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)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Bounds Processor: bound: 2 enrichment: match automaton: final states: {11,10,9,8,7,6,5} transitions: top1(23) -> 11* active1(2) -> 23* active1(4) -> 23* active1(1) -> 23* active1(3) -> 23* proper1(2) -> 23* proper1(4) -> 23* proper1(1) -> 23* proper1(3) -> 23* ok1(15) -> 15,7 ok1(17) -> 17,8 ok1(19) -> 19,9 ok1(21) -> 23,10 ok1(13) -> 13,6 plus1(3,1) -> 19* plus1(3,3) -> 19* plus1(4,2) -> 19* plus1(4,4) -> 19* plus1(1,2) -> 19* plus1(1,4) -> 19* plus1(2,1) -> 19* plus1(2,3) -> 19* plus1(3,2) -> 19* plus1(3,4) -> 19* plus1(4,1) -> 19* plus1(4,3) -> 19* plus1(1,1) -> 19* plus1(1,3) -> 19* plus1(2,2) -> 19* plus1(2,4) -> 19* s1(2) -> 17* s1(4) -> 17* s1(1) -> 17* s1(3) -> 17* U121(3,2,2) -> 15* U121(3,4,2) -> 15* U121(1,1,4) -> 15* U121(1,3,4) -> 15* U121(4,1,2) -> 15* U121(1,1,1) -> 15* U121(4,3,2) -> 15* U121(1,3,1) -> 15* U121(2,2,4) -> 15* U121(2,4,4) -> 15* U121(1,2,3) -> 15* U121(1,4,3) -> 15* U121(2,2,1) -> 15* U121(2,4,1) -> 15* U121(3,1,4) -> 15* U121(3,3,4) -> 15* U121(2,1,3) -> 15* U121(2,3,3) -> 15* U121(3,1,1) -> 15* U121(1,1,2) -> 15* U121(3,3,1) -> 15* U121(1,3,2) -> 15* U121(4,2,4) -> 15* U121(4,4,4) -> 15* U121(3,2,3) -> 15* U121(3,4,3) -> 15* U121(4,2,1) -> 15* U121(2,2,2) -> 15* U121(4,4,1) -> 15* U121(2,4,2) -> 15* U121(4,1,3) -> 15* U121(4,3,3) -> 15* U121(3,1,2) -> 15* U121(3,3,2) -> 15* U121(1,2,4) -> 15* U121(1,4,4) -> 15* U121(4,2,2) -> 15* U121(1,2,1) -> 15* U121(4,4,2) -> 15* U121(1,4,1) -> 15* U121(2,1,4) -> 15* U121(2,3,4) -> 15* U121(1,1,3) -> 15* U121(1,3,3) -> 15* U121(2,1,1) -> 15* U121(2,3,1) -> 15* U121(3,2,4) -> 15* U121(3,4,4) -> 15* U121(2,2,3) -> 15* U121(2,4,3) -> 15* U121(3,2,1) -> 15* U121(1,2,2) -> 15* U121(3,4,1) -> 15* U121(1,4,2) -> 15* U121(4,1,4) -> 15* U121(4,3,4) -> 15* U121(3,1,3) -> 15* U121(3,3,3) -> 15* U121(4,1,1) -> 15* U121(2,1,2) -> 15* U121(4,3,1) -> 15* U121(2,3,2) -> 15* U121(4,2,3) -> 15* U121(4,4,3) -> 15* U111(3,2,2) -> 13* U111(3,4,2) -> 13* U111(1,1,4) -> 13* U111(1,3,4) -> 13* U111(4,1,2) -> 13* U111(1,1,1) -> 