0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 AND
↳5 QDP
↳6 QDPOrderProof (⇔)
↳7 QDP
↳8 QDPOrderProof (⇔)
↳9 QDP
↳10 PisEmptyProof (⇔)
↳11 TRUE
↳12 QDP
↳13 QDPOrderProof (⇔)
↳14 QDP
↳15 QDPOrderProof (⇔)
↳16 QDP
↳17 PisEmptyProof (⇔)
↳18 TRUE
↳19 QDP
↳20 QDPOrderProof (⇔)
↳21 QDP
↳22 QDPOrderProof (⇔)
↳23 QDP
↳24 PisEmptyProof (⇔)
↳25 TRUE
↳26 QDP
↳27 QDPOrderProof (⇔)
↳28 QDP
↳29 QDPOrderProof (⇔)
↳30 QDP
↳31 PisEmptyProof (⇔)
↳32 TRUE
↳33 QDP
↳34 QDPOrderProof (⇔)
↳35 QDP
↳36 QDPOrderProof (⇔)
↳37 QDP
↳38 PisEmptyProof (⇔)
↳39 TRUE
↳40 QDP
↳41 QDPOrderProof (⇔)
↳42 QDP
↳43 QDPOrderProof (⇔)
↳44 QDP
↳45 PisEmptyProof (⇔)
↳46 TRUE
↳47 QDP
↳48 QDPOrderProof (⇔)
↳49 QDP
↳50 QDPOrderProof (⇔)
↳51 QDP
↳52 PisEmptyProof (⇔)
↳53 TRUE
↳54 QDP
↳55 QDPOrderProof (⇔)
↳56 QDP
↳57 QDPOrderProof (⇔)
↳58 QDP
↳59 PisEmptyProof (⇔)
↳60 TRUE
↳61 QDP
↳62 QDPOrderProof (⇔)
↳63 QDP
↳64 QDPOrderProof (⇔)
↳65 QDP
↳66 PisEmptyProof (⇔)
↳67 TRUE
↳68 QDP
↳69 QDPOrderProof (⇔)
↳70 QDP
↳71 QDPOrderProof (⇔)
↳72 QDP
↳73 QDPOrderProof (⇔)
↳74 QDP
↳75 PisEmptyProof (⇔)
↳76 TRUE
↳77 QDP
↳78 QDPOrderProof (⇔)
↳79 QDP
↳80 QDPOrderProof (⇔)
↳81 QDP
↳82 QDPOrderProof (⇔)
↳83 QDP
↳84 PisEmptyProof (⇔)
↳85 TRUE
↳86 QDP
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
ACTIVE(zeros) → CONS(0, zeros)
ACTIVE(U11(tt, L)) → U121(tt, L)
ACTIVE(U12(tt, L)) → S(length(L))
ACTIVE(U12(tt, L)) → LENGTH(L)
ACTIVE(U21(tt, IL, M, N)) → U221(tt, IL, M, N)
ACTIVE(U22(tt, IL, M, N)) → U231(tt, IL, M, N)
ACTIVE(U23(tt, IL, M, N)) → CONS(N, take(M, IL))
ACTIVE(U23(tt, IL, M, N)) → TAKE(M, IL)
ACTIVE(length(cons(N, L))) → U111(tt, L)
ACTIVE(take(s(M), cons(N, IL))) → U211(tt, IL, M, N)
ACTIVE(cons(X1, X2)) → CONS(active(X1), X2)
ACTIVE(cons(X1, X2)) → ACTIVE(X1)
ACTIVE(U11(X1, X2)) → U111(active(X1), X2)
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(X1, X2)) → U121(active(X1), X2)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
ACTIVE(s(X)) → S(active(X))
ACTIVE(s(X)) → ACTIVE(X)
ACTIVE(length(X)) → LENGTH(active(X))
ACTIVE(length(X)) → ACTIVE(X)
ACTIVE(U21(X1, X2, X3, X4)) → U211(active(X1), X2, X3, X4)
ACTIVE(U21(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U22(X1, X2, X3, X4)) → U221(active(X1), X2, X3, X4)
ACTIVE(U22(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U23(X1, X2, X3, X4)) → U231(active(X1), X2, X3, X4)
ACTIVE(U23(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → TAKE(active(X1), X2)
ACTIVE(take(X1, X2)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → TAKE(X1, active(X2))
ACTIVE(take(X1, X2)) → ACTIVE(X2)
CONS(mark(X1), X2) → CONS(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)
S(mark(X)) → S(X)
LENGTH(mark(X)) → LENGTH(X)
U211(mark(X1), X2, X3, X4) → U211(X1, X2, X3, X4)
U221(mark(X1), X2, X3, X4) → U221(X1, X2, X3, X4)
U231(mark(X1), X2, X3, X4) → U231(X1, X2, X3, X4)
TAKE(mark(X1), X2) → TAKE(X1, X2)
TAKE(X1, mark(X2)) → TAKE(X1, X2)
PROPER(cons(X1, X2)) → CONS(proper(X1), proper(X2))
PROPER(cons(X1, X2)) → PROPER(X1)
PROPER(cons(X1, X2)) → PROPER(X2)
PROPER(U11(X1, X2)) → U111(proper(X1), proper(X2))
PROPER(U11(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X2)
PROPER(U12(X1, X2)) → U121(proper(X1), proper(X2))
PROPER(U12(X1, X2)) → PROPER(X1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(s(X)) → S(proper(X))
PROPER(s(X)) → PROPER(X)
PROPER(length(X)) → LENGTH(proper(X))
PROPER(length(X)) → PROPER(X)
PROPER(U21(X1, X2, X3, X4)) → U211(proper(X1), proper(X2), proper(X3), proper(X4))
PROPER(U21(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U22(X1, X2, X3, X4)) → U221(proper(X1), proper(X2), proper(X3), proper(X4))
PROPER(U22(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U23(X1, X2, X3, X4)) → U231(proper(X1), proper(X2), proper(X3), proper(X4))
