We consider the following Problem:
Strict Trs:
{ active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, check(x) -> start(match(f(X()), x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(c()) -> ok(c())
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, start(ok(x)) -> found(x)
, f(found(x)) -> found(f(x))
, top(found(x)) -> top(active(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
We consider the following Problem:
Strict Trs:
{ active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, check(x) -> start(match(f(X()), x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(c()) -> ok(c())
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, start(ok(x)) -> found(x)
, f(found(x)) -> found(f(x))
, top(found(x)) -> top(active(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component:
{ active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [1]
[1 0] [1]
f(x1) = [1 0] x1 + [0]
[0 0] [1]
mark(x1) = [1 0] x1 + [0]
[0 0] [1]
top(x1) = [1 0] x1 + [0]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 0] x1 + [0]
[0 0] [1]
start(x1) = [1 0] x1 + [1]
[0 0] [1]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [1]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [1]
[0 0] [1]
ok(x1) = [1 0] x1 + [1]
[0 0] [1]
found(x1) = [1 0] x1 + [0]
[0 0] [1]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, check(x) -> start(match(f(X()), x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(c()) -> ok(c())
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, top(found(x)) -> top(active(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {proper(c()) -> ok(c())}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [0]
[0 0] [1]
f(x1) = [1 0] x1 + [1]
[0 0] [1]
mark(x1) = [1 0] x1 + [0]
[0 0] [1]
top(x1) = [1 0] x1 + [1]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 0] x1 + [0]
[0 0] [1]
start(x1) = [1 0] x1 + [1]
[0 0] [1]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [1]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [1]
[0 0] [1]
ok(x1) = [1 0] x1 + [0]
[0 0] [1]
found(x1) = [1 0] x1 + [0]
[0 0] [1]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, check(x) -> start(match(f(X()), x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, top(found(x)) -> top(active(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {top(found(x)) -> top(active(x))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [0]
[0 0] [1]
f(x1) = [1 0] x1 + [1]
[0 0] [1]
mark(x1) = [1 0] x1 + [0]
[0 0] [1]
top(x1) = [1 0] x1 + [1]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 0] x1 + [0]
[0 0] [1]
start(x1) = [1 0] x1 + [1]
[0 0] [1]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [1]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [1]
[0 0] [1]
ok(x1) = [1 0] x1 + [0]
[0 0] [1]
found(x1) = [1 0] x1 + [1]
[0 0] [1]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, check(x) -> start(match(f(X()), x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {check(x) -> start(match(f(X()), x))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [0]
[1 0] [1]
f(x1) = [1 0] x1 + [0]
[0 0] [2]
mark(x1) = [1 0] x1 + [0]
[0 0] [1]
top(x1) = [1 0] x1 + [0]
[1 0] [1]
c() = [0]
[0]
check(x1) = [0 0] x1 + [1]
[1 0] [2]
start(x1) = [1 0] x1 + [0]
[0 0] [1]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [1]
[0 1] [3]
ok(x1) = [1 0] x1 + [0]
[0 0] [1]
found(x1) = [1 0] x1 + [0]
[0 0] [1]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ top(mark(x)) -> top(check(x))
, check(f(x)) -> f(check(x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {top(mark(x)) -> top(check(x))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [0]
[0 1] [0]
f(x1) = [1 0] x1 + [0]
[0 0] [2]
mark(x1) = [1 0] x1 + [0]
[0 0] [1]
top(x1) = [1 2] x1 + [0]
[0 0] [1]
c() = [3]
