MAYBE
TRS:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
DP:
Strict:
{
mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> U12#(mark(X1), X2),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3),
mark#(tt()) -> active#(tt()),
mark#(U13(X)) -> mark#(X),
mark#(U13(X)) -> active#(U13(mark(X))),
mark#(U13(X)) -> U13#(mark(X)),
mark#(U22(X)) -> mark#(X),
mark#(U22(X)) -> active#(U22(mark(X))),
mark#(U22(X)) -> U22#(mark(X)),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U21(X1, X2)) -> U21#(mark(X1), X2),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U32(X1, X2)) -> U32#(mark(X1), X2),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3),
mark#(U33(X)) -> mark#(X),
mark#(U33(X)) -> active#(U33(mark(X))),
mark#(U33(X)) -> U33#(mark(X)),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(U41(X1, X2)) -> U41#(mark(X1), X2),
mark#(s(X)) -> mark#(X),
mark#(s(X)) -> active#(s(mark(X))),
mark#(s(X)) -> s#(mark(X)),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3),
mark#(0()) -> active#(0()),
mark#(U61(X)) -> mark#(X),
mark#(U61(X)) -> active#(U61(mark(X))),
mark#(U61(X)) -> U61#(mark(X)),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(and(X1, X2)) -> and#(mark(X1), X2),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(X1, active(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2),
isNat#(mark(X)) -> isNat#(X),
isNat#(active(X)) -> isNat#(X),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(U12(tt(), V2)) -> isNat#(V2),
active#(U12(tt(), V2)) -> U13#(isNat(V2)),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1),
active#(isNat(s(V1))) -> isNatKind#(V1),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2),
active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)),
active#(isNat(plus(V1, V2))) -> isNatKind#(V1),
active#(isNat(plus(V1, V2))) -> isNatKind#(V2),
active#(isNat(0())) -> mark#(tt()),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2),
active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)),
active#(isNat(x(V1, V2))) -> isNatKind#(V1),
active#(isNat(x(V1, V2))) -> isNatKind#(V2),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2),
active#(U11(tt(), V1, V2)) -> isNat#(V1),
active#(U13(tt())) -> mark#(tt()),
active#(U22(tt())) -> mark#(tt()),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U21(tt(), V1)) -> isNat#(V1),
active#(U21(tt(), V1)) -> U22#(isNat(V1)),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U32(tt(), V2)) -> isNat#(V2),
active#(U32(tt(), V2)) -> U33#(isNat(V2)),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U31(tt(), V1, V2)) -> isNat#(V1),
active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2),
active#(U33(tt())) -> mark#(tt()),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, s(M))) -> isNat#(N),
active#(plus(N, s(M))) -> isNat#(M),
active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N),
active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)),
active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)),
active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))),
active#(plus(N, s(M))) -> isNatKind#(N),
active#(plus(N, s(M))) -> isNatKind#(M),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(plus(N, 0())) -> isNat#(N),
active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N),
active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)),
active#(plus(N, 0())) -> isNatKind#(N),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(U51(tt(), M, N)) -> s#(plus(N, M)),
active#(U51(tt(), M, N)) -> plus#(N, M),
active#(U61(tt())) -> mark#(0()),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, s(M))) -> isNat#(N),
active#(x(N, s(M))) -> isNat#(M),
active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N),
active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)),
active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)),
active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))),
active#(x(N, s(M))) -> isNatKind#(N),
active#(x(N, s(M))) -> isNatKind#(M),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(x(N, 0())) -> isNat#(N),
active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))),
active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)),
active#(x(N, 0())) -> isNatKind#(N),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(U71(tt(), M, N)) -> plus#(x(N, M), N),
active#(U71(tt(), M, N)) -> x#(N, M),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(s(V1))) -> isNatKind#(V1),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)),
active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1),
active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2),
active#(isNatKind(0())) -> mark#(tt()),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)),
active#(isNatKind(x(V1, V2))) -> isNatKind#(V1),
active#(isNatKind(x(V1, V2))) -> isNatKind#(V2),
U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3),
U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3),
U13#(mark(X)) -> U13#(X),
U13#(active(X)) -> U13#(X),
U22#(mark(X)) -> U22#(X),
U22#(active(X)) -> U22#(X),
U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2),
U21#(active(X1), X2) -> U21#(X1, X2),
U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(mark(X1), X2) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2),
U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3),
U31#(active(X1), X2, X3) -> U31#(X1, X2, X3),
U33#(mark(X)) -> U33#(X),
U33#(active(X)) -> U33#(X),
U41#(X1, mark(X2)) -> U41#(X1, X2),
U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2),
s#(mark(X)) -> s#(X),
s#(active(X)) -> s#(X),
plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2),
plus#(active(X1), X2) -> plus#(X1, X2),
U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3),
U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3),
U61#(mark(X)) -> U61#(X),
U61#(active(X)) -> U61#(X),
x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2),
x#(active(X1), X2) -> x#(X1, X2),
U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3),
and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2),
and#(active(X1), X2) -> and#(X1, X2),
isNatKind#(mark(X)) -> isNatKind#(X),
isNatKind#(active(X)) -> isNatKind#(X)
}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
EDG:
{
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(and(tt(), X)) -> mark#(X))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, 0())) -> isNat#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> isNat#(M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> isNat#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U61(tt())) -> mark#(0()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, 0())) -> isNat#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U41(tt(), N)) -> mark#(N))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U33(tt())) -> mark#(tt()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U22(tt())) -> mark#(tt()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U13(tt())) -> mark#(tt()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(0())) -> mark#(tt()))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U22(X)) -> active#(U22(mark(X))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(s(X)) -> active#(s(mark(X))), active#(and(tt(), X)) -> mark#(X))
(mark#(s(X)) -> active#(s(mark(X))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(s(X)) -> active#(s(mark(X))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(s(X)) -> active#(s(mark(X))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> isNat#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNat#(M))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNat#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U61(tt())) -> mark#(0()))
(mark#(s(X)) -> active#(s(mark(X))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(s(X)) -> active#(s(mark(X))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> isNat#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U41(tt(), N)) -> mark#(N))
(mark#(s(X)) -> active#(s(mark(X))), active#(U33(tt())) -> mark#(tt()))
(mark#(s(X)) -> active#(s(mark(X))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(s(X)) -> active#(s(mark(X))), active#(U22(tt())) -> mark#(tt()))
(mark#(s(X)) -> active#(s(mark(X))), active#(U13(tt())) -> mark#(tt()))
(mark#(s(X)) -> active#(s(mark(X))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(0())) -> mark#(tt()))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(s(X)) -> active#(s(mark(X))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(s(X)) -> active#(s(mark(X))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(s(X)) -> active#(s(mark(X))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U61(X)) -> U61#(mark(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U61(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(s(X)) -> s#(mark(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(s(X)) -> active#(s(mark(X))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(s(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U33(X)) -> U33#(mark(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U33(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U22(X)) -> U22#(mark(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U22(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U13(X)) -> U13#(mark(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U13(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U61(X)) -> U61#(mark(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U61(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(s(X)) -> s#(mark(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(s(X)) -> active#(s(mark(X))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(s(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U33(X)) -> U33#(mark(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U33(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U22(X)) -> U22#(mark(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U22(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U13(X)) -> U13#(mark(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U13(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(and(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> mark#(X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U61(X)) -> U61#(mark(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U61(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U51(X1, X2, X3)) -> mark#(X1))
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(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(s(X)) -> s#(mark(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(s(X)) -> active#(s(mark(X))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(s(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U41(X1, X2)) -> mark#(X1))
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(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U33(X)) -> active#(U33(mark(X))))
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(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U32(X1, X2)) -> mark#(X1))
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(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U22(X)) -> U22#(mark(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U22(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U13(X)) -> U13#(mark(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U13(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> x#(N, M), x#(active(X1), X2) -> x#(X1, X2))
(active#(U71(tt(), M, N)) -> x#(N, M), x#(mark(X1), X2) -> x#(X1, X2))
(active#(U71(tt(), M, N)) -> x#(N, M), x#(X1, active(X2)) -> x#(X1, X2))
(active#(U71(tt(), M, N)) -> x#(N, M), x#(X1, mark(X2)) -> x#(X1, X2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U61(tt())) -> mark#(0()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, 0())) -> isNat#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U33(tt())) -> mark#(tt()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U22(tt())) -> mark#(tt()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U13(tt())) -> mark#(tt()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(0())) -> mark#(tt()))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
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(mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
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(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U13(X)) -> U13#(mark(X)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U13(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> s#(plus(N, M)), s#(active(X)) -> s#(X))
(active#(U51(tt(), M, N)) -> s#(plus(N, M)), s#(mark(X)) -> s#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U61(X)) -> U61#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U61(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(0()) -> active#(0()))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> s#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> active#(s(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U33(X)) -> U33#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U33(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U22(X)) -> U22#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U22(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U13(X)) -> U13#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U13(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(tt()) -> active#(tt()))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> isNat#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U61(tt())) -> mark#(0()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNat#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), N)) -> mark#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U33(tt())) -> mark#(tt()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U22(tt())) -> mark#(tt()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U13(tt())) -> mark#(tt()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(0())) -> mark#(tt()))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))), U61#(active(X)) -> U61#(X))