PROPER(U23(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X4)
PROPER(take(X1, X2)) → TAKE(proper(X1), proper(X2))
PROPER(take(X1, X2)) → PROPER(X1)
PROPER(take(X1, X2)) → PROPER(X2)
CONS(ok(X1), ok(X2)) → CONS(X1, X2)
U111(ok(X1), ok(X2)) → U111(X1, X2)
U121(ok(X1), ok(X2)) → U121(X1, X2)
S(ok(X)) → S(X)
LENGTH(ok(X)) → LENGTH(X)
U211(ok(X1), ok(X2), ok(X3), ok(X4)) → U211(X1, X2, X3, X4)
U221(ok(X1), ok(X2), ok(X3), ok(X4)) → U221(X1, X2, X3, X4)
U231(ok(X1), ok(X2), ok(X3), ok(X4)) → U231(X1, X2, X3, X4)
TAKE(ok(X1), ok(X2)) → TAKE(X1, X2)
TOP(mark(X)) → TOP(proper(X))
TOP(mark(X)) → PROPER(X)
TOP(ok(X)) → TOP(active(X))
TOP(ok(X)) → ACTIVE(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
TAKE(X1, mark(X2)) → TAKE(X1, X2)
TAKE(mark(X1), X2) → TAKE(X1, X2)
TAKE(ok(X1), ok(X2)) → TAKE(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
TAKE(X1, mark(X2)) → TAKE(X1, X2)
TAKE(mark(X1), X2) → TAKE(X1, X2)
TAKE2 > mark1
active1 > zeros > 0 > mark1
active1 > cons2 > U112 > mark1
active1 > cons2 > tt > length1 > mark1
active1 > cons2 > tt > U224 > mark1
active1 > cons2 > tt > take2 > mark1
active1 > cons2 > U214 > mark1
active1 > U122 > length1 > mark1
active1 > s1 > tt > length1 > mark1
active1 > s1 > tt > U224 > mark1
active1 > s1 > tt > take2 > mark1
active1 > s1 > U214 > mark1
active1 > U234 > take2 > mark1
active1 > nil > mark1
proper1 > zeros > 0 > mark1
proper1 > cons2 > U112 > mark1
proper1 > cons2 > tt > length1 > mark1
proper1 > cons2 > tt > U224 > mark1
proper1 > cons2 > tt > take2 > mark1
proper1 > cons2 > U214 > mark1
proper1 > U122 > length1 > mark1
proper1 > s1 > tt > length1 > mark1
proper1 > s1 > tt > U224 > mark1
proper1 > s1 > tt > take2 > mark1
proper1 > s1 > U214 > mark1
proper1 > U234 > take2 > mark1
proper1 > nil > mark1
top > mark1
TAKE2: multiset
mark1: multiset
active1: [1]
zeros: multiset
cons2: [1,2]
0: multiset
U112: [2,1]
tt: multiset
U122: [1,2]
s1: [1]
length1: [1]
U214: [1,3,4,2]
U224: [4,3,1,2]
U234: [1,3,4,2]
take2: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
TAKE(ok(X1), ok(X2)) → TAKE(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
TAKE(ok(X1), ok(X2)) → TAKE(X1, X2)
active1 > zeros > ok1
active1 > 0 > ok1
active1 > tt > ok1
active1 > nil > ok1
proper > zeros > ok1
proper > 0 > ok1
proper > tt > ok1
proper > nil > ok1
TAKE2: [1,2]
ok1: [1]
active1: [1]
zeros: multiset
0: multiset
tt: multiset
nil: multiset
proper: multiset
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U231(ok(X1), ok(X2), ok(X3), ok(X4)) → U231(X1, X2, X3, X4)
U231(mark(X1), X2, X3, X4) → U231(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U231(ok(X1), ok(X2), ok(X3), ok(X4)) → U231(X1, X2, X3, X4)
U23^13 > ok1
active1 > zeros > 0 > ok1
active1 > tt > U221 > U232 > ok1
active1 > U122 > ok1
active1 > length1 > 0 > ok1
active1 > U211 > ok1
active1 > nil > 0 > ok1
proper1 > zeros > 0 > ok1
proper1 > tt > U221 > U232 > ok1
proper1 > U122 > ok1
proper1 > length1 > 0 > ok1
proper1 > U211 > ok1
proper1 > nil > 0 > ok1
top > ok1
U23^13: [2,1,3]
ok1: multiset
active1: multiset
zeros: multiset
0: multiset
tt: multiset
U122: [2,1]
length1: [1]
U211: [1]
U221: [1]
U232: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U231(mark(X1), X2, X3, X4) → U231(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U231(mark(X1), X2, X3, X4) → U231(X1, X2, X3, X4)
active1 > zeros > cons2 > ok > U214 > mark1
active1 > zeros > 0 > nil
active1 > zeros > 0 > ok > U214 > mark1
active1 > U112 > ok > U214 > mark1
active1 > tt > s1 > ok > U214 > mark1
active1 > tt > U224 > ok > U214 > mark1
active1 > tt > U234 > ok > U214 > mark1
active1 > tt > take2 > nil
active1 > tt > take2 > ok > U214 > mark1
active1 > U122 > s1 > ok > U214 > mark1
proper1 > zeros > cons2 > ok > U214 > mark1
