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, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₁ ∧ 0 ≤ X₁
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, 1, X₂)
t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 100 < X₀ ∧ 1 ≤ X₁
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₁
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₄: l5(X₀, X₁, X₂) → l1(X₀-10, X₁-1, X₂) :|: 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₂₅: l6(X₀, X₁, X₂) → l1(X₀+11, X₁+1, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100

MPRF for transition t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂+101 {O(n)}

MPRF for transition t₂₅: l6(X₀, X₁, X₂) → l1(X₀+11, X₁+1, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₂+101 {O(n)}

MPRF for transition t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+204⋅X₂+10405 {O(n^2)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 100 < X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+385⋅X₂+28867 {O(n^2)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂) → l1(X₀-10, X₁-1, X₂) :|: 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+294⋅X₂+19585 {O(n^2)}

Chain transitions t₂₅: l6→l1 and t₁₉: l1→l4 to t₅₈: l6→l4

Chain transitions t₂₄: l5→l1 and t₁₉: l1→l4 to t₅₉: l5→l4

Chain transitions t₂₄: l5→l1 and t₁₈: l1→l3 to t₆₀: l5→l3

Chain transitions t₂₅: l6→l1 and t₁₈: l1→l3 to t₆₁: l6→l3

Chain transitions t₂₀: l2→l1 and t₁₈: l1→l3 to t₆₂: l2→l3

Chain transitions t₂₀: l2→l1 and t₁₉: l1→l4 to t₆₃: l2→l4

Chain transitions t₆₁: l6→l3 and t₂₂: l3→l6 to t₆₄: l6→l6

Chain transitions t₆₀: l5→l3 and t₂₂: l3→l6 to t₆₅: l5→l6

Chain transitions t₆₀: l5→l3 and t₂₁: l3→l5 to t₆₆: l5→l5

Chain transitions t₆₁: l6→l3 and t₂₁: l3→l5 to t₆₇: l6→l5

Chain transitions t₆₂: l2→l3 and t₂₁: l3→l5 to t₆₈: l2→l5

Chain transitions t₆₂: l2→l3 and t₂₂: l3→l6 to t₆₉: l2→l6

Analysing control-flow refined program

Cut unsatisfiable transition t₅₈: l6→l4

Cut unsatisfiable transition t₆₃: l2→l4

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

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

Found invariant 1 ≤ X₁ for location l3

MPRF for transition t₆₄: l6(X₀, X₁, X₂) -{3}> l6(11+X₀, 1+X₁, X₂) :|: 0 < 1+X₁ ∧ X₀ ≤ 89 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

10⋅X₂+1091 {O(n)}

MPRF for transition t₆₅: l5(X₀, X₁, X₂) -{3}> l6(X₀-10, X₁-1, X₂) :|: 1 < X₁ ∧ X₀ ≤ 110 ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

X₂+100 {O(n)}

MPRF for transition t₆₇: l6(X₀, X₁, X₂) -{3}> l5(11+X₀, 1+X₁, X₂) :|: 0 < 1+X₁ ∧ 89 < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₂+111 {O(n)}

MPRF for transition t₆₆: l5(X₀, X₁, X₂) -{3}> l5(X₀-10, X₁-1, X₂) :|: 1 < X₁ ∧ 110 < X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

11⋅X₂⋅X₂+2426⋅X₂+133756 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₁₉: l1→l4

Cut unsatisfiable transition t₂₀₀: n_l1___4→l4

Cut unsatisfiable transition t₂₀₁: n_l1___6→l4

Cut unsatisfiable transition t₂₀₂: 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 X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 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 X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 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 X₂ ≤ 100 ∧ X₂ ≤ 99+X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 200 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location n_l6___14

Found invariant X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 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 X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 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 X₂ ≤ X₀ ∧ 101 ≤ X₂ ∧ 102 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 202 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 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 X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 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 X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location n_l3___16