(active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))), U61#(mark(X)) -> U61#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
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(mark#(U41(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
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(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
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(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
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(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
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(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
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(mark#(U51(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(tt()) -> active#(tt()))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> U12#(mark(X1), X2), U12#(active(X1), X2) -> U12#(X1, X2))
(mark#(U12(X1, X2)) -> U12#(mark(X1), X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(mark#(U12(X1, X2)) -> U12#(mark(X1), X2), U12#(X1, active(X2)) -> U12#(X1, X2))
(mark#(U12(X1, X2)) -> U12#(mark(X1), X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(mark#(U32(X1, X2)) -> U32#(mark(X1), X2), U32#(active(X1), X2) -> U32#(X1, X2))
(mark#(U32(X1, X2)) -> U32#(mark(X1), X2), U32#(mark(X1), X2) -> U32#(X1, X2))
(mark#(U32(X1, X2)) -> U32#(mark(X1), X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(mark#(U32(X1, X2)) -> U32#(mark(X1), X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(mark#(and(X1, X2)) -> and#(mark(X1), X2), and#(active(X1), X2) -> and#(X1, X2))
(mark#(and(X1, X2)) -> and#(mark(X1), X2), and#(mark(X1), X2) -> and#(X1, X2))
(mark#(and(X1, X2)) -> and#(mark(X1), X2), and#(X1, active(X2)) -> and#(X1, X2))
(mark#(and(X1, X2)) -> and#(mark(X1), X2), and#(X1, mark(X2)) -> and#(X1, X2))
(mark#(U22(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U22(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U22(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U22(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U22(X)) -> mark#(X), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U22(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(0()) -> active#(0()))
(mark#(U22(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U22(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(mark#(U22(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U22(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(U22(X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U33(X)) -> U33#(mark(X)))
(mark#(U22(X)) -> mark#(X), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(U22(X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(U22(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(U22(X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(U22(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U22(X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U22(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U22(X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U22(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
(mark#(U22(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U22(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U22(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U22(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(s(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U61(X)) -> U61#(mark(X)))
(mark#(s(X)) -> mark#(X), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(s(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(0()) -> active#(0()))
(mark#(s(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(s(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(mark#(s(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(s(X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U33(X)) -> U33#(mark(X)))
(mark#(s(X)) -> mark#(X), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(s(X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(s(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(s(X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(s(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
(mark#(s(X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(s(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U13(X)) -> U13#(mark(X)))
(mark#(s(X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(s(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
(mark#(s(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(s(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(s(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(s(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(isNat#(mark(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))
(isNat#(mark(X)) -> isNat#(X), isNat#(mark(X)) -> isNat#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(and(tt(), X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U61(X)) -> U61#(mark(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(and(tt(), X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(0()) -> active#(0()))
(active#(and(tt(), X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(and(tt(), X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U33(X)) -> U33#(mark(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(and(tt(), X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(and(tt(), X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(and(tt(), X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(and(tt(), X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U13(X)) -> U13#(mark(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(and(tt(), X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(tt()) -> active#(tt()))
(active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(and(tt(), X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(U13#(active(X)) -> U13#(X), U13#(active(X)) -> U13#(X))
(U13#(active(X)) -> U13#(X), U13#(mark(X)) -> U13#(X))
(U22#(active(X)) -> U22#(X), U22#(active(X)) -> U22#(X))
(U22#(active(X)) -> U22#(X), U22#(mark(X)) -> U22#(X))
(U33#(active(X)) -> U33#(X), U33#(active(X)) -> U33#(X))
(U33#(active(X)) -> U33#(X), U33#(mark(X)) -> U33#(X))
(s#(active(X)) -> s#(X), s#(active(X)) -> s#(X))
(s#(active(X)) -> s#(X), s#(mark(X)) -> s#(X))
(U61#(active(X)) -> U61#(X), U61#(active(X)) -> U61#(X))
(U61#(active(X)) -> U61#(X), U61#(mark(X)) -> U61#(X))
(isNatKind#(active(X)) -> isNatKind#(X), isNatKind#(active(X)) -> isNatKind#(X))
(isNatKind#(active(X)) -> isNatKind#(X), isNatKind#(mark(X)) -> isNatKind#(X))
(U12#(X1, active(X2)) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(X1, active(X2)) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(X1, active(X2)) -> U12#(X1, X2), U12#(X1, active(X2)) -> U12#(X1, X2))
(U12#(X1, active(X2)) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(X1, active(X2)) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(active(X1), X2) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(active(X1), X2) -> U21#(X1, X2), U21#(active(X1), X2) -> U21#(X1, X2))
(U21#(active(X1), X2) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(active(X1), X2) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(active(X1), X2) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(mark(X1), X2) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(mark(X1), X2) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(X1, mark(X2)) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(X1, mark(X2)) -> U41#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(active(X1), X2) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
(plus#(active(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(active(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(active(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(active(X1), X2) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
(x#(active(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(active(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(active(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(active(X1), X2) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
(and#(active(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(active(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(active(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(active(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(mark(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(X1, active(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(X1, mark(X2)) -> and#(X1, X2))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(active(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(active#(plus(N, s(M))) -> isNatKind#(M), isNatKind#(active(X)) -> isNatKind#(X))
(active#(plus(N, s(M))) -> isNatKind#(M), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(x(N, s(M))) -> isNatKind#(M), isNatKind#(active(X)) -> isNatKind#(X))
(active#(x(N, s(M))) -> isNatKind#(M), isNatKind#(mark(X)) -> isNatKind#(X))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
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(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
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(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U33(tt())) -> mark#(tt()))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U22(tt())) -> mark#(tt()))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U13(tt())) -> mark#(tt()))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
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(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U61(tt())) -> mark#(0()))
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(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
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(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
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(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U33(tt())) -> mark#(tt()))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U22(tt())) -> mark#(tt()))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U13(tt())) -> mark#(tt()))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> U61#(mark(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> s#(mark(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> active#(s(mark(X))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> U33#(mark(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> U22#(mark(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> U13#(mark(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> U61#(mark(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> s#(mark(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> active#(s(mark(X))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> U33#(mark(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> U22#(mark(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> U13#(mark(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
(active#(plus(N, s(M))) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
(active#(plus(N, 0())) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
(active#(plus(N, 0())) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
(active#(x(N, s(M))) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
(active#(x(N, s(M))) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
(active#(x(N, 0())) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
(active#(x(N, 0())) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(and(tt(), X)) -> mark#(X))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> isNat#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNat#(M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNat#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U61(tt())) -> mark#(0()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> isNat#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), N)) -> mark#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U33(tt())) -> mark#(tt()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U22(tt())) -> mark#(tt()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U13(tt())) -> mark#(tt()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(0())) -> mark#(tt()))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U22(X)) -> U22#(mark(X)), U22#(active(X)) -> U22#(X))
(mark#(U22(X)) -> U22#(mark(X)), U22#(mark(X)) -> U22#(X))
(mark#(s(X)) -> s#(mark(X)), s#(active(X)) -> s#(X))
