Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1, X₃, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 101 ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀-1, X₁-10, X₂, X₃)
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, 11+X₁, X₂, X₃)
t₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables [X₂] that do not contribute to the problem

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb5_in

Found invariant 1 ≤ X₀ for location eval_foo_bb2_in

Found invariant 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_stop

Found invariant 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₇: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(1, X₂, X₂)
t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
t₁₉: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
t₂₁: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀-1, X₁-10, X₂) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁
t₂₃: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, 11+X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀
t₂₄: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₂₅: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂₁: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+101 {O(n)}

• eval_foo_bb1_in: [91+10⋅X₀-X₁]
• eval_foo_bb2_in: [91+10⋅X₀-X₁]
• eval_foo_bb3_in: [91+10⋅X₀-X₁]
• eval_foo_bb4_in: [90+10⋅X₀-X₁]

MPRF for transition t₂₃: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, 11+X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+101 {O(n)}

• eval_foo_bb1_in: [91+10⋅X₀-X₁]
• eval_foo_bb2_in: [91+10⋅X₀-X₁]
• eval_foo_bb3_in: [91+10⋅X₀-X₁]
• eval_foo_bb4_in: [91+10⋅X₀-X₁]

MPRF for transition t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+204⋅X₂+10405 {O(n^2)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]

MPRF for transition t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+204⋅X₂+10405 {O(n^2)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [1+X₀]

MPRF for transition t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀-1, X₁-10, X₂) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ of depth 1:

new bound:

X₂⋅X₂+203⋅X₂+10303 {O(n^2)}

• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]

Cut unsatisfiable transition [t₁₉: eval_foo_bb1_in→eval_foo_bb5_in; t₄₆: eval_foo_bb1_in→eval_foo_bb5_in]

Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb4_in_v2

Found invariant X₂ ≤ 10+X₁ ∧ 101 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ 10+X₁ ≤ X₂ ∧ 101 ≤ X₀+X₂ ∧ 101+X₀ ≤ X₂ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant X₂ ≤ 100 ∧ 11+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 211 ∧ X₂ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v5

Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb1_in_v2

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

Found invariant 1 ≤ 0 for location eval_foo_bb2_in_v2

Found invariant X₁ ≤ 91 ∧ X₁ ≤ 91+X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v4

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in_v3

Found invariant X₂ ≤ 100 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 200 ∧ X₂ ≤ 99+X₀ ∧ X₀+X₂ ≤ 101 ∧ X₁ ≤ X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb4_in_v1

Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v3

Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb3_in_v2

Found invariant X₂ ≤ 100 ∧ 11+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 211 ∧ X₂ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location eval_foo_bb1_in_v5

Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v4

Found invariant X₂ ≤ 89 ∧ 11+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 189 ∧ X₂ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀ for location eval_foo_bb4_in_v3

Found invariant X₂ ≤ X₁ ∧ 101 ≤ X₂ ∧ 202 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 102 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb3_in_v1

Cut unsatisfiable transition [t₅₂: eval_foo_bb1_in_v1→eval_foo_bb2_in_v2; t₅₃: eval_foo_bb2_in_v2→eval_foo_bb4_in_v2; t₅₄: eval_foo_bb2_in_v2→eval_foo_bb3_in_v1]

Cut unreachable locations [eval_foo_bb2_in_v2] from the program graph

Analysing control-flow refined program

MPRF for transition t₆₆: eval_foo_bb1_in_v5(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁+X₂ ≤ 211 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+143 {O(n)}

• eval_foo_bb1_in_v5: [112+10⋅X₀-X₁]
• eval_foo_bb2_in_v5: [111+10⋅X₀-X₁]
• eval_foo_bb4_in_v3: [111+10⋅X₀-X₁]

MPRF for transition t₆₇: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb4_in_v3(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₁+X₂ ≤ 211 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁ of depth 1:

new bound:

2⋅X₂+223 {O(n)}

• eval_foo_bb1_in_v5: [212-X₁-X₂]
• eval_foo_bb2_in_v5: [212-X₁-X₂]
• eval_foo_bb4_in_v3: [201-X₁-X₂]

