Problem: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) Proof: Bounds Processor: bound: 1 enrichment: match automaton: final states: {8,7,6,5,4,3} transitions: active1(10) -> 4* 01() -> 10* tt1() -> 10* active0(2) -> 3* active0(1) -> 3* U110(1,1,1) -> 5* U110(2,2,1) -> 5* U110(1,1,2) -> 5* U110(2,2,2) -> 5* U110(1,2,1) -> 5* U110(2,1,1) -> 5* U110(1,2,2) -> 5* U110(2,1,2) -> 5* tt0() -> 1* mark0(2) -> 4* mark0(1) -> 4* U120(1,1,1) -> 6* U120(2,2,1) -> 6* U120(1,1,2) -> 6* U120(2,2,2) -> 6* U120(1,2,1) -> 6* U120(2,1,1) -> 6* U120(1,2,2) -> 6* U120(2,1,2) -> 6* s0(2) -> 7* s0(1) -> 7* plus0(1,2) -> 8* plus0(2,1) -> 8* plus0(1,1) -> 8* plus0(2,2) -> 8* 00() -> 2* problem: Qed