(mark#(s(X)) -> s#(mark(X)), s#(mark(X)) -> s#(X))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(and(tt(), X)) -> mark#(X))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> isNat#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> isNat#(M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> isNat#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U61(tt())) -> mark#(0()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> isNat#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U41(tt(), N)) -> mark#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U33(tt())) -> mark#(tt()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U22(tt())) -> mark#(tt()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U13(tt())) -> mark#(tt()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(0())) -> mark#(tt()))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(active#(U32(tt(), V2)) -> U33#(isNat(V2)), U33#(active(X)) -> U33#(X))
(active#(U32(tt(), V2)) -> U33#(isNat(V2)), U33#(mark(X)) -> U33#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U61(X)) -> U61#(mark(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U61(X)) -> mark#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(s(X)) -> s#(mark(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(s(X)) -> active#(s(mark(X))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(s(X)) -> mark#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U33(X)) -> U33#(mark(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U33(X)) -> mark#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U22(X)) -> U22#(mark(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U22(X)) -> mark#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U13(X)) -> U13#(mark(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U13(X)) -> mark#(X))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> isNatKind#(V2), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNat(plus(V1, V2))) -> isNatKind#(V2), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(U32(tt(), V2)) -> isNat#(V2), isNat#(active(X)) -> isNat#(X))
(active#(U32(tt(), V2)) -> isNat#(V2), isNat#(mark(X)) -> isNat#(X))
(active#(isNatKind(x(V1, V2))) -> isNatKind#(V2), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNatKind(x(V1, V2))) -> isNatKind#(V2), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(active#(isNat(s(V1))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNat(s(V1))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNat(x(V1, V2))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNat(x(V1, V2))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(U21(tt(), V1)) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
(active#(U21(tt(), V1)) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
(active#(isNatKind(s(V1))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNatKind(s(V1))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNatKind(x(V1, V2))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNatKind(x(V1, V2))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(U13(tt())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
(active#(U33(tt())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
(active#(isNatKind(0())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
(active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2), U32#(active(X1), X2) -> U32#(X1, X2))
(active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2), U32#(mark(X1), X2) -> U32#(X1, X2))
(active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2), U32#(X1, active(X2)) -> U32#(X1, X2))
(active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(active(X1), X2) -> x#(X1, X2))
(mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(mark(X1), X2) -> x#(X1, X2))
(mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(X1, active(X2)) -> x#(X1, X2))
(mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(X1, mark(X2)) -> x#(X1, X2))
(active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(active(X1), X2) -> and#(X1, X2))
(active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(active(X1), X2) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(active(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(active(X1), X2) -> and#(X1, X2))
(active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(active(X1), X2) -> and#(X1, X2))
(active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(U71(tt(), M, N)) -> plus#(x(N, M), N), plus#(active(X1), X2) -> plus#(X1, X2))
(active#(U71(tt(), M, N)) -> plus#(x(N, M), N), plus#(mark(X1), X2) -> plus#(X1, X2))
(active#(U71(tt(), M, N)) -> plus#(x(N, M), N), plus#(X1, active(X2)) -> plus#(X1, X2))
(active#(U71(tt(), M, N)) -> plus#(x(N, M), N), plus#(X1, mark(X2)) -> plus#(X1, X2))
(active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N), U41#(X1, mark(X2)) -> U41#(X1, X2))
(active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N), U41#(X1, active(X2)) -> U41#(X1, X2))
(active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N), U41#(mark(X1), X2) -> U41#(X1, X2))
(active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N), U41#(active(X1), X2) -> U41#(X1, X2))
(active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(active(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)), and#(active(X1), X2) -> and#(X1, X2))
(active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)), and#(active(X1), X2) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)), and#(active(X1), X2) -> and#(X1, X2))
(active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(X1, active(X2)) -> and#(X1, X2))
(active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(mark(X1), X2) -> and#(X1, X2))
(active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)), and#(active(X1), X2) -> and#(X1, X2))
(mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(X1, mark(X2)) -> plus#(X1, X2))
(mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(X1, active(X2)) -> plus#(X1, X2))
(mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(mark(X1), X2) -> plus#(X1, X2))
(mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(active(X1), X2) -> plus#(X1, X2))
(active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2), U12#(X1, active(X2)) -> U12#(X1, X2))
(active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2), U12#(mark(X1), X2) -> U12#(X1, X2))
(active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2), U12#(active(X1), X2) -> U12#(X1, X2))
(active#(U61(tt())) -> mark#(0()), mark#(0()) -> active#(0()))
(active#(U22(tt())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
(active#(isNat(0())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
(active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(U31(tt(), V1, V2)) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
(active#(U31(tt(), V1, V2)) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
(active#(U11(tt(), V1, V2)) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
(active#(U11(tt(), V1, V2)) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
(active#(isNat(plus(V1, V2))) -> isNatKind#(V1), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNat(plus(V1, V2))) -> isNatKind#(V1), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1), U21#(X1, mark(X2)) -> U21#(X1, X2))
(active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1), U21#(X1, active(X2)) -> U21#(X1, X2))
(active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1), U21#(mark(X1), X2) -> U21#(X1, X2))
(active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1), U21#(active(X1), X2) -> U21#(X1, X2))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2), isNatKind#(active(X)) -> isNatKind#(X))
(active#(isNat(x(V1, V2))) -> isNatKind#(V2), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(isNat(x(V1, V2))) -> isNatKind#(V2), isNatKind#(active(X)) -> isNatKind#(X))
(active#(U12(tt(), V2)) -> isNat#(V2), isNat#(mark(X)) -> isNat#(X))
(active#(U12(tt(), V2)) -> isNat#(V2), isNat#(active(X)) -> isNat#(X))
(active#(U21(tt(), V1)) -> U22#(isNat(V1)), U22#(mark(X)) -> U22#(X))
(active#(U21(tt(), V1)) -> U22#(isNat(V1)), U22#(active(X)) -> U22#(X))
(active#(U12(tt(), V2)) -> U13#(isNat(V2)), U13#(mark(X)) -> U13#(X))
(active#(U12(tt(), V2)) -> U13#(isNat(V2)), U13#(active(X)) -> U13#(X))
(mark#(U61(X)) -> U61#(mark(X)), U61#(mark(X)) -> U61#(X))
(mark#(U61(X)) -> U61#(mark(X)), U61#(active(X)) -> U61#(X))
(mark#(U33(X)) -> U33#(mark(X)), U33#(mark(X)) -> U33#(X))
(mark#(U33(X)) -> U33#(mark(X)), U33#(active(X)) -> U33#(X))
(mark#(U13(X)) -> U13#(mark(X)), U13#(mark(X)) -> U13#(X))
(mark#(U13(X)) -> U13#(mark(X)), U13#(active(X)) -> U13#(X))
(active#(x(N, 0())) -> isNatKind#(N), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(x(N, 0())) -> isNatKind#(N), isNatKind#(active(X)) -> isNatKind#(X))
(active#(x(N, s(M))) -> isNatKind#(N), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(x(N, s(M))) -> isNatKind#(N), isNatKind#(active(X)) -> isNatKind#(X))
(active#(plus(N, 0())) -> isNatKind#(N), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(plus(N, 0())) -> isNatKind#(N), isNatKind#(active(X)) -> isNatKind#(X))
(active#(plus(N, s(M))) -> isNatKind#(N), isNatKind#(mark(X)) -> isNatKind#(X))
(active#(plus(N, s(M))) -> isNatKind#(N), isNatKind#(active(X)) -> isNatKind#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U41(tt(), N)) -> mark#(N), mark#(tt()) -> active#(tt()))
(active#(U41(tt(), N)) -> mark#(N), mark#(U13(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U13(X)) -> U13#(mark(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U22(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U22(X)) -> U22#(mark(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U41(tt(), N)) -> mark#(N), mark#(U33(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U33(X)) -> U33#(mark(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(s(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(s(X)) -> active#(s(mark(X))))
(active#(U41(tt(), N)) -> mark#(N), mark#(s(X)) -> s#(mark(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U41(tt(), N)) -> mark#(N), mark#(0()) -> active#(0()))
(active#(U41(tt(), N)) -> mark#(N), mark#(U61(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U61(X)) -> U61#(mark(X)))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U41(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> U13#(mark(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> U22#(mark(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> U33#(mark(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> active#(s(mark(X))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> s#(mark(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> U61#(mark(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> mark#(X))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> U13#(mark(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> mark#(X))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> U22#(mark(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> mark#(X1))
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(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> mark#(X1))
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(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
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(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> mark#(X))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> U33#(mark(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> mark#(X1))
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(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> mark#(X))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> active#(s(mark(X))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> s#(mark(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> mark#(X))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> U61#(mark(X)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U13(tt())) -> mark#(tt()))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U22(tt())) -> mark#(tt()))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U33(tt())) -> mark#(tt()))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNat#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U61(tt())) -> mark#(0()))
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(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U13(tt())) -> mark#(tt()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U22(tt())) -> mark#(tt()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U33(tt())) -> mark#(tt()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNat#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U61(tt())) -> mark#(0()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(active#(x(N, s(M))) -> isNat#(M), isNat#(mark(X)) -> isNat#(X))
(active#(x(N, s(M))) -> isNat#(M), isNat#(active(X)) -> isNat#(X))
(active#(plus(N, s(M))) -> isNat#(M), isNat#(mark(X)) -> isNat#(X))
(active#(plus(N, s(M))) -> isNat#(M), isNat#(active(X)) -> isNat#(X))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(active(X1), X2, X3) -> U31#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(X1, mark(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(X1, active(X2)) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(mark(X1), X2) -> and#(X1, X2))
(active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), and#(active(X1), X2) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(X1, mark(X2)) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U41#(X1, mark(X2)) -> U41#(X1, X2), U41#(X1, mark(X2)) -> U41#(X1, X2))
