R
↳Dependency Pair Analysis
ACTIVE(fact(X)) -> IF(zero(X), s(0), prod(X, fact(p(X))))
ACTIVE(fact(X)) -> ZERO(X)
ACTIVE(fact(X)) -> S(0)
ACTIVE(fact(X)) -> PROD(X, fact(p(X)))
ACTIVE(fact(X)) -> FACT(p(X))
ACTIVE(fact(X)) -> P(X)
ACTIVE(add(s(X), Y)) -> S(add(X, Y))
ACTIVE(add(s(X), Y)) -> ADD(X, Y)
ACTIVE(prod(s(X), Y)) -> ADD(Y, prod(X, Y))
ACTIVE(prod(s(X), Y)) -> PROD(X, Y)
ACTIVE(fact(X)) -> FACT(active(X))
ACTIVE(fact(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> IF(active(X1), X2, X3)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(zero(X)) -> ZERO(active(X))
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(s(X)) -> S(active(X))
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(prod(X1, X2)) -> PROD(active(X1), X2)
ACTIVE(prod(X1, X2)) -> ACTIVE(X1)
ACTIVE(prod(X1, X2)) -> PROD(X1, active(X2))
ACTIVE(prod(X1, X2)) -> ACTIVE(X2)
ACTIVE(p(X)) -> P(active(X))
ACTIVE(p(X)) -> ACTIVE(X)
ACTIVE(add(X1, X2)) -> ADD(active(X1), X2)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
ACTIVE(add(X1, X2)) -> ADD(X1, active(X2))
ACTIVE(add(X1, X2)) -> ACTIVE(X2)
FACT(mark(X)) -> FACT(X)
FACT(ok(X)) -> FACT(X)
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
ZERO(mark(X)) -> ZERO(X)
ZERO(ok(X)) -> ZERO(X)
S(mark(X)) -> S(X)
S(ok(X)) -> S(X)
PROD(mark(X1), X2) -> PROD(X1, X2)
PROD(X1, mark(X2)) -> PROD(X1, X2)
PROD(ok(X1), ok(X2)) -> PROD(X1, X2)
P(mark(X)) -> P(X)
P(ok(X)) -> P(X)
ADD(mark(X1), X2) -> ADD(X1, X2)
ADD(X1, mark(X2)) -> ADD(X1, X2)
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
PROPER(fact(X)) -> FACT(proper(X))
PROPER(fact(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> IF(proper(X1), proper(X2), proper(X3))
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(zero(X)) -> ZERO(proper(X))
PROPER(zero(X)) -> PROPER(X)
PROPER(s(X)) -> S(proper(X))
PROPER(s(X)) -> PROPER(X)
PROPER(prod(X1, X2)) -> PROD(proper(X1), proper(X2))
PROPER(prod(X1, X2)) -> PROPER(X1)
PROPER(prod(X1, X2)) -> PROPER(X2)
PROPER(p(X)) -> P(proper(X))
PROPER(p(X)) -> PROPER(X)
PROPER(add(X1, X2)) -> ADD(proper(X1), proper(X2))
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(add(X1, X2)) -> PROPER(X2)
TOP(mark(X)) -> TOP(proper(X))
TOP(mark(X)) -> PROPER(X)
TOP(ok(X)) -> TOP(active(X))
TOP(ok(X)) -> ACTIVE(X)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(IF(x1, x2, x3)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 11
↳Polynomial Ordering
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
POL(mark(x1)) = 1 + x1 POL(IF(x1, x2, x3)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 11
↳Polo
...
→DP Problem 12
↳Dependency Graph
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polynomial Ordering
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ZERO(ok(X)) -> ZERO(X)
ZERO(mark(X)) -> ZERO(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ZERO(ok(X)) -> ZERO(X)
POL(ZERO(x1)) = x1 POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 13
↳Polynomial Ordering
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ZERO(mark(X)) -> ZERO(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ZERO(mark(X)) -> ZERO(X)
POL(ZERO(x1)) = x1 POL(mark(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 13
↳Polo
...
