MAYBE Problem: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Proof: DP Processor: DPs: a__U11#(tt(),V2) -> a__isNat#(V2) a__U11#(tt(),V2) -> a__U12#(a__isNat(V2)) a__U31#(tt(),V2) -> a__isNat#(V2) a__U31#(tt(),V2) -> a__U32#(a__isNat(V2)) a__U41#(tt(),N) -> mark#(N) a__U51#(tt(),M,N) -> a__isNat#(N) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) a__U52#(tt(),M,N) -> mark#(M) a__U52#(tt(),M,N) -> mark#(N) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U71#(tt(),M,N) -> a__isNat#(N) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) a__U72#(tt(),M,N) -> mark#(M) a__U72#(tt(),M,N) -> mark#(N) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__plus#(N,0()) -> a__isNat#(N) a__plus#(N,0()) -> a__U41#(a__isNat(N),N) a__plus#(N,s(M)) -> a__isNat#(M) a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) a__x#(N,0()) -> a__isNat#(N) a__x#(N,0()) -> a__U61#(a__isNat(N)) a__x#(N,s(M)) -> a__isNat#(M) a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> a__U61#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) TRS: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) TDG Processor: DPs: a__U11#(tt(),V2) -> a__isNat#(V2) a__U11#(tt(),V2) -> a__U12#(a__isNat(V2)) a__U31#(tt(),V2) -> a__isNat#(V2) a__U31#(tt(),V2) -> a__U32#(a__isNat(V2)) a__U41#(tt(),N) -> mark#(N) a__U51#(tt(),M,N) -> a__isNat#(N) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) a__U52#(tt(),M,N) -> mark#(M) a__U52#(tt(),M,N) -> mark#(N) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U71#(tt(),M,N) -> a__isNat#(N) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) a__U72#(tt(),M,N) -> mark#(M) a__U72#(tt(),M,N) -> mark#(N) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__plus#(N,0()) -> a__isNat#(N) a__plus#(N,0()) -> a__U41#(a__isNat(N),N) a__plus#(N,s(M)) -> a__isNat#(M) a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) a__x#(N,0()) -> a__isNat#(N) a__x#(N,0()) -> a__U61#(a__isNat(N)) a__x#(N,s(M)) -> a__isNat#(M) a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> a__U61#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) TRS: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) graph: a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__x#(N,0()) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) -> a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) -> a__U71#(tt(),M,N) -> a__isNat#(N) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__x#(N,s(M)) -> a__isNat#(M) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,s(M)) -> a__isNat#(M) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,0()) -> a__U61#(a__isNat(N)) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,0()) -> a__isNat#(N) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,s(M)) -> a__isNat#(M) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,0()) -> a__U41#(a__isNat(N),N) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,0()) -> a__isNat#(N) a__U72#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U61(X)) -> a__U61#(mark(X)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U61(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U41(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U32(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U31(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U21(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(isNat(X)) -> a__isNat#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U12(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U72(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U71(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U61(X)) -> a__U61#(mark(X)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U61(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U52(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U41(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U32(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U31(X1,X2)) -> mark#(X1) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U21(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(isNat(X)) -> a__isNat#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U12(X)) -> mark#(X) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U72#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2)) -> mark#(X1) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) -> a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) -> a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) -> a__U72#(tt(),M,N) -> mark#(N) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) -> a__U72#(tt(),M,N) -> mark#(M) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__U71#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__plus#(N,0()) -> a__U41#(a__isNat(N),N) -> a__U41#(tt(),N) -> mark#(N) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__plus#(N,0()) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) -> a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) -> a__U51#(tt(),M,N) -> a__isNat#(N) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__plus#(N,s(M)) -> a__isNat#(M) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,s(M)) -> a__isNat#(M) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,0()) -> a__U41#(a__isNat(N),N) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,0()) -> a__isNat#(N) a__U52#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U61(X)) -> a__U61#(mark(X)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U61(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U41(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U32(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U31(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U21(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(isNat(X)) -> a__isNat#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U12(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U72(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U71(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U61(X)) -> a__U61#(mark(X)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U61(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U52(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U41(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U32(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U31(X1,X2)) -> mark#(X1) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U21(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(isNat(X)) -> a__isNat#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U12(X)) -> mark#(X) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U52#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2)) -> mark#(X1) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) -> a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) -> a__U52#(tt(),M,N) -> mark#(N) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) -> a__U52#(tt(),M,N) -> mark#(M) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__U51#(tt(),M,N) -> a__isNat#(N) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) -> a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) -> a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) -> a__U72#(tt(),M,N) -> mark#(N) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) -> a__U72#(tt(),M,N) -> mark#(M) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U72(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) -> a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) -> a__U71#(tt(),M,N) -> a__isNat#(N) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U71(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U61(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U61(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U61(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U61(X)) -> mark#(X) -> mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U61(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U61(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U61(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U61(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U61(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U61(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U61(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U61(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(U61(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U61(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U61(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U61(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U61(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