MPRF for transition t₁₇₂: n_l1___4(X₀, X₁, X₂) → n_l3___3(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 of depth 1:

new bound:

X₂+123 {O(n)}

MPRF for transition t₁₈₀: n_l3___3(X₀, X₁, X₂) → n_l6___1(X₀, X₁, X₂) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 of depth 1:

new bound:

X₂+112 {O(n)}

MPRF for transition t₁₈₈: n_l6___1(X₀, X₁, X₂) → n_l1___4(X₀+11, X₁+1, X₂) :|: 2 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₂+112 {O(n)}

MPRF for transition t₁₇₀: n_l1___13(X₀, X₁, X₂) → n_l3___12(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₂+114 {O(n)}

MPRF for transition t₁₇₃: n_l1___6(X₀, X₁, X₂) → n_l3___5(X₀, X₁, X₂) :|: 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:

112⋅X₂+12971 {O(n)}

MPRF for transition t₁₇₄: n_l1___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ of depth 1:

new bound:

10⋅X₂+1352 {O(n)}

MPRF for transition t₁₇₅: n_l3___12(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₂+114 {O(n)}

MPRF for transition t₁₇₆: n_l3___12(X₀, X₁, X₂) → n_l6___10(X₀, X₁, X₂) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀ of depth 1:

new bound:

X₂+115 {O(n)}

MPRF for transition t₁₈₁: n_l3___5(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

X₂+114 {O(n)}

MPRF for transition t₁₈₂: n_l3___5(X₀, X₁, X₂) → n_l6___10(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ of depth 1:

new bound:

9⋅X₂+1219 {O(n)}

MPRF for transition t₁₈₃: n_l3___8(X₀, X₁, X₂) → n_l5___7(X₀, X₁, X₂) :|: 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⋅X₂+1332 {O(n)}

MPRF for transition t₁₈₄: n_l5___11(X₀, X₁, X₂) → n_l1___13(X₀-10, X₁-1, X₂) :|: 100 < X₀ ∧ 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ of depth 1:

new bound:

X₂+316 {O(n)}

MPRF for transition t₁₈₇: n_l5___7(X₀, X₁, X₂) → n_l1___6(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ of depth 1:

new bound:

10⋅X₂+1332 {O(n)}

MPRF for transition t₁₈₉: n_l6___10(X₀, X₁, X₂) → n_l1___9(X₀+11, X₁+1, X₂) :|: 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ of depth 1:

new bound:

10⋅X₂+1332 {O(n)}

CFR did not improve the program. Rolling back

CFR: Improvement to new bound with the following program:

new bound:

169⋅X₂+20658 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
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:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₇₁: l1(X₀, X₁, X₂) → n_l3___16(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, 1, X₂)
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₉₉: n_l1___13(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₇₀: n_l1___13(X₀, X₁, X₂) → n_l3___12(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₇₂: n_l1___4(X₀, X₁, X₂) → n_l3___3(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₇₃: n_l1___6(X₀, X₁, X₂) → n_l3___5(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₇₄: n_l1___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 < X₁ ∧ 100 < X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₀ ≤ 111 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₇₅: n_l3___12(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₇₆: n_l3___12(X₀, X₁, X₂) → n_l6___10(X₀, X₁, X₂) :|: 0 < X₁ ∧ 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 91 ≤ X₀
t₁₇₇: n_l3___16(X₀, X₁, X₂) → n_l5___15(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁₇₈: n_l3___16(X₀, X₁, X₂) → n_l6___14(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁₇₉: n_l3___3(X₀, X₁, X₂) → n_l5___2(X₀, X₁, X₂) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₈₀: n_l3___3(X₀, X₁, X₂) → n_l6___1(X₀, X₁, X₂) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111
t₁₈₁: n_l3___5(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₈₂: n_l3___5(X₀, X₁, X₂) → n_l6___10(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀
t₁₈₃: n_l3___8(X₀, X₁, X₂) → n_l5___7(X₀, X₁, X₂) :|: X₀ ≤ 111 ∧ 101 ≤ X₀ ∧ 2 ≤ X₁ ∧ 100 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₈₄: n_l5___11(X₀, X₁, X₂) → n_l1___13(X₀-10, X₁-1, X₂) :|: 100 < X₀ ∧ 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₁₈₅: n_l5___15(X₀, X₁, X₂) → n_l1___13(X₀-10, X₁-1, X₂) :|: 100 < X₀ ∧ X₁ ≤ 1 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 101 ≤ X₂ ∧ 102 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 202 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 100+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀
t₁₈₆: n_l5___2(X₀, X₁, X₂) → n_l1___6(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ 100 < X₀ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 101 ≤ X₀
t₁₈₇: n_l5___7(X₀, X₁, X₂) → n_l1___6(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 101 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀
t₁₈₈: n_l6___1(X₀, X₁, X₂) → n_l1___4(X₀+11, X₁+1, X₂) :|: 2 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100
t₁₈₉: n_l6___10(X₀, X₁, X₂) → n_l1___9(X₀+11, X₁+1, X₂) :|: 91 ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀
t₁₉₀: n_l6___14(X₀, X₁, X₂) → n_l1___4(X₀+11, X₁+1, X₂) :|: X₁ ≤ 1 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 100 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 100 ∧ X₂ ≤ 100 ∧ X₂ ≤ 99+X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 200 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100

All Bounds

Timebounds

Overall timebound:169⋅X₂+20669 {O(n)}
t₁₇: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₃: 1 {O(1)}
t₁₇₀: X₂+114 {O(n)}
t₁₇₁: 1 {O(1)}
t₁₇₂: X₂+123 {O(n)}
t₁₇₃: 112⋅X₂+12971 {O(n)}
t₁₇₄: 10⋅X₂+1352 {O(n)}
t₁₇₅: X₂+114 {O(n)}
t₁₇₆: X₂+115 {O(n)}
t₁₇₇: 1 {O(1)}
t₁₇₈: 1 {O(1)}
t₁₇₉: 1 {O(1)}
t₁₈₀: X₂+112 {O(n)}
t₁₈₁: X₂+114 {O(n)}
t₁₈₂: 9⋅X₂+1219 {O(n)}
t₁₈₃: 10⋅X₂+1332 {O(n)}
t₁₈₄: X₂+316 {O(n)}
t₁₈₅: 1 {O(1)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 10⋅X₂+1332 {O(n)}
t₁₈₈: X₂+112 {O(n)}
t₁₈₉: 10⋅X₂+1332 {O(n)}
t₁₉₀: 1 {O(1)}
t₁₉₉: 1 {O(1)}