[1]
check(x1) = [1 0] x1 + [0]
[0 0] [0]
start(x1) = [1 0] x1 + [0]
[0 1] [0]
match(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
X() = [0]
[0]
proper(x1) = [1 0] x1 + [1]
[0 1] [3]
ok(x1) = [1 0] x1 + [0]
[0 1] [3]
found(x1) = [1 0] x1 + [0]
[0 1] [2]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ check(f(x)) -> f(check(x))
, match(f(x), f(y)) -> f(match(x, y))
, match(X(), x) -> proper(x)
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {match(f(x), f(y)) -> f(match(x, y))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 2] x1 + [0]
[0 0] [0]
f(x1) = [1 0] x1 + [0]
[0 1] [1]
mark(x1) = [1 2] x1 + [0]
[0 0] [0]
top(x1) = [1 0] x1 + [0]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 2] x1 + [0]
[0 0] [3]
start(x1) = [1 0] x1 + [0]
[0 1] [2]
match(x1, x2) = [0 0] x1 + [0 2] x2 + [0]
[0 1] [0 0] [0]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [0]
[0 0] [3]
ok(x1) = [1 2] x1 + [0]
[0 0] [2]
found(x1) = [1 2] x1 + [0]
[0 0] [0]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ check(f(x)) -> f(check(x))
, match(X(), x) -> proper(x)
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ match(f(x), f(y)) -> f(match(x, y))
, top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {match(X(), x) -> proper(x)}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 0] x1 + [1]
[0 0] [0]
f(x1) = [1 0] x1 + [0]
[0 0] [0]
mark(x1) = [1 0] x1 + [1]
[0 0] [0]
top(x1) = [1 0] x1 + [0]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 0] x1 + [1]
[0 0] [0]
start(x1) = [1 1] x1 + [0]
[0 0] [0]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [1]
[0 1] [0 0] [0]
X() = [0]
[2]
proper(x1) = [0 0] x1 + [0]
[0 0] [2]
ok(x1) = [1 0] x1 + [0]
[0 0] [2]
found(x1) = [1 0] x1 + [1]
[0 0] [0]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ check(f(x)) -> f(check(x))
, proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ match(X(), x) -> proper(x)
, match(f(x), f(y)) -> f(match(x, y))
, top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {check(f(x)) -> f(check(x))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 1] x1 + [0]
[0 0] [2]
f(x1) = [1 0] x1 + [0]
[0 1] [2]
mark(x1) = [1 1] x1 + [0]
[0 0] [0]
top(x1) = [1 0] x1 + [0]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 1] x1 + [0]
[0 1] [2]
start(x1) = [1 0] x1 + [0]
[0 0] [1]
match(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
X() = [0]
[0]
proper(x1) = [0 0] x1 + [0]
[0 0] [0]
ok(x1) = [1 2] x1 + [0]
[0 0] [0]
found(x1) = [1 2] x1 + [0]
[0 0] [0]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ proper(f(x)) -> f(proper(x))
, f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ check(f(x)) -> f(check(x))
, match(X(), x) -> proper(x)
, match(f(x), f(y)) -> f(match(x, y))
, top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The weightgap principle applies, where following rules are oriented strictly:
TRS Component: {proper(f(x)) -> f(proper(x))}
Interpretation of nonconstant growth:
-------------------------------------
The following argument positions are usable:
Uargs(active) = {}, Uargs(f) = {1}, Uargs(mark) = {1},
Uargs(top) = {1}, Uargs(check) = {}, Uargs(start) = {1},
Uargs(match) = {}, Uargs(proper) = {}, Uargs(ok) = {1},
Uargs(found) = {1}
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
active(x1) = [1 2] x1 + [0]
[0 0] [3]
f(x1) = [1 0] x1 + [0]
[0 1] [1]
mark(x1) = [1 2] x1 + [0]
[0 0] [0]
top(x1) = [1 0] x1 + [0]
[0 0] [1]
c() = [0]
[0]
check(x1) = [0 1] x1 + [0]
[0 1] [0]
start(x1) = [1 0] x1 + [0]
[0 0] [0]
match(x1, x2) = [0 0] x1 + [0 1] x2 + [0]
[0 0] [0 1] [0]
X() = [0]
[0]
proper(x1) = [0 1] x1 + [0]
[0 1] [0]
ok(x1) = [1 2] x1 + [0]
[0 0] [0]
found(x1) = [1 2] x1 + [0]
[0 0] [0]
The strictly oriented rules are moved into the weak component.