proper1 > zeros > 0 > nil
proper1 > zeros > 0 > ok > U214 > mark1
proper1 > U112 > ok > U214 > mark1
proper1 > tt > s1 > ok > U214 > mark1
proper1 > tt > U224 > ok > U214 > mark1
proper1 > tt > U234 > ok > U214 > mark1
proper1 > tt > take2 > nil
proper1 > tt > take2 > ok > U214 > mark1
proper1 > U122 > s1 > ok > U214 > mark1
U23^11: [1]
mark1: [1]
active1: [1]
zeros: multiset
cons2: [1,2]
0: multiset
U112: [1,2]
tt: multiset
U122: multiset
s1: [1]
U214: [1,2,3,4]
U224: [3,1,2,4]
U234: [1,4,3,2]
take2: [1,2]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U221(ok(X1), ok(X2), ok(X3), ok(X4)) → U221(X1, X2, X3, X4)
U221(mark(X1), X2, X3, X4) → U221(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U221(ok(X1), ok(X2), ok(X3), ok(X4)) → U221(X1, X2, X3, X4)
U22^13 > ok1
active1 > zeros > 0 > ok1
active1 > tt > U221 > U232 > ok1
active1 > U122 > ok1
active1 > length1 > 0 > ok1
active1 > U211 > ok1
active1 > nil > 0 > ok1
proper1 > zeros > 0 > ok1
proper1 > tt > U221 > U232 > ok1
proper1 > U122 > ok1
proper1 > length1 > 0 > ok1
proper1 > U211 > ok1
proper1 > nil > 0 > ok1
top > ok1
U22^13: [2,1,3]
ok1: multiset
active1: multiset
zeros: multiset
0: multiset
tt: multiset
U122: [2,1]
length1: [1]
U211: [1]
U221: [1]
U232: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U221(mark(X1), X2, X3, X4) → U221(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U221(mark(X1), X2, X3, X4) → U221(X1, X2, X3, X4)
active1 > zeros > cons2 > ok > U214 > mark1
active1 > zeros > 0 > nil
active1 > zeros > 0 > ok > U214 > mark1
active1 > U112 > ok > U214 > mark1
active1 > tt > s1 > ok > U214 > mark1
active1 > tt > U224 > ok > U214 > mark1
active1 > tt > U234 > ok > U214 > mark1
active1 > tt > take2 > nil
active1 > tt > take2 > ok > U214 > mark1
active1 > U122 > s1 > ok > U214 > mark1
proper1 > zeros > cons2 > ok > U214 > mark1
proper1 > zeros > 0 > nil
proper1 > zeros > 0 > ok > U214 > mark1
proper1 > U112 > ok > U214 > mark1
proper1 > tt > s1 > ok > U214 > mark1
proper1 > tt > U224 > ok > U214 > mark1
proper1 > tt > U234 > ok > U214 > mark1
proper1 > tt > take2 > nil
proper1 > tt > take2 > ok > U214 > mark1
proper1 > U122 > s1 > ok > U214 > mark1
U22^11: [1]
mark1: [1]
active1: [1]
zeros: multiset
cons2: [1,2]
0: multiset
U112: [1,2]
tt: multiset
U122: multiset
s1: [1]
U214: [1,2,3,4]
U224: [3,1,2,4]
U234: [1,4,3,2]
take2: [1,2]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U211(ok(X1), ok(X2), ok(X3), ok(X4)) → U211(X1, X2, X3, X4)
U211(mark(X1), X2, X3, X4) → U211(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U211(mark(X1), X2, X3, X4) → U211(X1, X2, X3, X4)
U21^14 > mark1
active1 > zeros > 0 > mark1
active1 > s1 > tt > cons2 > U112 > mark1
active1 > s1 > tt > cons2 > U214 > mark1
active1 > s1 > tt > U122 > mark1
active1 > s1 > tt > U224 > mark1
active1 > s1 > tt > take2 > mark1
active1 > U234 > cons2 > U112 > mark1
active1 > U234 > cons2 > U214 > mark1
active1 > U234 > take2 > mark1
active1 > nil > 0 > mark1
top > mark1
U21^14: [3,4,2,1]
mark1: [1]
active1: [1]
zeros: multiset
cons2: [1,2]
0: multiset
U112: [1,2]
tt: multiset
U122: [2,1]
s1: [1]
U214: [2,1,3,4]
U224: [3,2,4,1]
U234: [1,4,2,3]
take2: [1,2]
nil: multiset
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U211(ok(X1), ok(X2), ok(X3), ok(X4)) → U211(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U211(ok(X1), ok(X2), ok(X3), ok(X4)) → U211(X1, X2, X3, X4)
active1 > cons2 > ok1 > mark
active1 > U121 > length1 > ok1 > mark
active1 > U222 > ok1 > mark
zeros > cons2 > ok1 > mark
0 > nil > ok1 > mark
tt > cons2 > ok1 > mark
tt > U121 > length1 > ok1 > mark
tt > U222 > ok1 > mark
top > proper1 > cons2 > ok1 > mark
top > proper1 > U121 > length1 > ok1 > mark
top > proper1 > U222 > ok1 > mark
ok1: [1]
active1: [1]