→DP Problem 14
↳Dependency Graph
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polynomial Ordering
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
PROD(ok(X1), ok(X2)) -> PROD(X1, X2)
PROD(X1, mark(X2)) -> PROD(X1, X2)
PROD(mark(X1), X2) -> PROD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROD(ok(X1), ok(X2)) -> PROD(X1, X2)
POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1 POL(PROD(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 15
↳Polynomial Ordering
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
PROD(X1, mark(X2)) -> PROD(X1, X2)
PROD(mark(X1), X2) -> PROD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROD(X1, mark(X2)) -> PROD(X1, X2)
POL(mark(x1)) = 1 + x1 POL(PROD(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 15
↳Polo
...
→DP Problem 16
↳Polynomial Ordering
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
PROD(mark(X1), X2) -> PROD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROD(mark(X1), X2) -> PROD(X1, X2)
POL(mark(x1)) = 1 + x1 POL(PROD(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 15
↳Polo
...
→DP Problem 17
↳Dependency Graph
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polynomial Ordering
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
FACT(ok(X)) -> FACT(X)
FACT(mark(X)) -> FACT(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FACT(ok(X)) -> FACT(X)
POL(FACT(x1)) = x1 POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 18
↳Polynomial Ordering
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
FACT(mark(X)) -> FACT(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FACT(mark(X)) -> FACT(X)
POL(FACT(x1)) = x1 POL(mark(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 18
↳Polo
...
→DP Problem 19
↳Dependency Graph
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polynomial Ordering
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
P(ok(X)) -> P(X)
P(mark(X)) -> P(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
P(ok(X)) -> P(X)
POL(P(x1)) = x1 POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 20
↳Polynomial Ordering
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
P(mark(X)) -> P(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
P(mark(X)) -> P(X)
POL(P(x1)) = x1 POL(mark(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 20
↳Polo
...
→DP Problem 21
↳Dependency Graph
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polynomial Ordering
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
S(ok(X)) -> S(X)
S(mark(X)) -> S(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
S(ok(X)) -> S(X)
POL(S(x1)) = x1 POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 22
↳Polynomial Ordering
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
S(mark(X)) -> S(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
S(mark(X)) -> S(X)
POL(S(x1)) = x1 POL(mark(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 22
↳Polo
...
→DP Problem 23
↳Dependency Graph
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
ADD(X1, mark(X2)) -> ADD(X1, X2)
ADD(mark(X1), X2) -> ADD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
POL(mark(x1)) = x1 POL(ok(x1)) = 1 + x1 POL(ADD(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 24
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ADD(X1, mark(X2)) -> ADD(X1, X2)
ADD(mark(X1), X2) -> ADD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ADD(X1, mark(X2)) -> ADD(X1, X2)
POL(mark(x1)) = 1 + x1 POL(ADD(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 24
↳Polo
...
→DP Problem 25
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ADD(mark(X1), X2) -> ADD(X1, X2)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ADD(mark(X1), X2) -> ADD(X1, X2)
POL(mark(x1)) = 1 + x1 POL(ADD(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 24
↳Polo
...
→DP Problem 26
↳Dependency Graph
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(add(X1, X2)) -> ACTIVE(X2)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
ACTIVE(p(X)) -> ACTIVE(X)
ACTIVE(prod(X1, X2)) -> ACTIVE(X2)
ACTIVE(prod(X1, X2)) -> ACTIVE(X1)
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(add(X1, X2)) -> ACTIVE(X2)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(prod(x1, x2)) = x1 + x2 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(p(x1)) = x1 POL(zero(x1)) = x1 POL(add(x1, x2)) = 1 + x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(p(X)) -> ACTIVE(X)
ACTIVE(prod(X1, X2)) -> ACTIVE(X2)
ACTIVE(prod(X1, X2)) -> ACTIVE(X1)
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(p(X)) -> ACTIVE(X)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(prod(x1, x2)) = x1 + x2 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(p(x1)) = 1 + x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 28
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(prod(X1, X2)) -> ACTIVE(X2)
ACTIVE(prod(X1, X2)) -> ACTIVE(X1)
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(prod(X1, X2)) -> ACTIVE(X2)
ACTIVE(prod(X1, X2)) -> ACTIVE(X1)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(prod(x1, x2)) = 1 + x1 + x2 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 29