) -> a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) -> a__U52#(tt(),M,N) -> mark#(N) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) -> a__U52#(tt(),M,N) -> mark#(M) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U52(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),M,N) -> a__isNat#(N) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__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#(U61(X)) -> a__U61#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__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#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U41(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) -> a__U41#(tt(),N) -> mark#(N) mark#(U32(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U32(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U32(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U61(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U32(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U32(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U32(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) -> a__U31#(tt(),V2) -> a__U32#(a__isNat(V2)) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) -> a__U31#(tt(),V2) -> a__isNat#(V2) mark#(U21(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U21(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U21(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U21(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U21(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U61(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U21(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U21(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U21(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U21(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U21(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U21(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U21(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__isNat#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) mark#(U12(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U12(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U12(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U61(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U12(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V2) -> a__U12#(a__isNat(V2)) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V2) -> a__isNat#(V2) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,s(M)) -> a__isNat#(M) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,0()) -> a__U61#(a__isNat(N)) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,0()) -> a__isNat#(N) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U71(X1,X2,X3)) -> a__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#(U61(X)) -> a__U61#(mark(X)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U61(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U51(X1,X2,X3)) -> a__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#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U32(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(isNat(X)) -> a__isNat#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,s(M)) -> a__isNat#(M) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,0()) -> a__U41#(a__isNat(N),N) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,0()) -> a__isNat#(N) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U71(X1,X2,X3)) -> a__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#(U61(X)) -> a__U61#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U61(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U51(X1,X2,X3)) -> a__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#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U32(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(isNat(X)) -> a__isNat#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U61(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) 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#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U61(X)) -> a__U61#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U61(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) 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#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U41#(tt(),N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U41#(tt(),N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U41#(tt(),N) -> mark#(N) -> mark#(U72(X1,X2,X3)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) a__U41#(tt(),N) -> mark#(N) -> mark#(U71(X1,X2,X3)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U61(X)) -> a__U61#(mark(X)) a__U41#(tt(),N) -> mark#(N) -> mark#(U61(X)) -> mark#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U41#(tt(),N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U41#(tt(),N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U41#(tt(),N) -> mark#(N) -> mark#(U52(X1,X2,X3)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U41#(tt(),N) -> mark#(N) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U41#(tt(),N) -> mark#(N) -> mark#(U41(X1,X2)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U41#(tt(),N) -> mark#(N) -> mark#(U32(X)) -> mark#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U41#(tt(),N) -> mark#(N) -> mark#(U31(X1,X2)) -> mark#(X1) a__U41#(tt(),N) -> mark#(N) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U41#(tt(),N) -> mark#(N) -> mark#(U21(X)) -> mark#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(isNat(X)) -> a__isNat#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U41#(tt(),N) -> mark#(N) -> mark#(U12(X)) -> mark#(X) a__U41#(tt(),N) -> mark#(N) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U41#(tt(),N) -> mark#(N) -> mark#(U11(X1,X2)) -> mark#(X1) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__U31#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) -> a__U31#(tt(),V2) -> a__U32#(a__isNat(V2)) a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) -> a__U31#(tt(),V2) -> a__isNat#(V2) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__isNat#(x(V1,V2)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__isNat#(plus(V1,V2)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) -> a__U11#(tt(),V2) -> a__U12#(a__isNat(V2)) a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) -> a__U11#(tt(),V2) -> a__isNat#(V2) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(s(V1)) -> a__U21#(a__isNat(V1)) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__U11#(tt(),V2) -> a__isNat#(V2) -> a__isNat#(plus(V1,V2)) -> a__isNat#(V1) SCC Processor: #sccs: 2 #rules: 43 #arcs: 754/3600 DPs: a__x#(N,s(M)) -> a__U71#(a__isNat(M),M,N) a__U71#(tt(),M,N) -> a__U72#(a__isNat(N),M,N) a__U72#(tt(),M,N) -> mark#(M) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> a__U41#(mark(X1),X2) a__U41#(tt(),N) -> mark#(N) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U51#(tt(),M,N) -> a__U52#(a__isNat(N),M,N) a__U52#(tt(),M,N) -> mark#(M) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) a__U52#(tt(),M,N) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__plus#(N,0()) -> a__U41#(a__isNat(N),N) a__plus#(N,s(M)) -> a__U51#(a__isNat(M),M,N) mark#(U61(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2,X3)) -> a__U72#(mark(X1),X2,X3) a__U72#(tt(),M,N) -> mark#(N) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) a__U72#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U72#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__U52#(tt(),M,N) -> a__plus#(mark(N),mark(M)) TRS: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Open DPs: a__isNat#(plus(V1,V2)) -> a__isNat#(V1) a__isNat#(plus(V1,V2)) -> a__U11#(a__isNat(V1),V2) a__U11#(tt(),V2) -> a__isNat#(V2) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__isNat#(V1) a__isNat#(x(V1,V2)) -> a__U31#(a__isNat(V1),V2) a__U31#(tt(),V2) -> a__isNat#(V2) TRS: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(a__U11#) = 1 pi(a__isNat#) = 0 pi(a__U31#) = 1 problem: DPs: a__U11#(tt(),V2) -> a__isNat#(V2) a__U31#(tt(),V2) -> a__isNat#(V2) TRS: a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(tt()) -> tt() a__U21(tt()) -> tt() a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(tt()) -> tt() a__U41(tt(),N) -> mark(N) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt()) -> 0() a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U61(X) -> U61(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) SCC Processor: #sccs: 0 #rules: 0 #arcs: 27/4