We consider the following Problem:
Strict Trs:
{ f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ proper(f(x)) -> f(proper(x))
, check(f(x)) -> f(check(x))
, match(X(), x) -> proper(x)
, match(f(x), f(y)) -> f(match(x, y))
, top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
We consider the following Problem:
Strict Trs:
{ f(ok(x)) -> ok(f(x))
, f(found(x)) -> found(f(x))
, active(f(x)) -> f(active(x))
, f(mark(x)) -> mark(f(x))}
Weak Trs:
{ proper(f(x)) -> f(proper(x))
, check(f(x)) -> f(check(x))
, match(X(), x) -> proper(x)
, match(f(x), f(y)) -> f(match(x, y))
, top(mark(x)) -> top(check(x))
, check(x) -> start(match(f(X()), x))
, top(found(x)) -> top(active(x))
, proper(c()) -> ok(c())
, active(f(x)) -> mark(x)
, top(active(c())) -> top(mark(c()))
, start(ok(x)) -> found(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ active_0(3) -> 1
, active_0(5) -> 1
, active_0(9) -> 1
, active_0(11) -> 1
, active_0(12) -> 1
, f_0(3) -> 2
, f_0(5) -> 2
, f_0(9) -> 2
, f_0(11) -> 2
, f_0(12) -> 2
, f_1(3) -> 14
, f_1(5) -> 14
, f_1(9) -> 14
, f_1(11) -> 14
, f_1(12) -> 14
, f_1(17) -> 16
, mark_0(3) -> 3
, mark_0(5) -> 3
, mark_0(9) -> 3
, mark_0(11) -> 3
, mark_0(12) -> 3
, mark_1(14) -> 2
, mark_1(14) -> 14
, top_0(1) -> 4
, top_0(3) -> 4
, top_0(5) -> 4
, top_0(6) -> 4
, top_0(9) -> 4
, top_0(11) -> 4
, top_0(12) -> 4
, c_0() -> 5
, check_0(3) -> 6
, check_0(5) -> 6
, check_0(9) -> 6
, check_0(11) -> 6
, check_0(12) -> 6
, start_0(3) -> 7
, start_0(5) -> 7
, start_0(9) -> 7
, start_0(11) -> 7
, start_0(12) -> 7
, start_0(13) -> 6
, start_1(15) -> 6
, match_0(2, 3) -> 13
, match_0(2, 5) -> 13
, match_0(2, 9) -> 13
, match_0(2, 11) -> 13
, match_0(2, 12) -> 13
, match_0(3, 3) -> 8
, match_0(3, 5) -> 8
, match_0(3, 9) -> 8
, match_0(3, 11) -> 8
, match_0(3, 12) -> 8
, match_0(5, 3) -> 8
, match_0(5, 5) -> 8
, match_0(5, 9) -> 8
, match_0(5, 11) -> 8
, match_0(5, 12) -> 8
, match_0(9, 3) -> 8
, match_0(9, 5) -> 8
, match_0(9, 9) -> 8
, match_0(9, 11) -> 8
, match_0(9, 12) -> 8
, match_0(11, 3) -> 8
, match_0(11, 5) -> 8
, match_0(11, 9) -> 8
, match_0(11, 11) -> 8
, match_0(11, 12) -> 8
, match_0(12, 3) -> 8
, match_0(12, 5) -> 8
, match_0(12, 9) -> 8
, match_0(12, 11) -> 8
, match_0(12, 12) -> 8
, match_1(16, 3) -> 15
, match_1(16, 5) -> 15
, match_1(16, 9) -> 15
, match_1(16, 11) -> 15
, match_1(16, 12) -> 15
, X_0() -> 9
, X_1() -> 17
, proper_0(3) -> 8
, proper_0(3) -> 10
, proper_0(5) -> 8
, proper_0(5) -> 10
, proper_0(9) -> 8
, proper_0(9) -> 10
, proper_0(11) -> 8
, proper_0(11) -> 10
, proper_0(12) -> 8
, proper_0(12) -> 10
, ok_0(3) -> 11
, ok_0(5) -> 8
, ok_0(5) -> 10
, ok_0(5) -> 11
, ok_0(9) -> 11
, ok_0(11) -> 11
, ok_0(12) -> 11
, ok_1(14) -> 2
, ok_1(14) -> 14
, found_0(3) -> 7
, found_0(3) -> 12
, found_0(5) -> 7
, found_0(5) -> 12
, found_0(9) -> 7
, found_0(9) -> 12
, found_0(11) -> 7
, found_0(11) -> 12
, found_0(12) -> 7
, found_0(12) -> 12
, found_1(14) -> 2
, found_1(14) -> 14}
Hurray, we answered YES(?,O(n^1))