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(s(X)) -> ACTIVE(X)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(fact(x1)) = x1 POL(s(x1)) = 1 + x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 30
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(zero(X)) -> ACTIVE(X)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(zero(X)) -> ACTIVE(X)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(fact(x1)) = x1 POL(zero(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 31
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
POL(ACTIVE(x1)) = x1 POL(if(x1, x2, x3)) = 1 + x1 POL(fact(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 32
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
ACTIVE(fact(X)) -> ACTIVE(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(fact(X)) -> ACTIVE(X)
POL(ACTIVE(x1)) = x1 POL(fact(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 33
↳Dependency Graph
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(p(X)) -> PROPER(X)
PROPER(prod(X1, X2)) -> PROPER(X2)
PROPER(prod(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(zero(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(prod(x1, x2)) = x1 + x2 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(p(x1)) = x1 POL(zero(x1)) = x1 POL(add(x1, x2)) = 1 + x1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(p(X)) -> PROPER(X)
PROPER(prod(X1, X2)) -> PROPER(X2)
PROPER(prod(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(zero(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(p(X)) -> PROPER(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(prod(x1, x2)) = x1 + x2 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(p(x1)) = 1 + x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 35
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(prod(X1, X2)) -> PROPER(X2)
PROPER(prod(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(zero(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(prod(X1, X2)) -> PROPER(X2)
PROPER(prod(X1, X2)) -> PROPER(X1)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(prod(x1, x2)) = 1 + x1 + x2 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1 POL(s(x1)) = x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 36
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(s(X)) -> PROPER(X)
PROPER(zero(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(s(X)) -> PROPER(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1 POL(s(x1)) = 1 + x1 POL(zero(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 37
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(zero(X)) -> PROPER(X)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(zero(X)) -> PROPER(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1 POL(zero(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 38
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
POL(if(x1, x2, x3)) = 1 + x1 + x2 + x3 POL(PROPER(x1)) = x1 POL(fact(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 39
↳Polynomial Ordering
→DP Problem 10
↳Nar
PROPER(fact(X)) -> PROPER(X)
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(fact(X)) -> PROPER(X)
POL(PROPER(x1)) = x1 POL(fact(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 40
↳Dependency Graph
→DP Problem 10
↳Nar
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Narrowing Transformation
TOP(ok(X)) -> TOP(active(X))
TOP(mark(X)) -> TOP(proper(X))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
10 new Dependency Pairs are created:
TOP(mark(X)) -> TOP(proper(X))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(0)) -> TOP(ok(0))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
TOP(mark(true)) -> TOP(ok(true))
TOP(mark(false)) -> TOP(ok(false))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
→DP Problem 41
↳Narrowing Transformation
TOP(mark(false)) -> TOP(ok(false))
TOP(mark(true)) -> TOP(ok(true))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(0)) -> TOP(ok(0))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(ok(X)) -> TOP(active(X))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
19 new Dependency Pairs are created:
TOP(ok(X)) -> TOP(active(X))
TOP(ok(fact(X''))) -> TOP(mark(if(zero(X''), s(0), prod(X'', fact(p(X''))))))
TOP(ok(add(0, X''))) -> TOP(mark(X''))
TOP(ok(add(s(X''), Y'))) -> TOP(mark(s(add(X'', Y'))))
TOP(ok(prod(0, X''))) -> TOP(mark(0))
TOP(ok(prod(s(X''), Y'))) -> TOP(mark(add(Y', prod(X'', Y'))))
TOP(ok(if(true, X'', Y'))) -> TOP(mark(X''))
TOP(ok(if(false, X'', Y'))) -> TOP(mark(Y'))
TOP(ok(zero(0))) -> TOP(mark(true))
TOP(ok(zero(s(X'')))) -> TOP(mark(false))
TOP(ok(p(s(X'')))) -> TOP(mark(X''))
TOP(ok(fact(X''))) -> TOP(fact(active(X'')))
TOP(ok(if(X1', X2', X3'))) -> TOP(if(active(X1'), X2', X3'))
TOP(ok(zero(X''))) -> TOP(zero(active(X'')))
TOP(ok(s(X''))) -> TOP(s(active(X'')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(active(X1'), X2'))
TOP(ok(prod(X1', X2'))) -> TOP(prod(X1', active(X2')))
TOP(ok(p(X''))) -> TOP(p(active(X'')))
TOP(ok(add(X1', X2'))) -> TOP(add(active(X1'), X2'))
TOP(ok(add(X1', X2'))) -> TOP(add(X1', active(X2')))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
→DP Problem 41
↳Nar
...