zeros: multiset
mark: []
cons2: [2,1]
0: multiset
tt: multiset
U121: [1]
length1: multiset
U222: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
LENGTH(ok(X)) → LENGTH(X)
LENGTH(mark(X)) → LENGTH(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LENGTH(mark(X)) → LENGTH(X)
LENGTH1 > mark1
active1 > zeros > cons2 > mark1
active1 > zeros > 0 > mark1
active1 > tt > cons2 > mark1
active1 > tt > U122 > mark1
active1 > tt > s1 > U214 > mark1
active1 > tt > U224 > U234 > mark1
active1 > tt > take2 > U214 > mark1
active1 > length1 > 0 > mark1
active1 > length1 > U112 > U122 > mark1
active1 > nil > 0 > mark1
proper1 > zeros > cons2 > mark1
proper1 > zeros > 0 > mark1
proper1 > tt > cons2 > mark1
proper1 > tt > U122 > mark1
proper1 > tt > s1 > U214 > mark1
proper1 > tt > U224 > U234 > mark1
proper1 > tt > take2 > U214 > mark1
proper1 > length1 > 0 > mark1
proper1 > length1 > U112 > U122 > mark1
proper1 > nil > 0 > mark1
top > mark1
LENGTH1: [1]
mark1: multiset
active1: [1]
zeros: multiset
cons2: [2,1]
0: multiset
U112: [2,1]
tt: multiset
U122: [2,1]
s1: [1]
length1: [1]
U214: [1,2,4,3]
U224: [4,3,1,2]
U234: [3,2,1,4]
take2: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
LENGTH(ok(X)) → LENGTH(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LENGTH(ok(X)) → LENGTH(X)
LENGTH1 > mark
proper > zeros > mark
proper > 0 > nil > ok1 > mark
proper > tt > ok1 > mark
top > active1 > zeros > mark
top > active1 > 0 > nil > ok1 > mark
LENGTH1: [1]
ok1: [1]
active1: [1]
zeros: multiset
mark: []
0: multiset
tt: multiset
nil: multiset
proper: multiset
top: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
S(ok(X)) → S(X)
S(mark(X)) → S(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
S(mark(X)) → S(X)
S1 > mark1
active1 > zeros > cons2 > mark1
active1 > zeros > 0 > mark1
active1 > tt > cons2 > mark1
active1 > tt > U122 > mark1
active1 > tt > s1 > U214 > mark1
active1 > tt > U224 > U234 > mark1
active1 > tt > take2 > U214 > mark1
active1 > length1 > 0 > mark1
active1 > length1 > U112 > U122 > mark1
active1 > nil > 0 > mark1
proper1 > zeros > cons2 > mark1
proper1 > zeros > 0 > mark1
proper1 > tt > cons2 > mark1
proper1 > tt > U122 > mark1
proper1 > tt > s1 > U214 > mark1
proper1 > tt > U224 > U234 > mark1
proper1 > tt > take2 > U214 > mark1
proper1 > length1 > 0 > mark1
proper1 > length1 > U112 > U122 > mark1
proper1 > nil > 0 > mark1
top > mark1
S1: [1]
mark1: multiset
active1: [1]
zeros: multiset
cons2: [2,1]
0: multiset
U112: [2,1]
tt: multiset
U122: [2,1]
s1: [1]
length1: [1]
U214: [1,2,4,3]
U224: [4,3,1,2]
U234: [3,2,1,4]
take2: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
S(ok(X)) → S(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
S(ok(X)) → S(X)
S1 > mark
proper > zeros > mark
proper > 0 > nil > ok1 > mark
proper > tt > ok1 > mark
top > active1 > zeros > mark
top > active1 > 0 > nil > ok1 > mark
S1: [1]
ok1: [1]
active1: [1]
zeros: multiset
mark: []
0: multiset
tt: multiset
nil: multiset
proper: multiset
top: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U121(ok(X1), ok(X2)) → U121(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U121(ok(X1), ok(X2)) → U121(X1, X2)
U12^11 > mark
0 > nil > ok1 > mark
tt > s1 > ok1 > mark
tt > U223 > ok1 > mark
tt > U232 > take1 > ok1 > mark
proper1 > zeros > ok1 > mark
proper1 > s1 > ok1 > mark
proper1 > U212 > U223 > ok1 > mark
proper1 > U232 > take1 > ok1 > mark
proper1 > nil > ok1 > mark
top > mark
U12^11: multiset
ok1: [1]
mark: []
zeros: multiset
0: multiset
tt: multiset
s1: [1]
U212: [2,1]
U223: [2,1,3]
U232: [2,1]
take1: [1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U121(mark(X1), X2) → U121(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U121(mark(X1), X2) → U121(X1, X2)