(U41#(X1, mark(X2)) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(X1, mark(X2)) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(X1, mark(X2)) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U32#(mark(X1), X2) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(mark(X1), X2) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(mark(X1), X2) -> U32#(X1, X2), U32#(mark(X1), X2) -> U32#(X1, X2))
(U32#(mark(X1), X2) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(mark(X1), X2) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(active(X1), X2) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(active(X1), X2) -> U21#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(X1, active(X2)) -> U12#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(X1, active(X2)) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(isNatKind#(mark(X)) -> isNatKind#(X), isNatKind#(mark(X)) -> isNatKind#(X))
(isNatKind#(mark(X)) -> isNatKind#(X), isNatKind#(active(X)) -> isNatKind#(X))
(U61#(mark(X)) -> U61#(X), U61#(mark(X)) -> U61#(X))
(U61#(mark(X)) -> U61#(X), U61#(active(X)) -> U61#(X))
(s#(mark(X)) -> s#(X), s#(mark(X)) -> s#(X))
(s#(mark(X)) -> s#(X), s#(active(X)) -> s#(X))
(U33#(mark(X)) -> U33#(X), U33#(mark(X)) -> U33#(X))
(U33#(mark(X)) -> U33#(X), U33#(active(X)) -> U33#(X))
(U22#(mark(X)) -> U22#(X), U22#(mark(X)) -> U22#(X))
(U22#(mark(X)) -> U22#(X), U22#(active(X)) -> U22#(X))
(U13#(mark(X)) -> U13#(X), U13#(mark(X)) -> U13#(X))
(U13#(mark(X)) -> U13#(X), U13#(active(X)) -> U13#(X))
(isNat#(active(X)) -> isNat#(X), isNat#(mark(X)) -> isNat#(X))
(isNat#(active(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))
(mark#(U61(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U61(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U61(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U61(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U61(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U61(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
(mark#(U61(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(U61(X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U61(X)) -> mark#(X), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U61(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(U61(X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U61(X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U61(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U61(X)) -> mark#(X), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(U61(X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U61(X)) -> mark#(X), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(U61(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U61(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(U61(X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(mark#(U61(X)) -> mark#(X), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(U61(X)) -> mark#(X), mark#(U33(X)) -> U33#(mark(X)))
(mark#(U61(X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U61(X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(U61(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(mark#(U61(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U61(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(mark#(U61(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U61(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U61(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U61(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U61(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U61(X)) -> mark#(X), mark#(0()) -> active#(0()))
(mark#(U61(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(U61(X)) -> mark#(X), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U61(X)) -> mark#(X), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U61(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U61(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U61(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U61(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U61(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U61(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U61(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U61(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U61(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U33(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U33(X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U33(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U33(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U33(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U33(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U33(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U33(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
(mark#(U33(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(U33(X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U33(X)) -> mark#(X), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U33(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(U33(X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U33(X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U33(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U33(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
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(mark#(U33(X)) -> mark#(X), mark#(U33(X)) -> active#(U33(mark(X))))
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(mark#(U33(X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
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(mark#(U33(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U33(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(mark#(U33(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U33(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U33(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U33(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
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(mark#(U33(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U33(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U33(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U33(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
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(mark#(U33(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
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(mark#(U13(X)) -> mark#(X), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U13(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U13(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
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(mark#(U13(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(U13(X)) -> mark#(X), mark#(U13(X)) -> active#(U13(mark(X))))
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(mark#(U13(X)) -> mark#(X), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U13(X)) -> mark#(X), mark#(U22(X)) -> U22#(mark(X)))
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(mark#(U13(X)) -> mark#(X), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
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(mark#(U13(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
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(mark#(U13(X)) -> mark#(X), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
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(mark#(U13(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U13(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
(mark#(U13(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U13(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U13(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U13(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U13(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U13(X)) -> mark#(X), mark#(0()) -> active#(0()))
(mark#(U13(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(U13(X)) -> mark#(X), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U13(X)) -> mark#(X), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U13(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U13(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U13(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U13(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U13(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U41(X1, X2)) -> U41#(mark(X1), X2), U41#(X1, mark(X2)) -> U41#(X1, X2))
(mark#(U41(X1, X2)) -> U41#(mark(X1), X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(mark#(U41(X1, X2)) -> U41#(mark(X1), X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(mark#(U41(X1, X2)) -> U41#(mark(X1), X2), U41#(active(X1), X2) -> U41#(X1, X2))
(mark#(U21(X1, X2)) -> U21#(mark(X1), X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(mark#(U21(X1, X2)) -> U21#(mark(X1), X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(mark#(U21(X1, X2)) -> U21#(mark(X1), X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(mark#(U21(X1, X2)) -> U21#(mark(X1), X2), U21#(active(X1), X2) -> U21#(X1, X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(and(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U13(X)) -> U13#(mark(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U33(X)) -> U33#(mark(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
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(mark#(and(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(and(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
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(mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
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(mark#(x(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
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(mark#(x(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U13(X)) -> U13#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U33(X)) -> U33#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(tt()) -> active#(tt()))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> U33#(mark(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(0()) -> active#(0()))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U33(X)) -> U33#(mark(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U13(X)) -> U13#(mark(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U22(X)) -> U22#(mark(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U33(X)) -> U33#(mark(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U61(X)) -> U61#(mark(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U13(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U13(X)) -> U13#(mark(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U22(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U22(X)) -> U22#(mark(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U33(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U33(X)) -> U33#(mark(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(s(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(s(X)) -> active#(s(mark(X))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(s(X)) -> s#(mark(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U61(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U61(X)) -> U61#(mark(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(0())) -> mark#(tt()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U13(tt())) -> mark#(tt()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U22(tt())) -> mark#(tt()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U33(tt())) -> mark#(tt()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), N)) -> mark#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNat#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U61(tt())) -> mark#(0()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> isNat#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(mark#(x(X1, X2)) -> mark#(X2), mark#(tt()) -> active#(tt()))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U13(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U13(X)) -> active#(U13(mark(X))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U13(X)) -> U13#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U22(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U22(X)) -> active#(U22(mark(X))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U22(X)) -> U22#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> mark#(X1))
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(mark#(x(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U33(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U33(X)) -> active#(U33(mark(X))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U33(X)) -> U33#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> mark#(X1))
