MAYBE Time: 0.077308 TRS: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} DP: DP: { active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2), active# s X -> active# X, active# s X -> s# active X, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N), active# plus(N, s M) -> and#(isNat M, isNat N), active# plus(N, s M) -> isNat# N, active# plus(N, s M) -> isNat# M, active# plus(N, 0()) -> U11#(isNat N, N), active# plus(N, 0()) -> isNat# N, active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2, active# plus(X1, X2) -> plus#(X1, active X2), active# plus(X1, X2) -> plus#(active X1, X2), active# U21(X1, X2, X3) -> active# X1, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3), active# U21(tt(), M, N) -> s# plus(N, M), active# U21(tt(), M, N) -> plus#(N, M), active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2), active# isNat s V1 -> isNat# V1, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2), active# isNat plus(V1, V2) -> isNat# V1, active# isNat plus(V1, V2) -> isNat# V2, U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2), s# mark X -> s# X, s# ok X -> s# X, plus#(X1, mark X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3), and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2), isNat# ok X -> isNat# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2), proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# s X -> s# proper X, proper# s X -> proper# X, proper# plus(X1, X2) -> plus#(proper X1, proper X2), proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3), proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2), proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X, proper# isNat X -> proper# X, top# mark X -> proper# X, top# mark X -> top# proper X, top# ok X -> active# X, top# ok X -> top# active X} TRS: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} UR: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0()} EDG: { (U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (plus#(X1, mark X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (plus#(X1, mark X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (plus#(ok X1, ok X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (plus#(ok X1, ok X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (plus#(ok X1, ok X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# plus(X1, X2) -> plus#(X1, active X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (active# plus(X1, X2) -> plus#(X1, active X2), plus#(mark X1, X2) -> plus#(X1, X2)) (active# plus(X1, X2) -> plus#(X1, active X2), plus#(X1, mark X2) -> plus#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (active# plus(N, 0()) -> isNat# N, isNat# ok X -> isNat# X) (proper# U11(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3) (proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# U11(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X2, proper# isNat X -> proper# X) (proper# U21(X1, X2, X3) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# U21(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3) (proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# U21(X1, X2, X3) -> proper# X2, proper# plus(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X2, proper# plus(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X2, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X2, proper# s X -> proper# X) (proper# U21(X1, X2, X3) -> proper# X2, proper# s X -> s# proper X) (proper# U21(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (active# U11(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V2) (active# U11(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# U11(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U21(tt(), M, N) -> plus#(N, M)) (active# U11(X1, X2) -> active# X1, active# U21(tt(), M, N) -> s# plus(N, M)) (active# U11(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# U11(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> active# X1) (active# U11(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(X1, active X2)) (active# U11(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2) (active# U11(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# plus(N, 0()) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# plus(N, 0()) -> U11#(isNat N, N)) (active# U11(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# M) (active# U11(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# U11(X1, X2) -> active# X1, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# U11(X1, X2) -> active# X1, active# s X -> s# active X) (active# U11(X1, X2) -> active# X1, active# s X -> active# X) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U21(X1, X2, X3) -> active# X1, active# isNat plus(V1, V2) -> isNat# V2) (active# U21(X1, X2, X3) -> active# X1, active# isNat