active1 > 0 > nil > ok > cons2 > U112 > mark1 > U12^12
active1 > 0 > nil > ok > cons2 > U214 > mark1 > U12^12
active1 > 0 > nil > ok > U122 > length1 > mark1 > U12^12
active1 > 0 > nil > ok > s1 > U214 > mark1 > U12^12
active1 > 0 > nil > ok > U224 > mark1 > U12^12
active1 > 0 > nil > ok > U234 > mark1 > U12^12
active1 > 0 > nil > ok > take2 > U214 > mark1 > U12^12
active1 > tt > ok > cons2 > U112 > mark1 > U12^12
active1 > tt > ok > cons2 > U214 > mark1 > U12^12
active1 > tt > ok > U122 > length1 > mark1 > U12^12
active1 > tt > ok > s1 > U214 > mark1 > U12^12
active1 > tt > ok > U224 > mark1 > U12^12
active1 > tt > ok > U234 > mark1 > U12^12
active1 > tt > ok > take2 > U214 > mark1 > U12^12
zeros > 0 > nil > ok > cons2 > U112 > mark1 > U12^12
zeros > 0 > nil > ok > cons2 > U214 > mark1 > U12^12
zeros > 0 > nil > ok > U122 > length1 > mark1 > U12^12
zeros > 0 > nil > ok > s1 > U214 > mark1 > U12^12
zeros > 0 > nil > ok > U224 > mark1 > U12^12
zeros > 0 > nil > ok > U234 > mark1 > U12^12
zeros > 0 > nil > ok > take2 > U214 > mark1 > U12^12
top > proper1 > cons2 > U112 > mark1 > U12^12
top > proper1 > cons2 > U214 > mark1 > U12^12
top > proper1 > U122 > length1 > mark1 > U12^12
top > proper1 > s1 > U214 > mark1 > U12^12
top > proper1 > U224 > mark1 > U12^12
top > proper1 > U234 > mark1 > U12^12
top > proper1 > take2 > U214 > mark1 > U12^12
U12^12: multiset
mark1: [1]
active1: [1]
zeros: multiset
cons2: [1,2]
0: multiset
U112: [1,2]
tt: multiset
U122: [1,2]
s1: [1]
length1: [1]
U214: [2,4,3,1]
U224: [4,1,3,2]
U234: multiset
take2: [2,1]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U111(ok(X1), ok(X2)) → U111(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U111(ok(X1), ok(X2)) → U111(X1, X2)
active1 > zeros > cons1 > ok1
active1 > zeros > 0 > ok1
active1 > U213 > tt > U122 > ok1
active1 > U213 > tt > U232 > cons1 > ok1
active1 > U213 > tt > take2 > ok1
active1 > U213 > U223 > U232 > cons1 > ok1
active1 > nil > ok1
proper1 > zeros > cons1 > ok1
proper1 > zeros > 0 > ok1
proper1 > U213 > tt > U122 > ok1
proper1 > U213 > tt > U232 > cons1 > ok1
proper1 > U213 > tt > take2 > ok1
proper1 > U213 > U223 > U232 > cons1 > ok1
proper1 > nil > ok1
top > ok1
ok1: [1]
active1: multiset
zeros: multiset
cons1: [1]
0: multiset
tt: multiset
U122: [1,2]
U213: [2,3,1]
U223: [2,3,1]
U232: multiset
take2: [2,1]
nil: multiset
proper1: [1]
top: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
U111(mark(X1), X2) → U111(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U111(mark(X1), X2) → U111(X1, X2)
active1 > zeros > U11^12
active1 > 0 > mark1 > U11^12
active1 > 0 > ok > U11^12
active1 > tt > cons2 > U112 > U122 > s1 > mark1 > U11^12
active1 > tt > cons2 > U112 > U122 > s1 > ok > U11^12
active1 > tt > cons2 > U214 > U224 > mark1 > U11^12
active1 > tt > cons2 > U214 > U224 > ok > U11^12
active1 > tt > length1 > U112 > U122 > s1 > mark1 > U11^12
active1 > tt > length1 > U112 > U122 > s1 > ok > U11^12
active1 > tt > U234 > mark1 > U11^12
active1 > tt > U234 > ok > U11^12
active1 > take2 > U214 > U224 > mark1 > U11^12
active1 > take2 > U214 > U224 > ok > U11^12
active1 > take2 > nil > mark1 > U11^12
active1 > take2 > nil > ok > U11^12
proper1 > zeros > U11^12
proper1 > 0 > mark1 > U11^12
proper1 > 0 > ok > U11^12
proper1 > tt > cons2 > U112 > U122 > s1 > mark1 > U11^12
proper1 > tt > cons2 > U112 > U122 > s1 > ok > U11^12
proper1 > tt > cons2 > U214 > U224 > mark1 > U11^12
proper1 > tt > cons2 > U214 > U224 > ok > U11^12
proper1 > tt > length1 > U112 > U122 > s1 > mark1 > U11^12
proper1 > tt > length1 > U112 > U122 > s1 > ok > U11^12
proper1 > tt > U234 > mark1 > U11^12
proper1 > tt > U234 > ok > U11^12
proper1 > take2 > U214 > U224 > mark1 > U11^12
proper1 > take2 > U214 > U224 > ok > U11^12
proper1 > take2 > nil > mark1 > U11^12