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(mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(s(X)) -> active#(s(mark(X))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(s(X)) -> s#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(mark#(x(X1, X2)) -> mark#(X2), mark#(0()) -> active#(0()))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U61(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U61(X)) -> active#(U61(mark(X))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U61(X)) -> U61#(mark(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U13(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U13(X)) -> U13#(mark(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U22(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U22(X)) -> U22#(mark(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U33(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U33(X)) -> U33#(mark(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> active#(s(mark(X))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> s#(mark(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U61(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U61(X)) -> U61#(mark(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
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(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
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(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(0())) -> mark#(tt()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U13(tt())) -> mark#(tt()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U22(tt())) -> mark#(tt()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U33(tt())) -> mark#(tt()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> isNat#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U61(tt())) -> mark#(0()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(0())) -> mark#(tt()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U13(tt())) -> mark#(tt()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U22(tt())) -> mark#(tt()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U33(tt())) -> mark#(tt()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> isNat#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U61(tt())) -> mark#(0()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(active#(U51(tt(), M, N)) -> plus#(N, M), plus#(X1, mark(X2)) -> plus#(X1, X2))
(active#(U51(tt(), M, N)) -> plus#(N, M), plus#(X1, active(X2)) -> plus#(X1, X2))
(active#(U51(tt(), M, N)) -> plus#(N, M), plus#(mark(X1), X2) -> plus#(X1, X2))
(active#(U51(tt(), M, N)) -> plus#(N, M), plus#(active(X1), X2) -> plus#(X1, X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U13(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U13(X)) -> U13#(mark(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U22(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U22(X)) -> U22#(mark(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U33(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U33(X)) -> U33#(mark(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> active#(s(mark(X))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> s#(mark(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U61(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U61(X)) -> U61#(mark(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U12(X1, X2)) -> U12#(mark(X1), X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U11(X1, X2, X3)) -> U11#(mark(X1), X2, X3))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U13(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U13(X)) -> active#(U13(mark(X))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U13(X)) -> U13#(mark(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U22(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U22(X)) -> active#(U22(mark(X))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U22(X)) -> U22#(mark(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U21(X1, X2)) -> U21#(mark(X1), X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U32(X1, X2)) -> U32#(mark(X1), X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U31(X1, X2, X3)) -> U31#(mark(X1), X2, X3))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U33(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U33(X)) -> active#(U33(mark(X))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U33(X)) -> U33#(mark(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U41(X1, X2)) -> U41#(mark(X1), X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(s(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(s(X)) -> active#(s(mark(X))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(s(X)) -> s#(mark(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U51(X1, X2, X3)) -> U51#(mark(X1), X2, X3))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U61(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U61(X)) -> active#(U61(mark(X))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U61(X)) -> U61#(mark(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U71(X1, X2, X3)) -> U71#(mark(X1), X2, X3))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(0())) -> mark#(tt()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U13(tt())) -> mark#(tt()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U22(tt())) -> mark#(tt()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U33(tt())) -> mark#(tt()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U41(tt(), N)) -> mark#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, 0())) -> isNat#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U61(tt())) -> mark#(0()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> isNat#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> isNat#(M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, 0())) -> isNat#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(and(tt(), X)) -> mark#(X))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U61(X)) -> active#(U61(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(0())) -> mark#(tt()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U13(tt())) -> mark#(tt()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U22(tt())) -> mark#(tt()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U33(tt())) -> mark#(tt()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U41(tt(), N)) -> mark#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, 0())) -> isNat#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U61(tt())) -> mark#(0()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> isNat#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> isNat#(M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, 0())) -> isNat#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(and(tt(), X)) -> mark#(X))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U33(X)) -> active#(U33(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U12(tt(), V2)) -> isNat#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U12(tt(), V2)) -> U13#(isNat(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(s(V1))) -> U21#(isNatKind(V1), V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(s(V1))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(plus(V1, V2))) -> U11#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(0())) -> mark#(tt()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(x(V1, V2))) -> U31#(and(isNatKind(V1), isNatKind(V2)), V1, V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNat(x(V1, V2))) -> isNatKind#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U11(tt(), V1, V2)) -> U12#(isNat(V1), V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U11(tt(), V1, V2)) -> isNat#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U13(tt())) -> mark#(tt()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U22(tt())) -> mark#(tt()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U21(tt(), V1)) -> isNat#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U21(tt(), V1)) -> U22#(isNat(V1)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U32(tt(), V2)) -> isNat#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U32(tt(), V2)) -> U33#(isNat(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U31(tt(), V1, V2)) -> isNat#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U31(tt(), V1, V2)) -> U32#(isNat(V1), V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U33(tt())) -> mark#(tt()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U41(tt(), N)) -> mark#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> U51#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> isNatKind#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, s(M))) -> isNatKind#(M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, 0())) -> isNat#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, 0())) -> U41#(and(isNat(N), isNatKind(N)), N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(plus(N, 0())) -> isNatKind#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U51(tt(), M, N)) -> s#(plus(N, M)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U51(tt(), M, N)) -> plus#(N, M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U61(tt())) -> mark#(0()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> isNat#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> isNat#(M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> U71#(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> and#(isNat(N), isNatKind(N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNatKind(M)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> and#(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> isNatKind#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, s(M))) -> isNatKind#(M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, 0())) -> isNat#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, 0())) -> U61#(and(isNat(N), isNatKind(N))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, 0())) -> and#(isNat(N), isNatKind(N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(x(N, 0())) -> isNatKind#(N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U71(tt(), M, N)) -> plus#(x(N, M), N))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(U71(tt(), M, N)) -> x#(N, M))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(and(tt(), X)) -> mark#(X))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(s(V1))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(plus(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(plus(V1, V2))) -> isNatKind#(V2))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(0())) -> mark#(tt()))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(x(V1, V2))) -> and#(isNatKind(V1), isNatKind(V2)))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V1))
(mark#(U13(X)) -> active#(U13(mark(X))), active#(isNatKind(x(V1, V2))) -> isNatKind#(V2))
}
SCCS:
Scc:
{ isNatKind#(mark(X)) -> isNatKind#(X),
isNatKind#(active(X)) -> isNatKind#(X)}
Scc:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2),
and#(active(X1), X2) -> and#(X1, X2)}
Scc:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3)}
Scc:
{ x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2),
x#(active(X1), X2) -> x#(X1, X2)}
Scc:
{ U61#(mark(X)) -> U61#(X),
U61#(active(X)) -> U61#(X)}
Scc:
{ U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3),
U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
Scc:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2),
plus#(active(X1), X2) -> plus#(X1, X2)}
Scc:
{ s#(mark(X)) -> s#(X),
s#(active(X)) -> s#(X)}
Scc:
{ U41#(X1, mark(X2)) -> U41#(X1, X2),
U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2)}
Scc:
{ U33#(mark(X)) -> U33#(X),
U33#(active(X)) -> U33#(X)}
Scc:
{ U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3),
U31#(active(X1), X2, X3) -> U31#(X1, X2, X3)}
Scc:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(mark(X1), X2) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2)}
Scc:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2),
U21#(active(X1), X2) -> U21#(X1, X2)}
Scc:
{ U22#(mark(X)) -> U22#(X),
U22#(active(X)) -> U22#(X)}
Scc:
{ U13#(mark(X)) -> U13#(X),
U13#(active(X)) -> U13#(X)}
Scc:
{ U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3),
U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3)}
Scc:
{ isNat#(mark(X)) -> isNat#(X),
isNat#(active(X)) -> isNat#(X)}
Scc:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(X1, active(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
Scc:
{ mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U13(X)) -> mark#(X),
mark#(U13(X)) -> active#(U13(mark(X))),
mark#(U22(X)) -> mark#(X),
mark#(U22(X)) -> active#(U22(mark(X))),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U33(X)) -> mark#(X),
mark#(U33(X)) -> active#(U33(mark(X))),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(s(X)) -> mark#(X),
mark#(s(X)) -> active#(s(mark(X))),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U61(X)) -> mark#(X),
mark#(U61(X)) -> active#(U61(mark(X))),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2)))}
SCC:
Strict:
{ isNatKind#(mark(X)) -> isNatKind#(X),
isNatKind#(active(X)) -> isNatKind#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(isNatKind#) = 0
Strict:
{isNatKind#(active(X)) -> isNatKind#(X)}
EDG:
{(isNatKind#(active(X)) -> isNatKind#(X), isNatKind#(active(X)) -> isNatKind#(X))}
SCCS:
Scc:
{isNatKind#(active(X)) -> isNatKind#(X)}
SCC:
Strict:
{isNatKind#(active(X)) -> isNatKind#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(isNatKind#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2),
and#(active(X1), X2) -> and#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(and#) = 0
Strict:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2)}
EDG:
{(and#(X1, active(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(mark(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))}
SCCS:
Scc:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2)}
SCC:
Strict:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2),
and#(mark(X1), X2) -> and#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(and#) = 0
Strict:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2)}
EDG:
{(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
(and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))}
SCCS:
Scc:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2)}
SCC:
Strict:
{ and#(X1, mark(X2)) -> and#(X1, X2),
and#(X1, active(X2)) -> and#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(and#) = 1
Strict:
{and#(X1, active(X2)) -> and#(X1, X2)}
EDG:
{(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))}
SCCS:
Scc:
{and#(X1, active(X2)) -> and#(X1, X2)}
SCC:
Strict:
{and#(X1, active(X2)) -> and#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(and#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, X2, active(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 2
Strict:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3)}
EDG:
{(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(active(X1), X2, X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(active(X1), X2, X3) -> U71#(X1, X2, X3))}
SCCS:
Scc:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3)}
SCC:
Strict:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3),
U71#(active(X1), X2, X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 0
Strict:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
EDG:
{(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))}
SCCS:
Scc:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
SCC:
Strict:
{ U71#(X1, X2, mark(X3)) -> U71#(X1, X2, X3),
U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 2
Strict:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
EDG:
{(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3))}
SCCS:
Scc:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
SCC:
Strict:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3),
U71#(mark(X1), X2, X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 0
Strict:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
EDG:
{(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3))
(U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))}
SCCS:
Scc:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
SCC:
Strict:
{ U71#(X1, mark(X2), X3) -> U71#(X1, X2, X3),
U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 1
Strict:
{U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
EDG:
{(U71#(X1, active(X2), X3) -> U71#(X1, X2, X3), U71#(X1, active(X2), X3) -> U71#(X1, X2, X3))}
SCCS:
Scc:
{U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
SCC:
Strict:
{U71#(X1, active(X2), X3) -> U71#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U71#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2),
x#(active(X1), X2) -> x#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(x#) = 0
Strict:
{ x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
EDG:
{(x#(X1, active(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))}
SCCS:
Scc:
{ x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
SCC:
Strict:
{ x#(X1, mark(X2)) -> x#(X1, X2),
x#(X1, active(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(x#) = 1
Strict:
{x#(X1, mark(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
EDG:
{(x#(mark(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
(x#(mark(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
(x#(X1, mark(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))}
SCCS:
Scc:
{x#(X1, mark(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
SCC:
Strict:
{x#(X1, mark(X2)) -> x#(X1, X2),
x#(mark(X1), X2) -> x#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(x#) = 0
Strict:
{x#(X1, mark(X2)) -> x#(X1, X2)}
EDG:
{(x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))}
SCCS:
Scc:
{x#(X1, mark(X2)) -> x#(X1, X2)}
SCC:
Strict:
{x#(X1, mark(X2)) -> x#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(x#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U61#(mark(X)) -> U61#(X),
U61#(active(X)) -> U61#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U61#) = 0
Strict:
{U61#(active(X)) -> U61#(X)}
EDG:
{(U61#(active(X)) -> U61#(X), U61#(active(X)) -> U61#(X))}
SCCS:
Scc:
{U61#(active(X)) -> U61#(X)}
SCC:
Strict:
{U61#(active(X)) -> U61#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U61#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U51#(X1, X2, mark(X3)) -> U51#(X1, X2, X3),
U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 2
Strict:
{U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
EDG:
{(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))}
SCCS:
Scc:
{U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
SCC:
Strict:
{U51#(X1, X2, active(X3)) -> U51#(X1, X2, X3),
U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 2
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
EDG:
{(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(active(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(active(X1), X2, X3) -> U51#(X1, X2, X3))}
SCCS:
Scc:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
SCC:
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3),
U51#(active(X1), X2, X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 0
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3)}
EDG:
{(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3))}
SCCS:
Scc:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3)}
SCC:
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3),
U51#(mark(X1), X2, X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 0
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
EDG:
{(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3))
(U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))}
SCCS:
Scc:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
SCC:
Strict:
{ U51#(X1, mark(X2), X3) -> U51#(X1, X2, X3),
U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 1
Strict:
{U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
EDG:
{(U51#(X1, active(X2), X3) -> U51#(X1, X2, X3), U51#(X1, active(X2), X3) -> U51#(X1, X2, X3))}
SCCS:
Scc:
{U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
SCC:
Strict:
{U51#(X1, active(X2), X3) -> U51#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U51#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2),
plus#(active(X1), X2) -> plus#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(plus#) = 0
Strict:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2)}
EDG:
{(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(mark(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))}
SCCS:
Scc:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2)}
SCC:
Strict:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2),
plus#(mark(X1), X2) -> plus#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(plus#) = 0
Strict:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2)}
EDG:
{(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
(plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))}
SCCS:
Scc:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2)}
SCC:
Strict:
{ plus#(X1, mark(X2)) -> plus#(X1, X2),
plus#(X1, active(X2)) -> plus#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(plus#) = 1
Strict:
{plus#(X1, active(X2)) -> plus#(X1, X2)}
EDG:
{(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))}
SCCS:
Scc:
{plus#(X1, active(X2)) -> plus#(X1, X2)}
SCC:
Strict:
{plus#(X1, active(X2)) -> plus#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(plus#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ s#(mark(X)) -> s#(X),
s#(active(X)) -> s#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(s#) = 0
Strict:
{s#(active(X)) -> s#(X)}
EDG:
{(s#(active(X)) -> s#(X), s#(active(X)) -> s#(X))}
SCCS:
Scc:
{s#(active(X)) -> s#(X)}
SCC:
Strict:
{s#(active(X)) -> s#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(s#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U41#(X1, mark(X2)) -> U41#(X1, X2),
U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U41#) = 1
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2)}
EDG:
{(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(active(X1), X2) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(active(X1), X2) -> U41#(X1, X2))}
SCCS:
Scc:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2)}
SCC:
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2),
U41#(active(X1), X2) -> U41#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U41#) = 0
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2)}
EDG:
{(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))
(U41#(mark(X1), X2) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))
(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(mark(X1), X2) -> U41#(X1, X2))}
SCCS:
Scc:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2)}
SCC:
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2),
U41#(mark(X1), X2) -> U41#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U41#) = 0
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2)}
EDG:
{(U41#(X1, active(X2)) -> U41#(X1, X2), U41#(X1, active(X2)) -> U41#(X1, X2))}
SCCS:
Scc:
{U41#(X1, active(X2)) -> U41#(X1, X2)}
SCC:
Strict:
{U41#(X1, active(X2)) -> U41#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U41#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U33#(mark(X)) -> U33#(X),
U33#(active(X)) -> U33#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U33#) = 0
Strict:
{U33#(active(X)) -> U33#(X)}
EDG:
{(U33#(active(X)) -> U33#(X), U33#(active(X)) -> U33#(X))}
SCCS:
Scc:
{U33#(active(X)) -> U33#(X)}
SCC:
Strict:
{U33#(active(X)) -> U33#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U33#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3),
U31#(active(X1), X2, X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 0
Strict:
{ U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
EDG:
{(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))}
SCCS:
Scc:
{ U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
SCC:
Strict:
{ U31#(X1, X2, mark(X3)) -> U31#(X1, X2, X3),
U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 2
Strict:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
EDG:
{(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3))}
SCCS:
Scc:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
SCC:
Strict:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3),
U31#(mark(X1), X2, X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 0
Strict:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
EDG:
{(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))}
SCCS:
Scc:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
SCC:
Strict:
{U31#(X1, X2, active(X3)) -> U31#(X1, X2, X3),
U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 2
Strict:
{ U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
EDG:
{(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3))
(U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))}
SCCS:
Scc:
{ U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
SCC:
Strict:
{ U31#(X1, mark(X2), X3) -> U31#(X1, X2, X3),
U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 1
Strict:
{U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
EDG:
{(U31#(X1, active(X2), X3) -> U31#(X1, X2, X3), U31#(X1, active(X2), X3) -> U31#(X1, X2, X3))}
SCCS:
Scc:
{U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
SCC:
Strict:
{U31#(X1, active(X2), X3) -> U31#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U31#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(mark(X1), X2) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U32#) = 0
Strict:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2)}
EDG:
{(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(active(X1), X2) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(active(X1), X2) -> U32#(X1, X2))}
SCCS:
Scc:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2)}
SCC:
Strict:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2),
U32#(active(X1), X2) -> U32#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U32#) = 0
Strict:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2)}
EDG:
{(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))
(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, mark(X2)) -> U32#(X1, X2))
(U32#(X1, mark(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))}
SCCS:
Scc:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2)}
SCC:
Strict:
{ U32#(X1, mark(X2)) -> U32#(X1, X2),
U32#(X1, active(X2)) -> U32#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U32#) = 1
Strict:
{U32#(X1, active(X2)) -> U32#(X1, X2)}
EDG:
{(U32#(X1, active(X2)) -> U32#(X1, X2), U32#(X1, active(X2)) -> U32#(X1, X2))}
SCCS:
Scc:
{U32#(X1, active(X2)) -> U32#(X1, X2)}
SCC:
Strict:
{U32#(X1, active(X2)) -> U32#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U32#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2),
U21#(active(X1), X2) -> U21#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U21#) = 0
Strict:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2)}
EDG:
{(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(mark(X1), X2) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(mark(X1), X2) -> U21#(X1, X2))}
SCCS:
Scc:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2)}
SCC:
Strict:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2),