plus(V1, V2) -> isNat# V1) (active# U21(X1, X2, X3) -> active# X1, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# U21(X1, X2, X3) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U21(X1, X2, X3) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U21(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1) (active# U21(X1, X2, X3) -> active# X1, active# U21(tt(), M, N) -> plus#(N, M)) (active# U21(X1, X2, X3) -> active# X1, active# U21(tt(), M, N) -> s# plus(N, M)) (active# U21(X1, X2, X3) -> active# X1, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# U21(X1, X2, X3) -> active# X1, active# U21(X1, X2, X3) -> active# X1) (active# U21(X1, X2, X3) -> active# X1, active# plus(X1, X2) -> plus#(active X1, X2)) (active# U21(X1, X2, X3) -> active# X1, active# plus(X1, X2) -> plus#(X1, active X2)) (active# U21(X1, X2, X3) -> active# X1, active# plus(X1, X2) -> active# X2) (active# U21(X1, X2, X3) -> active# X1, active# plus(X1, X2) -> active# X1) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, 0()) -> isNat# N) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, 0()) -> U11#(isNat N, N)) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, s M) -> isNat# M) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, s M) -> isNat# N) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# U21(X1, X2, X3) -> active# X1, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# U21(X1, X2, X3) -> active# X1, active# s X -> s# active X) (active# U21(X1, X2, X3) -> active# X1, active# s X -> active# X) (active# U21(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U21(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> active# X1) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X3) (proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# U11(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X1, proper# isNat X -> proper# X) (proper# U21(X1, X2, X3) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U21(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X3) (proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# U21(X1, X2, X3) -> proper# X1, proper# plus(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X1, proper# plus(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X1, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X1, proper# s X -> proper# X) (proper# U21(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X) (proper# U21(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)) (proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3)) (active# isNat plus(V1, V2) -> isNat# V2, isNat# ok X -> isNat# X) (active# isNat plus(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (s# mark X -> s# X, s# ok X -> s# X) (s# mark X -> s# X, s# mark X -> s# X) (isNat# ok X -> isNat# X, isNat# ok X -> isNat# X) (proper# isNat X -> proper# X, proper# isNat X -> proper# X) (proper# isNat X -> proper# X, proper# isNat X -> isNat# proper X) (proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# U21(X1, X2, X3) -> proper# X3) (proper# isNat X -> proper# X, proper# U21(X1, X2, X3) -> proper# X2) (proper# isNat X -> proper# X, proper# U21(X1, X2, X3) -> proper# X1) (proper# isNat X -> proper# X, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# isNat X -> proper# X, proper# plus(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# plus(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# s X -> proper# X) (proper# isNat X -> proper# X, proper# s X -> s# proper X) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (top# ok X -> active# X, active# isNat plus(V1, V2) -> isNat# V2) (top# ok X -> active# X, active# isNat plus(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (top# ok X -> active# X, active# isNat s V1 -> isNat# V1) (top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (top# ok X -> active# X, active# and(X1, X2) -> active# X1) (top# ok X -> active# X, active# U21(tt(), M, N) -> plus#(N, M)) (top# ok X -> active# X, active# U21(tt(), M, N) -> s# plus(N, M)) (top# ok X -> active# X, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (top# ok X -> active# X, active# U21(X1, X2, X3) -> active# X1) (top# ok X -> active# X, active# plus(X1, X2) -> plus#(active X1, X2)) (top# ok X -> active# X, active# plus(X1, X2) -> plus#(X1, active X2)) (top# ok X -> active# X, active# plus(X1, X2) -> active# X2) (top# ok X -> active# X, active# plus(X1, X2) -> active# X1) (top# ok X -> active# X, active# plus(N, 0()) -> isNat# N) (top# ok X -> active# X, active# plus(N, 0()) -> U11#(isNat N, N)) (top# ok X -> active# X, active# plus(N, s M) -> isNat# M) (top# ok X -> active# X, active# plus(N, s M) -> isNat# N) (top# ok X -> active# X, active# plus(N, s M) -> and#(isNat M, isNat N)) (top# ok X -> active# X, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (top# ok X -> active# X, active# U11(X1, X2) -> active# X1) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# s X -> s# proper X, s# mark X -> s# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (active# plus(X1, X2) -> plus#(active