MAYBE Problem: a__U11(tt(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(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,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Proof: DP Processor: DPs: a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) a__U12#(tt(),M,N) -> mark#(M) a__U12#(tt(),M,N) -> mark#(N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> mark#(M) a__U22#(tt(),M,N) -> mark#(N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) -> mark#(N) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(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#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(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(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(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,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) TDG Processor: DPs: a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) a__U12#(tt(),M,N) -> mark#(M) a__U12#(tt(),M,N) -> mark#(N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> mark#(M) a__U22#(tt(),M,N) -> mark#(N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) -> mark#(N) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(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#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(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(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(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,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) graph: a__x#(N,s(M)) -> a__U21#(tt(),M,N) -> a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,s(M)) -> a__U21#(tt(),M,N) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,0()) -> mark#(N) a__U22#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> mark#(N) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> mark#(M) a__plus#(N,0()) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__plus#(N,0()) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__plus#(N,0()) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) -> a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,s(M)) -> a__U21#(tt(),M,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#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> mark#(X1) 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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> 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#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) 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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> mark#(N) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> mark#(M) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) -> a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,0()) -> mark#(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#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> mark#(X1) 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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> 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#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) 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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> mark#(N) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> mark#(M) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) -> a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) 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#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> mark#(X1) 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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,0()) -> mark#(N) a__U12#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> mark#(N) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> mark#(M) Open