U21#(mark(X1), X2) -> U21#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U21#) = 0
Strict:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2)}
EDG:
{(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))
(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, mark(X2)) -> U21#(X1, X2))
(U21#(X1, mark(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))}
SCCS:
Scc:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2)}
SCC:
Strict:
{ U21#(X1, mark(X2)) -> U21#(X1, X2),
U21#(X1, active(X2)) -> U21#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U21#) = 1
Strict:
{U21#(X1, active(X2)) -> U21#(X1, X2)}
EDG:
{(U21#(X1, active(X2)) -> U21#(X1, X2), U21#(X1, active(X2)) -> U21#(X1, X2))}
SCCS:
Scc:
{U21#(X1, active(X2)) -> U21#(X1, X2)}
SCC:
Strict:
{U21#(X1, active(X2)) -> U21#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U21#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ U22#(mark(X)) -> U22#(X),
U22#(active(X)) -> U22#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U22#) = 0
Strict:
{U22#(active(X)) -> U22#(X)}
EDG:
{(U22#(active(X)) -> U22#(X), U22#(active(X)) -> U22#(X))}
SCCS:
Scc:
{U22#(active(X)) -> U22#(X)}
SCC:
Strict:
{U22#(active(X)) -> U22#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U22#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U13#(mark(X)) -> U13#(X),
U13#(active(X)) -> U13#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U13#) = 0
Strict:
{U13#(active(X)) -> U13#(X)}
EDG:
{(U13#(active(X)) -> U13#(X), U13#(active(X)) -> U13#(X))}
SCCS:
Scc:
{U13#(active(X)) -> U13#(X)}
SCC:
Strict:
{U13#(active(X)) -> U13#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U13#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U11#(X1, X2, mark(X3)) -> U11#(X1, X2, X3),
U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 2
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3)}
EDG:
{(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(active(X1), X2, X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(active(X1), X2, X3) -> U11#(X1, X2, X3))}
SCCS:
Scc:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3)}
SCC:
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3),
U11#(active(X1), X2, X3) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 0
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3)}
EDG:
{(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3))}
SCCS:
Scc:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3)}
SCC:
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3),
U11#(mark(X1), X2, X3) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 0
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3)}
EDG:
{(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, active(X2), X3) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, active(X2), X3) -> U11#(X1, X2, X3))}
SCCS:
Scc:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3)}
SCC:
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3),
U11#(X1, active(X2), X3) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 1
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3)}
EDG:
{(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))
(U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))
(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3))}
SCCS:
Scc:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3)}
SCC:
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3),
U11#(X1, mark(X2), X3) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 1
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3)}
EDG:
{(U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3), U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3))}
SCCS:
Scc:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3)}
SCC:
Strict:
{U11#(X1, X2, active(X3)) -> U11#(X1, X2, X3)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U11#) = 2
Strict:
{}
Qed
SCC:
Strict:
{ isNat#(mark(X)) -> isNat#(X),
isNat#(active(X)) -> isNat#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(isNat#) = 0
Strict:
{isNat#(active(X)) -> isNat#(X)}
EDG:
{(isNat#(active(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))}
SCCS:
Scc:
{isNat#(active(X)) -> isNat#(X)}
SCC:
Strict:
{isNat#(active(X)) -> isNat#(X)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(isNat#) = 0
Strict:
{}
Qed
SCC:
Strict:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(X1, active(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U12#) = 1
Strict:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
EDG:
{(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(mark(X1), X2) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(mark(X1), X2) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))}
SCCS:
Scc:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
SCC:
Strict:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(mark(X1), X2) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U12#) = 0
Strict:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
EDG:
{(U12#(active(X1), X2) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))
(U12#(active(X1), X2) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))
(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(active(X1), X2) -> U12#(X1, X2))}
SCCS:
Scc:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
SCC:
Strict:
{ U12#(X1, mark(X2)) -> U12#(X1, X2),
U12#(active(X1), X2) -> U12#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U12#) = 0
Strict:
{U12#(X1, mark(X2)) -> U12#(X1, X2)}
EDG:
{(U12#(X1, mark(X2)) -> U12#(X1, X2), U12#(X1, mark(X2)) -> U12#(X1, X2))}
SCCS:
Scc:
{U12#(X1, mark(X2)) -> U12#(X1, X2)}
SCC:
Strict:
{U12#(X1, mark(X2)) -> U12#(X1, X2)}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
SPSC:
Simple Projection:
pi(U12#) = 1
Strict:
{}
Qed
SCC:
Strict:
{ mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U13(X)) -> mark#(X),
mark#(U13(X)) -> active#(U13(mark(X))),
mark#(U22(X)) -> mark#(X),
mark#(U22(X)) -> active#(U22(mark(X))),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U33(X)) -> mark#(X),
mark#(U33(X)) -> active#(U33(mark(X))),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(s(X)) -> mark#(X),
mark#(s(X)) -> active#(s(mark(X))),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U61(X)) -> mark#(X),
mark#(U61(X)) -> active#(U61(mark(X))),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2)))}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
POLY:
Argument Filtering:
pi(isNatKind) = [], pi(and) = [], pi(U71) = [], pi(x) = [], pi(U61) = [], pi(0) = [], pi(U51) = [], pi(plus) = [], pi(s) = [], pi(U41) = [], pi(U33) = [], pi(U31) = [], pi(U32) = [], pi(U21) = [], pi(U22) = [], pi(U13) = [], pi(tt) = [], pi(U11) = [], pi(active#) = 0, pi(active) = [], pi(isNat) = [], pi(U12) = [], pi(mark#) = [], pi(mark) = []
Usable Rules:
{}
Interpretation:
[mark#] = 1,
[U71] = 1,
[U51] = 1,
[U31] = 1,
[U11] = 1,
[and] = 1,
[x] = 1,
[plus] = 1,
[U41] = 1,
[U32] = 1,
[U21] = 1,
[U12] = 1,
[isNatKind] = 1,
[U61] = 0,
[s] = 0,
[U33] = 0,
[U22] = 0,
[U13] = 0,
[isNat] = 1
Strict:
{ mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U13(X)) -> mark#(X),
mark#(U22(X)) -> mark#(X),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U33(X)) -> mark#(X),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(s(X)) -> mark#(X),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U61(X)) -> mark#(X),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2)))}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
EDG:
{
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U11(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U32(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U41(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
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(mark#(U71(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
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(mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
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(active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNat(X)) -> active#(isNat(X)))
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(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
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(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
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(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(s(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U33(X)) -> mark#(X))
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(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U22(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> mark#(X))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U61(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(s(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U33(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U22(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U13(X)) -> mark#(X))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U61(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(s(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U33(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U22(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U13(X)) -> mark#(X))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(and(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> mark#(X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(x(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U61(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(s(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U33(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U22(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U13(X)) -> mark#(X))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(and(tt(), X)) -> mark#(X))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), N)) -> mark#(N))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(isNat(X)) -> active#(isNat(X)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U13(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U13(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U13(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U13(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U13(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U13(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
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(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U22(X)) -> mark#(X))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U13(X)) -> mark#(X))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(and(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(x(X1, X2)) -> mark#(X2))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(x(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U61(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(s(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U33(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U22(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U13(X)) -> mark#(X))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U61(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U33(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U22(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U13(X)) -> mark#(X))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U61(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U33(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U22(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U13(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), N)) -> mark#(N))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U61(X)) -> mark#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(s(X)) -> mark#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U33(X)) -> mark#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U22(X)) -> mark#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U13(X)) -> mark#(X))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U13(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U22(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U33(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(s(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U61(X)) -> mark#(X))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), N)) -> mark#(N))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U13(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U22(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U33(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U61(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X2), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U13(X)) -> mark#(X))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U22(X)) -> mark#(X))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U33(X)) -> mark#(X))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
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(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U51(X1, X2, X3)) -> mark#(X1))