MPRF for transition t₆₉: eval_foo_bb4_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v5(1+X₀, 11+X₁, X₂) :|: X₁+X₂ ≤ 189 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₁ ≤ 98+X₀ ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁ of depth 1:

new bound:

X₂+112 {O(n)}

• eval_foo_bb1_in_v5: [101-X₁]
• eval_foo_bb2_in_v5: [101-X₁]
• eval_foo_bb4_in_v3: [101-X₁]

MPRF for transition t₅₅: eval_foo_bb4_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v2(1+X₀, 11+X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1562 {O(n)}

• eval_foo_bb1_in_v2: [101+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [101+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [101+10⋅X₀-X₁]
• eval_foo_bb2_in_v3: [101+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [101+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [101+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [101+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [101+10⋅X₀-X₁]

MPRF for transition t₅₆: eval_foo_bb1_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

10⋅X₂+1572 {O(n)}

• eval_foo_bb1_in_v2: [112+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [111+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [20+10⋅X₀]
• eval_foo_bb2_in_v3: [111+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [111+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [111+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [111+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [111+10⋅X₀-X₁]

MPRF for transition t₅₇: eval_foo_bb2_in_v3(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1642 {O(n)}

• eval_foo_bb1_in_v2: [182+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [181+10⋅X₀-X₁]
• eval_foo_bb2_in_v3: [182+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [181+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [181+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [181+10⋅X₀-X₁]

MPRF for transition t₅₈: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v3(X₀-1, X₁-10, X₂) :|: X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 103 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1563 {O(n)}

• eval_foo_bb1_in_v2: [102+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [101+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [10+10⋅X₀]
• eval_foo_bb2_in_v3: [102+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [101+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [102+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [101+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [101+10⋅X₀-X₁]

MPRF for transition t₅₉: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

10⋅X₂+1643 {O(n)}

• eval_foo_bb1_in_v2: [182+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [182+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [90+10⋅X₀]
• eval_foo_bb2_in_v3: [182+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [181+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [182+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [181+10⋅X₀-X₁]

MPRF for transition t₆₀: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb4_in_v2(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1642 {O(n)}

• eval_foo_bb1_in_v2: [181+10⋅X₀-X₁]
• eval_foo_bb1_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb1_in_v4: [90+10⋅X₀]
• eval_foo_bb2_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb2_in_v4: [181+10⋅X₀-X₁]
• eval_foo_bb3_in_v2: [181+10⋅X₀-X₁]
• eval_foo_bb3_in_v3: [181+10⋅X₀-X₁]
• eval_foo_bb4_in_v2: [180+10⋅X₀-X₁]

MPRF for transition t₆₁: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb3_in_v3(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

X₂+136 {O(n)}

• eval_foo_bb1_in_v2: [X₀-1]
• eval_foo_bb1_in_v3: [X₀]
• eval_foo_bb1_in_v4: [X₀]
• eval_foo_bb2_in_v3: [X₀-1]
• eval_foo_bb2_in_v4: [X₀]
• eval_foo_bb3_in_v2: [X₀-1]
• eval_foo_bb3_in_v3: [X₀-1]
• eval_foo_bb4_in_v2: [X₀]

MPRF for transition t₆₂: eval_foo_bb3_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v4(X₀-1, X₁-10, X₂) :|: X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ of depth 1:

new bound:

X₂+136 {O(n)}

• eval_foo_bb1_in_v2: [X₀-1]
• eval_foo_bb1_in_v3: [X₀]
• eval_foo_bb1_in_v4: [X₀]
• eval_foo_bb2_in_v3: [X₀-1]
• eval_foo_bb2_in_v4: [X₀]
• eval_foo_bb3_in_v2: [X₀-1]
• eval_foo_bb3_in_v3: [X₀]
• eval_foo_bb4_in_v2: [X₀]

MPRF for transition t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 91+X₀ ∧ X₁ ≤ 91 ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+137 {O(n)}