X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (active# plus(X1, X2) -> plus#(active X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (active# plus(X1, X2) -> plus#(active X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (active# U21(tt(), M, N) -> plus#(N, M), plus#(ok X1, ok X2) -> plus#(X1, X2)) (active# U21(tt(), M, N) -> plus#(N, M), plus#(mark X1, X2) -> plus#(X1, X2)) (active# U21(tt(), M, N) -> plus#(N, M), plus#(X1, mark X2) -> plus#(X1, X2)) (U21#(mark X1, X2, X3) -> U21#(X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)) (U21#(mark X1, X2, X3) -> U21#(X1, X2, X3), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3)) (active# plus(N, s M) -> isNat# M, isNat# ok X -> isNat# X) (proper# U21(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X) (proper# U21(X1, X2, X3) -> proper# X3, proper# s X -> proper# X) (proper# U21(X1, X2, X3) -> proper# X3, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X3, proper# plus(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X3, proper# plus(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X3, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# U21(X1, X2, X3) -> proper# X3, proper# U21(X1, X2, X3) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X3, proper# U21(X1, X2, X3) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X3, proper# U21(X1, X2, X3) -> proper# X3) (proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1) (proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X2) (proper# U21(X1, X2, X3) -> proper# X3, proper# isNat X -> isNat# proper X) (proper# U21(X1, X2, X3) -> proper# X3, proper# isNat X -> proper# X) (U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3)) (U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)) (active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# U21(X1, X2, X3) -> U21#(active X1, X2, X3), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3)) (active# U21(X1, X2, X3) -> U21#(active X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)) (active# plus(N, 0()) -> U11#(isNat N, N), U11#(mark X1, X2) -> U11#(X1, X2)) (active# plus(N, 0()) -> U11#(isNat N, N), U11#(ok X1, ok X2) -> U11#(X1, X2)) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (active# s X -> s# active X, s# mark X -> s# X) (active# s X -> s# active X, s# ok X -> s# X) (top# mark X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (top# mark X -> proper# X, proper# plus(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# plus(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (top# mark X -> proper# X, proper# U21(X1, X2, X3) -> proper# X1) (top# mark X -> proper# X, proper# U21(X1, X2, X3) -> proper# X2) (top# mark X -> proper# X, proper# U21(X1, X2, X3) -> proper# X3) (top# mark X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# and(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# isNat X -> isNat# proper X) (top# mark X -> proper# X, proper# isNat X -> proper# X) (proper# s X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# s X -> proper# X, proper# plus(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# plus(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# s X -> proper# X, proper# U21(X1, X2, X3) -> proper# X1) (proper# s X -> proper# X, proper# U21(X1, X2, X3) -> proper# X2) (proper# s X -> proper# X, proper# U21(X1, X2, X3) -> proper# X3) (proper# s X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# isNat X -> isNat# proper X) (proper# s X -> proper# X, proper# isNat X -> proper# X) (s# ok X -> s# X, s# mark X -> s# X) (s# ok X -> s# X, s# ok X -> s# X) (active# s X -> active# X, active# U11(X1, X2) -> active# X1) (active# s X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# s X -> active# X, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# s X -> active# X, active# plus(N, s M) -> isNat# N) (active# s X -> active# X, active# plus(N, s M) -> isNat# M) (active# s X -> active# X, active# plus(N, 0()) -> U11#(isNat N, N)) (active# s X -> active# X, active# plus(N, 0()) -> isNat# N) (active# s X -> active# X, active# plus(X1, X2) -> active# X1) (active# s X -> active# X, active# plus(X1, X2) -> active# X2) (active# s X -> active# X, active# plus(X1, X2) -> plus#(X1, active X2)) (active# s X -> active# X, active# plus(X1, X2) -> plus#(active X1, X2)) (active# s X -> active# X, active# U21(X1, X2, X3) -> active# X1) (active# s X -> active# X, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# s X -> active# X, active# U21(tt(), M, N) -> s# plus(N, M)) (active# s X -> active# X, active# U21(tt(), M, N) -> plus#(N, M)) (active# s X -> active# X, active# and(X1, X2) -> active# X1) (active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# s X -> active# X, active# isNat s V1 -> isNat# V1) (active# s X -> active# X, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# s X -> active# X, active# isNat plus(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNat plus(V1, V2) -> isNat# V2) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# U21(tt(), M, N) -> s# plus(N, M), s# mark X -> s# X) (active# U21(tt(), M, N) -> s# plus(N, M), s# ok X -> s# X) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# plus(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# plus(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# plus(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X1) (proper# plus(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2) (proper# plus(X1, X2) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X3) (proper# plus(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# plus(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# s X -> active# X) (active# and(X1, X2) -> active# X1, active# s X -> s# active X) (active# and(X1, X2) -> active# X1, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# and(X1, X2) -> active# X1, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# and(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# N) (active# and(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# M) (active# and(X1, X2) -> active# X1, active# plus(N, 0()) -> U11#(isNat N, N)) (active# and(X1, X2) -> active# X1, active# plus(N, 0()) -> isNat# N) (active# and(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2) (active# and(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(X1, active X2)) (active# and(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> active# X1) (active# and(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# and(X1, X2) -> active# X1, active# U21(tt(), M, N) -> s# plus(N, M)) (active# and(X1, X2) -> active# X1, active# U21(tt(), M, N) -> plus#(N, M)) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# and(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# and(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V1) (active# and(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V2) (active# plus(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# plus(X1, X2) -> active# X1, active# s X -> active# X) (active# plus(X1, X2) -> active# X1, active# s X -> s# active X) (active# plus(X1, X2) -> active# X1, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# plus(X1, X2) -> active# X1, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# plus(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# N) (active# plus(X1, X2) -> active# X1, active# plus(N, s M) -> isNat# M) (active# plus(X1, X2) -> active# X1, active# plus(N, 0()) -> U11#(isNat N, N)) (active# plus(X1, X2) -> active# X1, active# plus(N, 0()) -> isNat# N) (active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2) (active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(X1, active X2)) (active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> plus#(active X1, X2)) (active# plus(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> active# X1) (active# plus(X1, X2) -> active# X1, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# plus(X1, X2) -> active# X1, active# U21(tt(), M, N) -> s# plus(N, M)) (active# plus(X1, X2) -> active# X1, active# U21(tt(), M, N) -> plus#(N, M)) (active# plus(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# plus(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# plus(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# plus(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V1) (active# plus(X1, X2) -> active# X1, active# isNat plus(V1, V2) -> isNat# V2) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# plus(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# plus(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# plus(X1, X2) -> proper# X2, proper# plus(X1, X2) -> plus#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X2, proper# plus(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> U21#(proper X1, proper X2, proper X3)) (proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1) (proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X2) (proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3) (proper# plus(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# plus(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# plus(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# plus(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# plus(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (active# plus(X1, X2) -> active# X2, active# U11(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X2, active# U11(X1, X2) -> U11#(active X1, X2)) (active# plus(X1, X2) -> active# X2, active# s X -> active# X) (active# plus(X1, X2) -> active# X2, active# s X -> s# active X) (active# plus(X1, X2) -> active# X2, active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N)) (active# plus(X1, X2) -> active# X2, active# plus(N, s M) -> and#(isNat M, isNat N)) (active# plus(X1, X2) -> active# X2, active# plus(N, s M) -> isNat# N) (active# plus(X1, X2) -> active# X2, active# plus(N, s