MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(X) -> U12(X) a__U12(tt()) -> tt() a__U21(X) -> U21(X) a__U21(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),N) -> mark(N) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U41(tt(),M,N) -> a__U42(a__isNat(N),M,N) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U42(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__isNat(X) -> isNat(X) 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__plus(N,0()) -> a__U31(a__isNat(N),N) a__plus(N,s(M)) -> a__U41(a__isNat(M),M,N) a__plus(X1,X2) -> plus(X1,X2) mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(isNat(X)) -> a__isNat(X) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(tt()) -> tt() - Signature: {a__U11/2,a__U12/1,a__U21/1,a__U31/2,a__U41/3,a__U42/3,a__isNat/1,a__plus/2,mark/1} / {0/0,U11/2,U12/1,U21/1 ,U31/2,U41/3,U42/3,isNat/1,plus/2,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U31,a__U41,a__U42,a__isNat ,a__plus,mark} and constructors {0,U11,U12,U21,U31,U41,U42,isNat,plus,s,tt} + Applied Processor: NaturalPI {shape = Mixed 3, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: Incompatible MAYBE