proper1 > take2 > nil > ok > U11^12
top > U11^12
U11^12: [2,1]
mark1: [1]
active1: [1]
zeros: multiset
cons2: [2,1]
0: multiset
U112: [2,1]
tt: multiset
U122: [1,2]
s1: [1]
length1: multiset
U214: [1,3,2,4]
U224: [1,3,4,2]
U234: [1,3,4,2]
take2: [1,2]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
CONS(ok(X1), ok(X2)) → CONS(X1, X2)
CONS(mark(X1), X2) → CONS(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONS(ok(X1), ok(X2)) → CONS(X1, X2)
active1 > zeros > cons1 > ok1
active1 > zeros > 0 > ok1
active1 > U213 > tt > U122 > ok1
active1 > U213 > tt > U232 > cons1 > ok1
active1 > U213 > tt > take2 > ok1
active1 > U213 > U223 > U232 > cons1 > ok1
active1 > nil > ok1
proper1 > zeros > cons1 > ok1
proper1 > zeros > 0 > ok1
proper1 > U213 > tt > U122 > ok1
proper1 > U213 > tt > U232 > cons1 > ok1
proper1 > U213 > tt > take2 > ok1
proper1 > U213 > U223 > U232 > cons1 > ok1
proper1 > nil > ok1
top > ok1
ok1: [1]
active1: multiset
zeros: multiset
cons1: [1]
0: multiset
tt: multiset
U122: [1,2]
U213: [2,3,1]
U223: [2,3,1]
U232: multiset
take2: [2,1]
nil: multiset
proper1: [1]
top: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
CONS(mark(X1), X2) → CONS(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONS(mark(X1), X2) → CONS(X1, X2)
active1 > zeros > CONS2
active1 > 0 > mark1 > CONS2
active1 > 0 > ok > CONS2
active1 > tt > cons2 > U112 > U122 > s1 > mark1 > CONS2
active1 > tt > cons2 > U112 > U122 > s1 > ok > CONS2
active1 > tt > cons2 > U214 > U224 > mark1 > CONS2
active1 > tt > cons2 > U214 > U224 > ok > CONS2
active1 > tt > length1 > U112 > U122 > s1 > mark1 > CONS2
active1 > tt > length1 > U112 > U122 > s1 > ok > CONS2
active1 > tt > U234 > mark1 > CONS2
active1 > tt > U234 > ok > CONS2
active1 > take2 > U214 > U224 > mark1 > CONS2
active1 > take2 > U214 > U224 > ok > CONS2
active1 > take2 > nil > mark1 > CONS2
active1 > take2 > nil > ok > CONS2
proper1 > zeros > CONS2
proper1 > 0 > mark1 > CONS2
proper1 > 0 > ok > CONS2
proper1 > tt > cons2 > U112 > U122 > s1 > mark1 > CONS2
proper1 > tt > cons2 > U112 > U122 > s1 > ok > CONS2
proper1 > tt > cons2 > U214 > U224 > mark1 > CONS2
proper1 > tt > cons2 > U214 > U224 > ok > CONS2
proper1 > tt > length1 > U112 > U122 > s1 > mark1 > CONS2
proper1 > tt > length1 > U112 > U122 > s1 > ok > CONS2
proper1 > tt > U234 > mark1 > CONS2
proper1 > tt > U234 > ok > CONS2
proper1 > take2 > U214 > U224 > mark1 > CONS2
proper1 > take2 > U214 > U224 > ok > CONS2
proper1 > take2 > nil > mark1 > CONS2
proper1 > take2 > nil > ok > CONS2
top > CONS2
CONS2: [2,1]
mark1: [1]
active1: [1]
zeros: multiset
cons2: [2,1]
0: multiset
U112: [2,1]
tt: multiset
U122: [1,2]
s1: [1]
length1: multiset
U214: [1,3,2,4]
U224: [1,3,4,2]
U234: [1,3,4,2]
take2: [1,2]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
PROPER(cons(X1, X2)) → PROPER(X2)
PROPER(cons(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X2)
PROPER(U12(X1, X2)) → PROPER(X1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(s(X)) → PROPER(X)
PROPER(length(X)) → PROPER(X)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X4)
PROPER(take(X1, X2)) → PROPER(X1)
PROPER(take(X1, X2)) → PROPER(X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PROPER(cons(X1, X2)) → PROPER(X2)
PROPER(cons(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X2)
PROPER(U12(X1, X2)) → PROPER(X1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U21(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U22(X1, X2, X3, X4)) → PROPER(X4)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X1)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X2)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X3)
PROPER(U23(X1, X2, X3, X4)) → PROPER(X4)
PROPER(take(X1, X2)) → PROPER(X1)
PROPER(take(X1, X2)) → PROPER(X2)