Costbounds

Overall costbound: 169⋅X₂+20669 {O(n)}
t₁₇: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₃: 1 {O(1)}
t₁₇₀: X₂+114 {O(n)}
t₁₇₁: 1 {O(1)}
t₁₇₂: X₂+123 {O(n)}
t₁₇₃: 112⋅X₂+12971 {O(n)}
t₁₇₄: 10⋅X₂+1352 {O(n)}
t₁₇₅: X₂+114 {O(n)}
t₁₇₆: X₂+115 {O(n)}
t₁₇₇: 1 {O(1)}
t₁₇₈: 1 {O(1)}
t₁₇₉: 1 {O(1)}
t₁₈₀: X₂+112 {O(n)}
t₁₈₁: X₂+114 {O(n)}
t₁₈₂: 9⋅X₂+1219 {O(n)}
t₁₈₃: 10⋅X₂+1332 {O(n)}
t₁₈₄: X₂+316 {O(n)}
t₁₈₅: 1 {O(1)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 10⋅X₂+1332 {O(n)}
t₁₈₈: X₂+112 {O(n)}
t₁₈₉: 10⋅X₂+1332 {O(n)}
t₁₉₀: 1 {O(1)}
t₁₉₉: 1 {O(1)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: 1 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₃, X₀: X₂+101 {O(n)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₁₇₀, X₀: 101 {O(1)}
t₁₇₀, X₁: 11⋅X₂+1446 {O(n)}
t₁₇₀, X₂: X₂ {O(n)}
t₁₇₁, X₀: X₂ {O(n)}
t₁₇₁, X₁: 1 {O(1)}
t₁₇₁, X₂: X₂ {O(n)}
t₁₇₂, X₀: 12⋅X₂+1243 {O(n)}
t₁₇₂, X₁: X₂+114 {O(n)}
t₁₇₂, X₂: X₂ {O(n)}
t₁₇₃, X₀: 101 {O(1)}
t₁₇₃, X₁: 11⋅X₂+1446 {O(n)}
t₁₇₃, X₂: X₂ {O(n)}
t₁₇₄, X₀: 111 {O(1)}
t₁₇₄, X₁: 11⋅X₂+1446 {O(n)}
t₁₇₄, X₂: X₂ {O(n)}
t₁₇₅, X₀: 101 {O(1)}
t₁₇₅, X₁: 11⋅X₂+1446 {O(n)}
t₁₇₅, X₂: X₂ {O(n)}
t₁₇₆, X₀: 100 {O(1)}
t₁₇₆, X₁: 11⋅X₂+1446 {O(n)}
t₁₇₆, X₂: X₂ {O(n)}
t₁₇₇, X₀: X₂ {O(n)}
t₁₇₇, X₁: 1 {O(1)}
t₁₇₇, X₂: X₂ {O(n)}
t₁₇₈, X₀: X₂ {O(n)}
t₁₇₈, X₁: 1 {O(1)}
t₁₇₈, X₂: X₂ {O(n)}
t₁₇₉, X₀: 111 {O(1)}
t₁₇₉, X₁: X₂+114 {O(n)}
t₁₇₉, X₂: X₂ {O(n)}
t₁₈₀, X₀: 12⋅X₂+1243 {O(n)}
t₁₈₀, X₁: X₂+114 {O(n)}
t₁₈₀, X₂: X₂ {O(n)}
t₁₈₁, X₀: 101 {O(1)}
t₁₈₁, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₁, X₂: X₂ {O(n)}
t₁₈₂, X₀: 100 {O(1)}
t₁₈₂, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₂, X₂: X₂ {O(n)}
t₁₈₃, X₀: 111 {O(1)}
t₁₈₃, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₃, X₂: X₂ {O(n)}
t₁₈₄, X₀: 101 {O(1)}
t₁₈₄, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₄, X₂: X₂ {O(n)}
t₁₈₅, X₀: X₂ {O(n)}
t₁₈₅, X₁: 0 {O(1)}
t₁₈₅, X₂: X₂ {O(n)}
t₁₈₆, X₀: 101 {O(1)}
t₁₈₆, X₁: X₂+114 {O(n)}
t₁₈₆, X₂: X₂ {O(n)}
t₁₈₇, X₀: 101 {O(1)}
t₁₈₇, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₇, X₂: X₂ {O(n)}
t₁₈₈, X₀: 12⋅X₂+1243 {O(n)}
t₁₈₈, X₁: X₂+114 {O(n)}
t₁₈₈, X₂: X₂ {O(n)}
t₁₈₉, X₀: 111 {O(1)}
t₁₈₉, X₁: 11⋅X₂+1446 {O(n)}
t₁₈₉, X₂: X₂ {O(n)}
t₁₉₀, X₀: X₂+11 {O(n)}
t₁₉₀, X₁: 2 {O(1)}
t₁₉₀, X₂: X₂ {O(n)}
t₁₉₉, X₀: X₂+101 {O(n)}
t₁₉₉, X₁: 0 {O(1)}
t₁₉₉, X₂: 2⋅X₂ {O(n)}