• eval_foo_bb1_in_v2: [X₀-2]
• eval_foo_bb1_in_v3: [X₀-1]
• eval_foo_bb1_in_v4: [X₀]
• eval_foo_bb2_in_v3: [X₀-2]
• eval_foo_bb2_in_v4: [X₀-1]
• eval_foo_bb3_in_v2: [X₀-2]
• eval_foo_bb3_in_v3: [X₀-1]
• eval_foo_bb4_in_v2: [X₀-1]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb1_in_v1, eval_foo_bb1_in_v2, eval_foo_bb1_in_v3, eval_foo_bb1_in_v4, eval_foo_bb1_in_v5, eval_foo_bb2_in_v1, eval_foo_bb2_in_v3, eval_foo_bb2_in_v4, eval_foo_bb2_in_v5, eval_foo_bb3_in_v1, eval_foo_bb3_in_v2, eval_foo_bb3_in_v3, eval_foo_bb4_in_v1, eval_foo_bb4_in_v2, eval_foo_bb4_in_v3, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₇: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(1, X₂, X₂)
t₄₇: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₅₁: eval_foo_bb1_in_v1(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ 10+X₁ ∧ 10+X₁ ≤ X₂ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ 91 ≤ X₁ ∧ 101 ≤ X₀+X₂ ∧ 101+X₀ ≤ X₂ ∧ 101 ≤ X₂ ∧ 192 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₅₆: eval_foo_bb1_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅₉: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 91+X₀ ∧ X₁ ≤ 91 ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
t₆₃: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₁ ≤ 111 ∧ X₁ ≤ 91+X₀ ∧ X₁ ≤ 91 ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
t₆₆: eval_foo_bb1_in_v5(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₁+X₂ ≤ 211 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁ ∧ 0 ≤ X₀
t₄₉: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb3_in_v1(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₄₈: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb4_in_v1(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₅₇: eval_foo_bb2_in_v3(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁
t₆₁: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb3_in_v3(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁
t₆₀: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb4_in_v2(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁
t₆₈: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₁ ∧ X₁+X₂ ≤ 211 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁
t₆₇: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb4_in_v3(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₁+X₂ ≤ 211 ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁
t₅₀: eval_foo_bb3_in_v1(X₀, X₁, X₂) → eval_foo_bb1_in_v1(X₀-1, X₁-10, X₂) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 100+X₀ ≤ X₁ ∧ 100+X₀ ≤ X₂ ∧ 101 ≤ X₁ ∧ 101 ≤ X₂ ∧ 102 ≤ X₀+X₁ ∧ 102 ≤ X₀+X₂ ∧ 202 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₅₈: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v3(X₀-1, X₁-10, X₂) :|: X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 103 ≤ X₀+X₁
t₆₂: eval_foo_bb3_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v4(X₀-1, X₁-10, X₂) :|: X₁ ≤ 111 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁
t₆₅: eval_foo_bb4_in_v1(X₀, X₁, X₂) → eval_foo_bb1_in_v5(1+X₀, 11+X₁, X₂) :|: X₁+X₂ ≤ 200 ∧ X₀+X₁ ≤ 101 ∧ X₀+X₂ ≤ 101 ∧ X₁ ≤ 100 ∧ X₂ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₂ ≤ 99+X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₅₅: eval_foo_bb4_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v2(1+X₀, 11+X₁, X₂) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁
t₆₉: eval_foo_bb4_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v5(1+X₀, 11+X₁, X₂) :|: X₁+X₂ ≤ 189 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₁ ≤ 98+X₀ ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 11+X₂ ≤ X₁
t₂₄: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
t₂₅: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:67⋅X₂+10522 {O(n)}
t₁₇: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₅: 10⋅X₂+1562 {O(n)}
t₅₆: 10⋅X₂+1572 {O(n)}
t₅₇: 10⋅X₂+1642 {O(n)}
t₅₈: 10⋅X₂+1563 {O(n)}
t₅₉: 10⋅X₂+1643 {O(n)}
t₆₀: 10⋅X₂+1642 {O(n)}
t₆₁: X₂+136 {O(n)}
t₆₂: X₂+136 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₂+137 {O(n)}
t₆₅: 1 {O(1)}
t₆₆: X₂+143 {O(n)}
t₆₇: 2⋅X₂+223 {O(n)}
t₆₈: 1 {O(1)}
t₆₉: X₂+112 {O(n)}