13* U111(4,3,2) -> 13* U111(1,3,1) -> 13* U111(2,2,4) -> 13* U111(2,4,4) -> 13* U111(1,2,3) -> 13* U111(1,4,3) -> 13* U111(2,2,1) -> 13* U111(2,4,1) -> 13* U111(3,1,4) -> 13* U111(3,3,4) -> 13* U111(2,1,3) -> 13* U111(2,3,3) -> 13* U111(3,1,1) -> 13* U111(1,1,2) -> 13* U111(3,3,1) -> 13* U111(1,3,2) -> 13* U111(4,2,4) -> 13* U111(4,4,4) -> 13* U111(3,2,3) -> 13* U111(3,4,3) -> 13* U111(4,2,1) -> 13* U111(2,2,2) -> 13* U111(4,4,1) -> 13* U111(2,4,2) -> 13* U111(4,1,3) -> 13* U111(4,3,3) -> 13* U111(3,1,2) -> 13* U111(3,3,2) -> 13* U111(1,2,4) -> 13* U111(1,4,4) -> 13* U111(4,2,2) -> 13* U111(1,2,1) -> 13* U111(4,4,2) -> 13* U111(1,4,1) -> 13* U111(2,1,4) -> 13* U111(2,3,4) -> 13* U111(1,1,3) -> 13* U111(1,3,3) -> 13* U111(2,1,1) -> 13* U111(2,3,1) -> 13* U111(3,2,4) -> 13* U111(3,4,4) -> 13* U111(2,2,3) -> 13* U111(2,4,3) -> 13* U111(3,2,1) -> 13* U111(1,2,2) -> 13* U111(3,4,1) -> 13* U111(1,4,2) -> 13* U111(4,1,4) -> 13* U111(4,3,4) -> 13* U111(3,1,3) -> 13* U111(3,3,3) -> 13* U111(4,1,1) -> 13* U111(2,1,2) -> 13* U111(4,3,1) -> 13* U111(2,3,2) -> 13* U111(4,2,3) -> 13* U111(4,4,3) -> 13* 01() -> 21* tt1() -> 21* mark1(15) -> 15,7 mark1(17) -> 17,8 mark1(19) -> 19,9 mark1(13) -> 13,6 top2(24) -> 11* active0(2) -> 5* active0(4) -> 5* active0(1) -> 5* active0(3) -> 5* active2(21) -> 24* U110(3,4,2) -> 6* U110(1,1,4) -> 6* U110(1,3,4) -> 6* U110(4,1,2) -> 6* U110(1,1,1) -> 6* U110(4,3,2) -> 6* U110(1,3,1) -> 6* U110(2,2,4) -> 6* U110(2,4,4) -> 6* U110(1,2,3) -> 6* U110(1,4,3) -> 6* U110(2,2,1) -> 6* U110(2,4,1) -> 6* U110(3,1,4) -> 6* U110(3,3,4) -> 6* U110(2,1,3) -> 6* U110(2,3,3) -> 6* U110(3,1,1) -> 6* U110(1,1,2) -> 6* U110(3,3,1) -> 6* U110(1,3,2) -> 6* U110(4,2,4) -> 6* U110(4,4,4) -> 6* U110(3,2,3) -> 6* U110(3,4,3) -> 6* U110(4,2,1) -> 6* U110(2,2,2) -> 6* U110(4,4,1) -> 6* U110(2,4,2) -> 6* U110(4,1,3) -> 6* U110(4,3,3) -> 6* U110(3,1,2) -> 6* U110(3,3,2) -> 6* U110(1,2,4) -> 6* U110(1,4,4) -> 6* U110(4,2,2) -> 6* U110(1,2,1) -> 6* U110(4,4,2) -> 6* U110(1,4,1) -> 6* U110(2,1,4) -> 6* U110(2,3,4) -> 6* U110(1,1,3) -> 6* U110(1,3,3) -> 6* U110(2,1,1) -> 