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(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U61(X)) -> mark#(X))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U13(X)) -> mark#(X))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U22(X)) -> mark#(X))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U33(X)) -> mark#(X))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(s(X)) -> mark#(X))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U61(X)) -> mark#(X))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(x(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(x(X1, X2)) -> mark#(X2))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(and(X1, X2)) -> mark#(X1))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(active#(and(tt(), X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(and(tt(), X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(and(tt(), X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(and(tt(), X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(s(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(s(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(s(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(s(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(s(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U22(X)) -> mark#(X), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U22(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U13(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U22(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U33(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U22(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U22(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(U61(X)) -> mark#(X))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U22(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U22(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U22(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U22(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U22(X)) -> mark#(X), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U41(tt(), N)) -> mark#(N))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(and(tt(), X)) -> mark#(X))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(isNatKind(X)) -> active#(isNatKind(X)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(isNat(X)) -> active#(isNat(X)))
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(active#(U41(tt(), N)) -> mark#(N), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
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(active#(U41(tt(), N)) -> mark#(N), mark#(U21(X1, X2)) -> mark#(X1))
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(active#(U41(tt(), N)) -> mark#(N), mark#(U32(X1, X2)) -> mark#(X1))
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(active#(U41(tt(), N)) -> mark#(N), mark#(U31(X1, X2, X3)) -> mark#(X1))
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(active#(U41(tt(), N)) -> mark#(N), mark#(U33(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(s(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(U61(X)) -> mark#(X))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X2))
(active#(U41(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U41(tt(), N)) -> mark#(N), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U41(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> mark#(X1))
(active#(U41(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U41(tt(), N)) -> mark#(N), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U13(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U22(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U33(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U61(X)) -> mark#(X))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U12(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(isNat(X)) -> active#(isNat(X)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U13(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U22(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U21(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U32(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U33(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U41(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(s(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> mark#(X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U61(X)) -> mark#(X))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> mark#(X2))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(and(X1, X2)) -> mark#(X1))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U13(X)) -> mark#(X))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
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(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U61(X)) -> mark#(X))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> mark#(X2))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> mark#(X1))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNat(X)) -> active#(isNat(X)))
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(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U13(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U22(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U33(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(s(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> mark#(X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U61(X)) -> mark#(X))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> mark#(X2))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> mark#(X1))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U41(tt(), N)) -> mark#(N))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)), active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(and(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(x(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(plus(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U31(X1, X2, X3)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U21(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U13(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U22(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U33(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U61(X)) -> mark#(X))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
(mark#(U12(X1, X2)) -> mark#(X1), mark#(isNatKind(X)) -> active#(isNatKind(X)))
}
SCCS:
Scc:
{ mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U13(X)) -> mark#(X),
mark#(U22(X)) -> mark#(X),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U33(X)) -> mark#(X),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(s(X)) -> mark#(X),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U61(X)) -> mark#(X),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2)))}
SCC:
Strict:
{ mark#(U12(X1, X2)) -> mark#(X1),
mark#(U12(X1, X2)) -> active#(U12(mark(X1), X2)),
mark#(isNat(X)) -> active#(isNat(X)),
mark#(U11(X1, X2, X3)) -> mark#(X1),
mark#(U11(X1, X2, X3)) -> active#(U11(mark(X1), X2, X3)),
mark#(U13(X)) -> mark#(X),
mark#(U22(X)) -> mark#(X),
mark#(U21(X1, X2)) -> mark#(X1),
mark#(U21(X1, X2)) -> active#(U21(mark(X1), X2)),
mark#(U32(X1, X2)) -> mark#(X1),
mark#(U32(X1, X2)) -> active#(U32(mark(X1), X2)),
mark#(U31(X1, X2, X3)) -> mark#(X1),
mark#(U31(X1, X2, X3)) -> active#(U31(mark(X1), X2, X3)),
mark#(U33(X)) -> mark#(X),
mark#(U41(X1, X2)) -> mark#(X1),
mark#(U41(X1, X2)) -> active#(U41(mark(X1), X2)),
mark#(s(X)) -> mark#(X),
mark#(plus(X1, X2)) -> mark#(X1),
mark#(plus(X1, X2)) -> mark#(X2),
mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
mark#(U51(X1, X2, X3)) -> mark#(X1),
mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)),
mark#(U61(X)) -> mark#(X),
mark#(x(X1, X2)) -> mark#(X1),
mark#(x(X1, X2)) -> mark#(X2),
mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
mark#(U71(X1, X2, X3)) -> mark#(X1),
mark#(U71(X1, X2, X3)) -> active#(U71(mark(X1), X2, X3)),
mark#(and(X1, X2)) -> mark#(X1),
mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
mark#(isNatKind(X)) -> active#(isNatKind(X)),
active#(U12(tt(), V2)) -> mark#(U13(isNat(V2))),
active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1), V1)),
active#(isNat(plus(V1, V2))) -> mark#(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(isNat(x(V1, V2))) -> mark#(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active#(U11(tt(), V1, V2)) -> mark#(U12(isNat(V1), V2)),
active#(U21(tt(), V1)) -> mark#(U22(isNat(V1))),
active#(U32(tt(), V2)) -> mark#(U33(isNat(V2))),
active#(U31(tt(), V1, V2)) -> mark#(U32(isNat(V1), V2)),
active#(U41(tt(), N)) -> mark#(N),
active#(plus(N, s(M))) -> mark#(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(plus(N, 0())) -> mark#(U41(and(isNat(N), isNatKind(N)), N)),
active#(U51(tt(), M, N)) -> mark#(s(plus(N, M))),
active#(x(N, s(M))) -> mark#(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active#(x(N, 0())) -> mark#(U61(and(isNat(N), isNatKind(N)))),
active#(U71(tt(), M, N)) -> mark#(plus(x(N, M), N)),
active#(and(tt(), X)) -> mark#(X),
active#(isNatKind(s(V1))) -> mark#(isNatKind(V1)),
active#(isNatKind(plus(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2))),
active#(isNatKind(x(V1, V2))) -> mark#(and(isNatKind(V1), isNatKind(V2)))}
Weak:
{ mark(U12(X1, X2)) -> active(U12(mark(X1), X2)),
mark(isNat(X)) -> active(isNat(X)),
mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)),
mark(tt()) -> active(tt()),
mark(U13(X)) -> active(U13(mark(X))),
mark(U22(X)) -> active(U22(mark(X))),
mark(U21(X1, X2)) -> active(U21(mark(X1), X2)),
mark(U32(X1, X2)) -> active(U32(mark(X1), X2)),
mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)),
mark(U33(X)) -> active(U33(mark(X))),
mark(U41(X1, X2)) -> active(U41(mark(X1), X2)),
mark(s(X)) -> active(s(mark(X))),
mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)),
mark(0()) -> active(0()),
mark(U61(X)) -> active(U61(mark(X))),
mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)),
mark(and(X1, X2)) -> active(and(mark(X1), X2)),
mark(isNatKind(X)) -> active(isNatKind(X)),
U12(X1, mark(X2)) -> U12(X1, X2),
U12(X1, active(X2)) -> U12(X1, X2),
U12(mark(X1), X2) -> U12(X1, X2),
U12(active(X1), X2) -> U12(X1, X2),
isNat(mark(X)) -> isNat(X),
isNat(active(X)) -> isNat(X),
active(U12(tt(), V2)) -> mark(U13(isNat(V2))),
active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)),
active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(isNat(0())) -> mark(tt()),
active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)),
active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2)),
active(U13(tt())) -> mark(tt()),
active(U22(tt())) -> mark(tt()),
active(U21(tt(), V1)) -> mark(U22(isNat(V1))),
active(U32(tt(), V2)) -> mark(U33(isNat(V2))),
active(U31(tt(), V1, V2)) -> mark(U32(isNat(V1), V2)),
active(U33(tt())) -> mark(tt()),
active(U41(tt(), N)) -> mark(N),
active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(plus(N, 0())) -> mark(U41(and(isNat(N), isNatKind(N)), N)),
active(U51(tt(), M, N)) -> mark(s(plus(N, M))),
active(U61(tt())) -> mark(0()),
active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)),
active(x(N, 0())) -> mark(U61(and(isNat(N), isNatKind(N)))),
active(U71(tt(), M, N)) -> mark(plus(x(N, M), N)),
active(and(tt(), X)) -> mark(X),
active(isNatKind(s(V1))) -> mark(isNatKind(V1)),
active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
active(isNatKind(0())) -> mark(tt()),
active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))),
U11(X1, X2, mark(X3)) -> U11(X1, X2, X3),
U11(X1, X2, active(X3)) -> U11(X1, X2, X3),
U11(X1, mark(X2), X3) -> U11(X1, X2, X3),
U11(X1, active(X2), X3) -> U11(X1, X2, X3),
U11(mark(X1), X2, X3) -> U11(X1, X2, X3),
U11(active(X1), X2, X3) -> U11(X1, X2, X3),
U13(mark(X)) -> U13(X),
U13(active(X)) -> U13(X),
U22(mark(X)) -> U22(X),
U22(active(X)) -> U22(X),
U21(X1, mark(X2)) -> U21(X1, X2),
U21(X1, active(X2)) -> U21(X1, X2),
U21(mark(X1), X2) -> U21(X1, X2),
U21(active(X1), X2) -> U21(X1, X2),
U32(X1, mark(X2)) -> U32(X1, X2),
U32(X1, active(X2)) -> U32(X1, X2),
U32(mark(X1), X2) -> U32(X1, X2),
U32(active(X1), X2) -> U32(X1, X2),
U31(X1, X2, mark(X3)) -> U31(X1, X2, X3),
U31(X1, X2, active(X3)) -> U31(X1, X2, X3),
U31(X1, mark(X2), X3) -> U31(X1, X2, X3),
U31(X1, active(X2), X3) -> U31(X1, X2, X3),
U31(mark(X1), X2, X3) -> U31(X1, X2, X3),
U31(active(X1), X2, X3) -> U31(X1, X2, X3),
U33(mark(X)) -> U33(X),
U33(active(X)) -> U33(X),
U41(X1, mark(X2)) -> U41(X1, X2),
U41(X1, active(X2)) -> U41(X1, X2),
U41(mark(X1), X2) -> U41(X1, X2),
U41(active(X1), X2) -> U41(X1, X2),
s(mark(X)) -> s(X),
s(active(X)) -> s(X),
plus(X1, mark(X2)) -> plus(X1, X2),
plus(X1, active(X2)) -> plus(X1, X2),
plus(mark(X1), X2) -> plus(X1, X2),
plus(active(X1), X2) -> plus(X1, X2),
U51(X1, X2, mark(X3)) -> U51(X1, X2, X3),
U51(X1, X2, active(X3)) -> U51(X1, X2, X3),
U51(X1, mark(X2), X3) -> U51(X1, X2, X3),
U51(X1, active(X2), X3) -> U51(X1, X2, X3),
U51(mark(X1), X2, X3) -> U51(X1, X2, X3),
U51(active(X1), X2, X3) -> U51(X1, X2, X3),
U61(mark(X)) -> U61(X),
U61(active(X)) -> U61(X),
x(X1, mark(X2)) -> x(X1, X2),
x(X1, active(X2)) -> x(X1, X2),
x(mark(X1), X2) -> x(X1, X2),
x(active(X1), X2) -> x(X1, X2),
U71(X1, X2, mark(X3)) -> U71(X1, X2, X3),
U71(X1, X2, active(X3)) -> U71(X1, X2, X3),
U71(X1, mark(X2), X3) -> U71(X1, X2, X3),
U71(X1, active(X2), X3) -> U71(X1, X2, X3),
U71(mark(X1), X2, X3) -> U71(X1, X2, X3),
U71(active(X1), X2, X3) -> U71(X1, X2, X3),
and(X1, mark(X2)) -> and(X1, X2),
and(X1, active(X2)) -> and(X1, X2),
and(mark(X1), X2) -> and(X1, X2),
and(active(X1), X2) -> and(X1, X2),
isNatKind(mark(X)) -> isNatKind(X),
isNatKind(active(X)) -> isNatKind(X)}
Fail