₈: n_l1___13(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₆₉: 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
t₇₁: 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
t₇₂: 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
t₇₃: 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
t₇₄: 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
t₇₅: 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
t₇₆: 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
t₇₇: 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
t₇₈: 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
t₇₉: 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
t₈₀: 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
t₈₁: 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
t₈₂: 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
t₈₃: 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
t₈₄: 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
t₈₅: 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
t₈₆: 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
t₈₇: 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
t₈₈: 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
t₈₉: 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:1058⋅X₃+140073 {O(n)}
t₁₈: 1 {O(1)}
t₇₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₆₉: X₃+114 {O(n)}
t₉₈: 1 {O(1)}
t₇₁: X₃+123 {O(n)}
t₇₂: 910⋅X₃+122213 {O(n)}
t₇₃: 101⋅X₃+11615 {O(n)}
t₇₄: X₃+114 {O(n)}
t₇₅: X₃+216 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: X₃+112 {O(n)}
t₈₀: X₃+114 {O(n)}
t₈₁: 9⋅X₃+1219 {O(n)}
t₈₂: 10⋅X₃+1332 {O(n)}
t₈₃: X₃+114 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 10⋅X₃+1332 {O(n)}
t₈₇: X₃+112 {O(n)}
t₈₈: 10⋅X₃+1332 {O(n)}
t₈₉: 1 {O(1)}

Costbounds

Overall costbound: 1058⋅X₃+140073 {O(n)}
t₁₈: 1 {O(1)}
t₇₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₆₉: X₃+114 {O(n)}
t₉₈: 1 {O(1)}
t₇₁: X₃+123 {O(n)}
t₇₂: 910⋅X₃+122213 {O(n)}
t₇₃: 101⋅X₃+11615 {O(n)}
t₇₄: X₃+114 {O(n)}
t₇₅: X₃+216 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: X₃+112 {O(n)}
t₈₀: X₃+114 {O(n)}
t₈₁: 9⋅X₃+1219 {O(n)}
t₈₂: 10⋅X₃+1332 {O(n)}
t₈₃: X₃+114 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 10⋅X₃+1332 {O(n)}
t₈₇: X₃+112 {O(n)}
t₈₈: 10⋅X₃+1332 {O(n)}
t₈₉: 1 {O(1)}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₇₀, X₀: X₃ {O(n)}
t₇₀, X₁: 1 {O(1)}
t₇₀, 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)}
t₆₉, X₀: 101 {O(1)}
t₆₉, X₁: 11⋅X₃+1446 {O(n)}
t₆₉, X₃: X₃ {O(n)}
t₉₈, X₀: X₃+101 {O(n)}
t₉₈, X₁: 0 {O(1)}
t₉₈, X₃: 2⋅X₃ {O(n)}
t₇₁, X₀: 12⋅X₃+1243 {O(n)}
t₇₁, X₁: X₃+114 {O(n)}
t₇₁, X₃: X₃ {O(n)}
t₇₂, X₀: 101 {O(1)}
t₇₂, X₁: 11⋅X₃+1446 {O(n)}
t₇₂, X₃: X₃ {O(n)}
t₇₃, X₀: 111 {O(1)}
t₇₃, X₁: 11⋅X₃+1446 {O(n)}
t₇₃, X₃: X₃ {O(n)}
t₇₄, X₀: 101 {O(1)}
t₇₄, X₁: 11⋅X₃+1446 {O(n)}
t₇₄, X₃: X₃ {O(n)}
t₇₅, X₀: 100 {O(1)}
t₇₅, X₁: 11⋅X₃+1446 {O(n)}
t₇₅, X₃: X₃ {O(n)}
t₇₆, X₀: X₃ {O(n)}
t₇₆, X₁: 1 {O(1)}
t₇₆, X₃: X₃ {O(n)}
t₇₇, X₀: X₃ {O(n)}
t₇₇, X₁: 1 {O(1)}
t₇₇, X₃: X₃ {O(n)}
t₇₈, X₀: 111 {O(1)}
t₇₈, X₁: X₃+114 {O(n)}
t₇₈, X₃: X₃ {O(n)}
t₇₉, X₀: 12⋅X₃+1243 {O(n)}
t₇₉, X₁: X₃+114 {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₈₀, X₀: 101 {O(1)}
t₈₀, X₁: 11⋅X₃+1446 {O(n)}
t₈₀, X₃: X₃ {O(n)}
t₈₁, X₀: 100 {O(1)}
t₈₁, X₁: 11⋅X₃+1446 {O(n)}
t₈₁, X₃: X₃ {O(n)}
t₈₂, X₀: 111 {O(1)}
t₈₂, X₁: 11⋅X₃+1446 {O(n)}
t₈₂, X₃: X₃ {O(n)}
t₈₃, X₀: 101 {O(1)}
t₈₃, X₁: 11⋅X₃+1446 {O(n)}
t₈₃, X₃: X₃ {O(n)}
t₈₄, X₀: X₃ {O(n)}
t₈₄, X₁: 0 {O(1)}
t₈₄, X₃: X₃ {O(n)}
t₈₅, X₀: 101 {O(1)}
t₈₅, X₁: X₃+114 {O(n)}
t₈₅, X₃: X₃ {O(n)}
t₈₆, X₀: 101 {O(1)}
t₈₆, X₁: 11⋅X₃+1446 {O(n)}
t₈₆, X₃: X₃ {O(n)}
t₈₇, X₀: 12⋅X₃+1243 {O(n)}
t₈₇, X₁: X₃+114 {O(n)}
t₈₇, X₃: X₃ {O(n)}
t₈₈, X₀: 111 {O(1)}
t₈₈, X₁: 11⋅X₃+1446 {O(n)}
t₈₈, X₃: X₃ {O(n)}
t₈₉, X₀: X₃+11 {O(n)}
t₈₉, X₁: 2 {O(1)}
t₈₉, X₃: X₃ {O(n)}