M) -> isNat# M) (active# plus(X1, X2) -> active# X2, active# plus(N, 0()) -> U11#(isNat N, N)) (active# plus(X1, X2) -> active# X2, active# plus(N, 0()) -> isNat# N) (active# plus(X1, X2) -> active# X2, active# plus(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X2, active# plus(X1, X2) -> active# X2) (active# plus(X1, X2) -> active# X2, active# plus(X1, X2) -> plus#(X1, active X2)) (active# plus(X1, X2) -> active# X2, active# plus(X1, X2) -> plus#(active X1, X2)) (active# plus(X1, X2) -> active# X2, active# U21(X1, X2, X3) -> active# X1) (active# plus(X1, X2) -> active# X2, active# U21(X1, X2, X3) -> U21#(active X1, X2, X3)) (active# plus(X1, X2) -> active# X2, active# U21(tt(), M, N) -> s# plus(N, M)) (active# plus(X1, X2) -> active# X2, active# U21(tt(), M, N) -> plus#(N, M)) (active# plus(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1) (active# plus(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2)) (active# plus(X1, X2) -> active# X2, active# isNat s V1 -> isNat# V1) (active# plus(X1, X2) -> active# X2, active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2)) (active# plus(X1, X2) -> active# X2, active# isNat plus(V1, V2) -> isNat# V1) (active# plus(X1, X2) -> active# X2, active# isNat plus(V1, V2) -> isNat# V2) (active# plus(N, s M) -> isNat# N, isNat# ok X -> isNat# X) (proper# plus(X1, X2) -> plus#(proper X1, proper X2), plus#(X1, mark X2) -> plus#(X1, X2)) (proper# plus(X1, X2) -> plus#(proper X1, proper X2), plus#(mark X1, X2) -> plus#(X1, X2)) (proper# plus(X1, X2) -> plus#(proper X1, proper X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2), and#(mark X1, X2) -> and#(X1, X2)) (active# isNat plus(V1, V2) -> and#(isNat V1, isNat V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# plus(N, s M) -> and#(isNat M, isNat N), and#(mark X1, X2) -> and#(X1, X2)) (active# plus(N, s M) -> and#(isNat M, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (plus#(mark X1, X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (plus#(mark X1, X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (plus#(mark X1, X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N), U21#(mark X1, X2, X3) -> U21#(X1, X2, X3)) (active# plus(N, s M) -> U21#(and(isNat M, isNat N), M, N), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)) } STATUS: arrows: 0.861188 SCCS (9): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X} Scc: { active# U11(X1, X2) -> active# X1, active# s X -> active# X, active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2, active# U21(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: {isNat# ok X -> isNat# X} Scc: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Scc: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)} Scc: { U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)} Scc: { U21#(mark X1, X2, X3) -> U21#(X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (11): Strict: { proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# plus(X1, X2) -> proper# X1, proper# plus(X1, X2) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X1, proper# U21(X1, X2, X3) -> proper# X2, proper# U21(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (6): Strict: { active# U11(X1, X2) -> active# X1, active# s X -> active# X, active# plus(X1, X2) -> active# X1, active# plus(X1, X2) -> active# X2, active# U21(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {isNat# ok X -> isNat# X} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (3): Strict: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(ok X1, ok X2) -> plus#(X1, X2)} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U21#(mark X1, X2, X3) -> U21#(X1, X2, X3), U21#(ok X1, ok X2, ok X3) -> U21#(X1, X2, X3)} Weak: { active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), N) -> mark N, active s X -> s active X, active plus(N, s M) -> mark U21(and(isNat M, isNat N), M, N), active plus(N, 0()) -> mark U11(isNat N, N), active plus(X1, X2) -> plus(X1, active X2), active plus(X1, X2) -> plus(active X1, X2), active U21(X1, X2, X3) -> U21(active X1, X2, X3), active U21(tt(), M, N) -> mark s plus(N, M), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat s V1 -> mark isNat V1, active isNat plus(V1, V2) -> mark and(isNat V1, isNat V2), active isNat 0() -> mark tt(), U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), s mark X -> mark s X, s ok X -> ok s X, plus(X1, mark X2) -> mark plus(X1, X2), plus(mark X1, X2) -> mark plus(X1, X2), plus(ok X1, ok X2) -> ok plus(X1, X2), U21(mark X1, X2, X3) -> mark U21(X1, X2, X3), U21(ok X1, ok X2, ok X3) -> ok U21(X1, X2, X3), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper s X -> s proper X, proper plus(X1, X2) -> plus(proper X1, proper X2), proper U21(X1, X2, X3) -> U21(proper X1, proper X2, proper X3), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper 0() -> ok 0(), top mark X -> top proper X, top ok X -> top active X} Open