Costbounds

Overall costbound: 67⋅X₂+10522 {O(n)}
t₁₇: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₅: 10⋅X₂+1562 {O(n)}
t₅₆: 10⋅X₂+1572 {O(n)}
t₅₇: 10⋅X₂+1642 {O(n)}
t₅₈: 10⋅X₂+1563 {O(n)}
t₅₉: 10⋅X₂+1643 {O(n)}
t₆₀: 10⋅X₂+1642 {O(n)}
t₆₁: X₂+136 {O(n)}
t₆₂: X₂+136 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₂+137 {O(n)}
t₆₅: 1 {O(1)}
t₆₆: X₂+143 {O(n)}
t₆₇: 2⋅X₂+223 {O(n)}
t₆₈: 1 {O(1)}
t₆₉: X₂+112 {O(n)}

Sizebounds

t₁₇, X₀: 1 {O(1)}
t₁₇, X₁: X₂ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₂₄, X₀: 0 {O(1)}
t₂₄, X₁: X₂+91 {O(n)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₄₇, X₀: 1 {O(1)}
t₄₇, X₁: X₂ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₈, X₀: 1 {O(1)}
t₄₈, X₁: X₂ {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₉, X₀: 1 {O(1)}
t₄₉, X₁: X₂ {O(n)}
t₄₉, X₂: X₂ {O(n)}
t₅₀, X₀: 0 {O(1)}
t₅₀, X₁: X₂ {O(n)}
t₅₀, X₂: X₂ {O(n)}
t₅₁, X₀: 0 {O(1)}
t₅₁, X₁: X₂ {O(n)}
t₅₁, X₂: X₂ {O(n)}
t₅₅, X₀: 11⋅X₂+1697 {O(n)}
t₅₅, X₁: 111 {O(1)}
t₅₅, X₂: X₂ {O(n)}
t₅₆, X₀: 11⋅X₂+1697 {O(n)}
t₅₆, X₁: 111 {O(1)}
t₅₆, X₂: X₂ {O(n)}
t₅₇, X₀: 11⋅X₂+1697 {O(n)}
t₅₇, X₁: 111 {O(1)}
t₅₇, X₂: X₂ {O(n)}
t₅₈, X₀: 11⋅X₂+1697 {O(n)}
t₅₈, X₁: 101 {O(1)}
t₅₈, X₂: X₂ {O(n)}
t₅₉, X₀: 11⋅X₂+1697 {O(n)}
t₅₉, X₁: 101 {O(1)}
t₅₉, X₂: X₂ {O(n)}
t₆₀, X₀: 11⋅X₂+1697 {O(n)}
t₆₀, X₁: 100 {O(1)}
t₆₀, X₂: X₂ {O(n)}
t₆₁, X₀: 11⋅X₂+1697 {O(n)}
t₆₁, X₁: 101 {O(1)}
t₆₁, X₂: X₂ {O(n)}
t₆₂, X₀: 11⋅X₂+1697 {O(n)}
t₆₂, X₁: 91 {O(1)}
t₆₂, X₂: X₂ {O(n)}
t₆₃, X₀: 0 {O(1)}
t₆₃, X₁: 91 {O(1)}
t₆₃, X₂: X₂ {O(n)}
t₆₄, X₀: 11⋅X₂+1697 {O(n)}
t₆₄, X₁: 91 {O(1)}
t₆₄, X₂: X₂ {O(n)}
t₆₅, X₀: 2 {O(1)}
t₆₅, X₁: X₂+11 {O(n)}
t₆₅, X₂: X₂ {O(n)}
t₆₆, X₀: X₂+135 {O(n)}
t₆₆, X₁: 12⋅X₂+1375 {O(n)}
t₆₆, X₂: X₂ {O(n)}
t₆₇, X₀: X₂+136 {O(n)}
t₆₇, X₁: 12⋅X₂+1375 {O(n)}
t₆₇, X₂: X₂ {O(n)}
t₆₈, X₀: X₂+135 {O(n)}
t₆₈, X₁: 111 {O(1)}
t₆₈, X₂: X₂ {O(n)}
t₆₉, X₀: X₂+115 {O(n)}
t₆₉, X₁: 12⋅X₂+1254 {O(n)}
t₆₉, X₂: X₂ {O(n)}