top > proper1 > U214 > tt > cons2 > U112
top > proper1 > U214 > tt > cons2 > mark
top > proper1 > U214 > tt > U122 > mark
top > proper1 > U214 > tt > U224 > mark
top > proper1 > U234 > cons2 > U112
top > proper1 > U234 > cons2 > mark
top > proper1 > take2 > tt > cons2 > U112
top > proper1 > take2 > tt > cons2 > mark
top > proper1 > take2 > tt > U122 > mark
top > proper1 > take2 > tt > U224 > mark
top > proper1 > take2 > nil > mark
top > proper1 > take2 > nil > 0
top > proper1 > zeros > mark
top > proper1 > zeros > 0
cons2: multiset
U112: multiset
U122: [1,2]
U214: [3,4,1,2]
U224: [2,3,1,4]
U234: [1,4,2,3]
take2: [1,2]
zeros: multiset
mark: []
0: multiset
tt: multiset
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
PROPER(s(X)) → PROPER(X)
PROPER(length(X)) → PROPER(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PROPER(s(X)) → PROPER(X)
active1 > zeros > U222
active1 > tt > ok > s1 > PROPER1 > U222
active1 > tt > ok > U112 > U222
active1 > tt > ok > U211 > U222
active1 > tt > ok > U232 > U222
active1 > nil > 0 > U222
proper1 > zeros > U222
proper1 > nil > 0 > U222
proper1 > ok > s1 > PROPER1 > U222
proper1 > ok > U112 > U222
proper1 > ok > U211 > U222
proper1 > ok > U232 > U222
top > U222
PROPER1: multiset
s1: [1]
active1: [1]
zeros: multiset
0: multiset
U112: [1,2]
tt: multiset
U211: [1]
U222: [1,2]
U232: [2,1]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
PROPER(length(X)) → PROPER(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PROPER(length(X)) → PROPER(X)
PROPER1 > take2
cons > proper1 > 0 > mark > take2
cons > proper1 > s > active1 > length1 > mark > take2
cons > proper1 > s > active1 > length1 > U112 > take2
cons > proper1 > s > active1 > length1 > tt > take2
cons > proper1 > s > active1 > zeros > mark > take2
cons > proper1 > s > active1 > U213 > mark > take2
cons > proper1 > s > active1 > U213 > tt > take2
cons > proper1 > s > active1 > U213 > U224 > take2
cons > proper1 > s > active1 > U233 > take2
nil > 0 > mark > take2
top > proper1 > 0 > mark > take2
top > proper1 > s > active1 > length1 > mark > take2
top > proper1 > s > active1 > length1 > U112 > take2
top > proper1 > s > active1 > length1 > tt > take2
top > proper1 > s > active1 > zeros > mark > take2
top > proper1 > s > active1 > U213 > mark > take2
top > proper1 > s > active1 > U213 > tt > take2
top > proper1 > s > active1 > U213 > U224 > take2
top > proper1 > s > active1 > U233 > take2
PROPER1: [1]
length1: [1]
active1: [1]
zeros: multiset
mark: []
cons: []
0: multiset
U112: multiset
tt: multiset
s: []
U213: multiset
U224: [2,4,1,3]
U233: [3,2,1]
take2: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
ACTIVE(cons(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
ACTIVE(s(X)) → ACTIVE(X)
ACTIVE(length(X)) → ACTIVE(X)
ACTIVE(U21(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U22(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U23(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → ACTIVE(X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
ACTIVE(cons(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
ACTIVE(U21(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U22(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(U23(X1, X2, X3, X4)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → ACTIVE(X1)
ACTIVE(take(X1, X2)) → ACTIVE(X2)
ACTIVE1 > top
U111 > U122 > mark > top
U111 > tt > top
U234 > cons2 > mark > top
U234 > cons2 > tt > top
take2 > U212 > U223 > mark > top
take2 > U212 > U223 > tt > top
take2 > nil > mark > top
zeros > mark > top
0 > nil > mark > top
ACTIVE1: [1]
U111: [1]
cons2: [1,2]
U122: [1,2]
U212: multiset
U223: multiset
U234: [4,3,2,1]
take2: [1,2]
zeros: multiset
mark: []
0: multiset
tt: multiset
nil: multiset