→DP Problem 42
↳Polynomial Ordering
TOP(ok(add(X1', X2'))) -> TOP(add(X1', active(X2')))
TOP(ok(add(X1', X2'))) -> TOP(add(active(X1'), X2'))
TOP(ok(p(X''))) -> TOP(p(active(X'')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(X1', active(X2')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(active(X1'), X2'))
TOP(ok(s(X''))) -> TOP(s(active(X'')))
TOP(ok(zero(X''))) -> TOP(zero(active(X'')))
TOP(ok(if(X1', X2', X3'))) -> TOP(if(active(X1'), X2', X3'))
TOP(ok(fact(X''))) -> TOP(fact(active(X'')))
TOP(ok(p(s(X'')))) -> TOP(mark(X''))
TOP(ok(if(false, X'', Y'))) -> TOP(mark(Y'))
TOP(ok(if(true, X'', Y'))) -> TOP(mark(X''))
TOP(ok(prod(s(X''), Y'))) -> TOP(mark(add(Y', prod(X'', Y'))))
TOP(ok(add(s(X''), Y'))) -> TOP(mark(s(add(X'', Y'))))
TOP(ok(add(0, X''))) -> TOP(mark(X''))
TOP(ok(fact(X''))) -> TOP(mark(if(zero(X''), s(0), prod(X'', fact(p(X''))))))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(ok(p(s(X'')))) -> TOP(mark(X''))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
POL(proper(x1)) = x1 POL(prod(x1, x2)) = 0 POL(false) = 0 POL(fact(x1)) = 0 POL(true) = 0 POL(mark(x1)) = x1 POL(TOP(x1)) = 1 + x1 POL(ok(x1)) = x1 POL(add(x1, x2)) = x2 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 + x3 POL(0) = 0 POL(s(x1)) = x1 POL(p(x1)) = 1 + x1 POL(zero(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
→DP Problem 41
↳Nar
...
→DP Problem 43
↳Polynomial Ordering
TOP(ok(add(X1', X2'))) -> TOP(add(X1', active(X2')))
TOP(ok(add(X1', X2'))) -> TOP(add(active(X1'), X2'))
TOP(ok(p(X''))) -> TOP(p(active(X'')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(X1', active(X2')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(active(X1'), X2'))
TOP(ok(s(X''))) -> TOP(s(active(X'')))
TOP(ok(zero(X''))) -> TOP(zero(active(X'')))
TOP(ok(if(X1', X2', X3'))) -> TOP(if(active(X1'), X2', X3'))
TOP(ok(fact(X''))) -> TOP(fact(active(X'')))
TOP(ok(if(false, X'', Y'))) -> TOP(mark(Y'))
TOP(ok(if(true, X'', Y'))) -> TOP(mark(X''))
TOP(ok(prod(s(X''), Y'))) -> TOP(mark(add(Y', prod(X'', Y'))))
TOP(ok(add(s(X''), Y'))) -> TOP(mark(s(add(X'', Y'))))
TOP(ok(add(0, X''))) -> TOP(mark(X''))
TOP(ok(fact(X''))) -> TOP(mark(if(zero(X''), s(0), prod(X'', fact(p(X''))))))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(ok(if(false, X'', Y'))) -> TOP(mark(Y'))
TOP(ok(if(true, X'', Y'))) -> TOP(mark(X''))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
POL(proper(x1)) = x1 POL(prod(x1, x2)) = 0 POL(false) = 0 POL(fact(x1)) = 1 POL(true) = 0 POL(mark(x1)) = x1 POL(TOP(x1)) = 1 + x1 POL(ok(x1)) = x1 POL(add(x1, x2)) = x2 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 1 + x2 + x3 POL(0) = 0 POL(s(x1)) = x1 POL(p(x1)) = x1 POL(zero(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
→DP Problem 41
↳Nar
...