6* U110(2,3,1) -> 6* U110(3,2,4) -> 6* U110(3,4,4) -> 6* U110(2,2,3) -> 6* U110(2,4,3) -> 6* U110(3,2,1) -> 6* U110(1,2,2) -> 6* U110(3,4,1) -> 6* U110(1,4,2) -> 6* U110(4,1,4) -> 6* U110(4,3,4) -> 6* U110(3,1,3) -> 6* U110(3,3,3) -> 6* U110(4,1,1) -> 6* U110(2,1,2) -> 6* U110(4,3,1) -> 6* U110(2,3,2) -> 6* U110(4,2,3) -> 6* U110(4,4,3) -> 6* U110(3,2,2) -> 6* tt0() -> 1* mark0(2) -> 2* mark0(4) -> 2* mark0(1) -> 2* mark0(3) -> 2* U120(3,2,2) -> 7* U120(3,4,2) -> 7* U120(1,1,4) -> 7* U120(1,3,4) -> 7* U120(4,1,2) -> 7* U120(1,1,1) -> 7* U120(4,3,2) -> 7* U120(1,3,1) -> 7* U120(2,2,4) -> 7* U120(2,4,4) -> 7* U120(1,2,3) -> 7* U120(1,4,3) -> 7* U120(2,2,1) -> 7* U120(2,4,1) -> 7* U120(3,1,4) -> 7* U120(3,3,4) -> 7* U120(2,1,3) -> 7* U120(2,3,3) -> 7* U120(3,1,1) -> 7* U120(1,1,2) -> 7* U120(3,3,1) -> 7* U120(1,3,2) -> 7* U120(4,2,4) -> 7* U120(4,4,4) -> 7* U120(3,2,3) -> 7* U120(3,4,3) -> 7* U120(4,2,1) -> 7* U120(2,2,2) -> 7* U120(4,4,1) -> 7* U120(2,4,2) -> 7* U120(4,1,3) -> 7* U120(4,3,3) -> 7* U120(3,1,2) -> 7* U120(3,3,2) -> 7* U120(1,2,4) -> 7* U120(1,4,4) -> 7* U120(4,2,2) -> 7* U120(1,2,1) -> 7* U120(4,4,2) -> 7* U120(1,4,1) -> 7* U120(2,1,4) -> 7* U120(2,3,4) -> 7* U120(1,1,3) -> 7* U120(1,3,3) -> 7* U120(2,1,1) -> 7* U120(2,3,1) -> 7* U120(3,2,4) -> 7* U120(3,4,4) -> 7* U120(2,2,3) -> 7* U120(2,4,3) -> 7* U120(3,2,1) -> 7* U120(1,2,2) -> 7* U120(3,4,1) -> 7* U120(1,4,2) -> 7* U120(4,1,4) -> 7* U120(4,3,4) -> 7* U120(3,1,3) -> 7* U120(3,3,3) -> 7* U120(4,1,1) -> 7* U120(2,1,2) -> 7* U120(4,3,1) -> 7* U120(2,3,2) -> 7* U120(4,2,3) -> 7* U120(4,4,3) -> 7* s0(2) -> 8* s0(4) -> 8* s0(1) -> 8* s0(3) -> 8* plus0(3,1) -> 9* plus0(3,3) -> 9* plus0(4,2) -> 9* plus0(4,4) -> 9* plus0(1,2) -> 9* plus0(1,4) -> 9* plus0(2,1) -> 9* plus0(2,3) -> 9* plus0(3,2) -> 9* plus0(3,4) -> 9* plus0(4,1) -> 9* plus0(4,3) -> 9* plus0(1,1) -> 9* plus0(1,3) -> 9* plus0(2,2) -> 9* plus0(2,4) -> 9* 00() -> 3* proper0(2) -> 10* proper0(4) -> 10* proper0(1) -> 10* proper0(3) -> 10* ok0(2) -> 4* ok0(4) -> 4* ok0(1) -> 4* ok0(3) -> 4* top0(2) -> 11* top0(4) -> 11* top0(1) -> 11* top0(3) -> 11* problem: Qed