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
ACTIVE(s(X)) → ACTIVE(X)
ACTIVE(length(X)) → ACTIVE(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(s(X)) → ACTIVE(X)
active1 > zeros > U222
active1 > tt > ok > s1 > ACTIVE1 > U222
active1 > tt > ok > U112 > U222
active1 > tt > ok > U211 > U222
active1 > tt > ok > U232 > U222
active1 > nil > 0 > U222
proper1 > zeros > U222
proper1 > nil > 0 > U222
proper1 > ok > s1 > ACTIVE1 > U222
proper1 > ok > U112 > U222
proper1 > ok > U211 > U222
proper1 > ok > U232 > U222
top > U222
ACTIVE1: multiset
s1: [1]
active1: [1]
zeros: multiset
0: multiset
U112: [1,2]
tt: multiset
U211: [1]
U222: [1,2]
U232: [2,1]
nil: multiset
proper1: [1]
ok: []
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
ACTIVE(length(X)) → ACTIVE(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(length(X)) → ACTIVE(X)
ACTIVE1 > take2
cons > proper1 > 0 > mark > take2
cons > proper1 > s > active1 > length1 > mark > take2
cons > proper1 > s > active1 > length1 > U112 > take2
cons > proper1 > s > active1 > length1 > tt > take2
cons > proper1 > s > active1 > zeros > mark > take2
cons > proper1 > s > active1 > U213 > mark > take2
cons > proper1 > s > active1 > U213 > tt > take2
cons > proper1 > s > active1 > U213 > U224 > take2
cons > proper1 > s > active1 > U233 > take2
nil > 0 > mark > take2
top > proper1 > 0 > mark > take2
top > proper1 > s > active1 > length1 > mark > take2
top > proper1 > s > active1 > length1 > U112 > take2
top > proper1 > s > active1 > length1 > tt > take2
top > proper1 > s > active1 > zeros > mark > take2
top > proper1 > s > active1 > U213 > mark > take2
top > proper1 > s > active1 > U213 > tt > take2
top > proper1 > s > active1 > U213 > U224 > take2
top > proper1 > s > active1 > U233 > take2
ACTIVE1: [1]
length1: [1]
active1: [1]
zeros: multiset
mark: []
cons: []
0: multiset
U112: multiset
tt: multiset
s: []
U213: multiset
U224: [2,4,1,3]
U233: [3,2,1]
take2: [2,1]
nil: multiset
proper1: [1]
top: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
TOP(ok(X)) → TOP(active(X))
TOP(mark(X)) → TOP(proper(X))
active(zeros) → mark(cons(0, zeros))
active(U11(tt, L)) → mark(U12(tt, L))
active(U12(tt, L)) → mark(s(length(L)))
active(U21(tt, IL, M, N)) → mark(U22(tt, IL, M, N))
active(U22(tt, IL, M, N)) → mark(U23(tt, IL, M, N))
active(U23(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U11(tt, L))
active(take(0, IL)) → mark(nil)
active(take(s(M), cons(N, IL))) → mark(U21(tt, IL, M, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
active(U21(X1, X2, X3, X4)) → U21(active(X1), X2, X3, X4)
active(U22(X1, X2, X3, X4)) → U22(active(X1), X2, X3, X4)
active(U23(X1, X2, X3, X4)) → U23(active(X1), X2, X3, X4)
active(take(X1, X2)) → take(active(X1), X2)
active(take(X1, X2)) → take(X1, active(X2))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
U21(mark(X1), X2, X3, X4) → mark(U21(X1, X2, X3, X4))
U22(mark(X1), X2, X3, X4) → mark(U22(X1, X2, X3, X4))
U23(mark(X1), X2, X3, X4) → mark(U23(X1, X2, X3, X4))
take(mark(X1), X2) → mark(take(X1, X2))
take(X1, mark(X2)) → mark(take(X1, X2))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(U21(X1, X2, X3, X4)) → U21(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U22(X1, X2, X3, X4)) → U22(proper(X1), proper(X2), proper(X3), proper(X4))
proper(U23(X1, X2, X3, X4)) → U23(proper(X1), proper(X2), proper(X3), proper(X4))
proper(take(X1, X2)) → take(proper(X1), proper(X2))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
U21(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U21(X1, X2, X3, X4))
U22(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U22(X1, X2, X3, X4))
U23(ok(X1), ok(X2), ok(X3), ok(X4)) → ok(U23(X1, X2, X3, X4))
take(ok(X1), ok(X2)) → ok(take(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))