→DP Problem 44
↳Polynomial Ordering
TOP(ok(add(X1', X2'))) -> TOP(add(X1', active(X2')))
TOP(ok(add(X1', X2'))) -> TOP(add(active(X1'), X2'))
TOP(ok(p(X''))) -> TOP(p(active(X'')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(X1', active(X2')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(active(X1'), X2'))
TOP(ok(s(X''))) -> TOP(s(active(X'')))
TOP(ok(zero(X''))) -> TOP(zero(active(X'')))
TOP(ok(if(X1', X2', X3'))) -> TOP(if(active(X1'), X2', X3'))
TOP(ok(fact(X''))) -> TOP(fact(active(X'')))
TOP(ok(prod(s(X''), Y'))) -> TOP(mark(add(Y', prod(X'', Y'))))
TOP(ok(add(s(X''), Y'))) -> TOP(mark(s(add(X'', Y'))))
TOP(ok(add(0, X''))) -> TOP(mark(X''))
TOP(ok(fact(X''))) -> TOP(mark(if(zero(X''), s(0), prod(X'', fact(p(X''))))))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(ok(fact(X''))) -> TOP(mark(if(zero(X''), s(0), prod(X'', fact(p(X''))))))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
POL(proper(x1)) = x1 POL(prod(x1, x2)) = 0 POL(false) = 0 POL(fact(x1)) = 1 POL(true) = 0 POL(mark(x1)) = x1 POL(TOP(x1)) = 1 + x1 POL(ok(x1)) = x1 POL(add(x1, x2)) = x2 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 + x3 POL(0) = 0 POL(s(x1)) = x1 POL(p(x1)) = x1 POL(zero(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Nar
→DP Problem 41
↳Nar
...
→DP Problem 45
↳Remaining Obligation(s)
TOP(ok(add(X1', X2'))) -> TOP(add(X1', active(X2')))
TOP(ok(add(X1', X2'))) -> TOP(add(active(X1'), X2'))
TOP(ok(p(X''))) -> TOP(p(active(X'')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(X1', active(X2')))
TOP(ok(prod(X1', X2'))) -> TOP(prod(active(X1'), X2'))
TOP(ok(s(X''))) -> TOP(s(active(X'')))
TOP(ok(zero(X''))) -> TOP(zero(active(X'')))
TOP(ok(if(X1', X2', X3'))) -> TOP(if(active(X1'), X2', X3'))
TOP(ok(fact(X''))) -> TOP(fact(active(X'')))
TOP(ok(prod(s(X''), Y'))) -> TOP(mark(add(Y', prod(X'', Y'))))
TOP(ok(add(s(X''), Y'))) -> TOP(mark(s(add(X'', Y'))))
TOP(ok(add(0, X''))) -> TOP(mark(X''))
TOP(mark(p(X''))) -> TOP(p(proper(X'')))
TOP(mark(prod(X1', X2'))) -> TOP(prod(proper(X1'), proper(X2')))
TOP(mark(s(X''))) -> TOP(s(proper(X'')))
TOP(mark(zero(X''))) -> TOP(zero(proper(X'')))
TOP(mark(if(X1', X2', X3'))) -> TOP(if(proper(X1'), proper(X2'), proper(X3')))
TOP(mark(fact(X''))) -> TOP(fact(proper(X'')))
TOP(mark(add(X1', X2'))) -> TOP(add(proper(X1'), proper(X2')))
active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(prod(0, X)) -> mark(0)
active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(zero(0)) -> mark(true)
active(zero(s(X))) -> mark(false)
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1, X2)) -> prod(active(X1), X2)
active(prod(X1, X2)) -> prod(X1, active(X2))
active(p(X)) -> p(active(X))
active(add(X1, X2)) -> add(active(X1), X2)
active(add(X1, X2)) -> add(X1, active(X2))
fact(mark(X)) -> mark(fact(X))
fact(ok(X)) -> ok(fact(X))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
zero(mark(X)) -> mark(zero(X))
zero(ok(X)) -> ok(zero(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
prod(mark(X1), X2) -> mark(prod(X1, X2))
prod(X1, mark(X2)) -> mark(prod(X1, X2))
prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
add(mark(X1), X2) -> mark(add(X1, X2))
add(X1, mark(X2)) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0) -> ok(0)
proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))