YES Time: 5.184293 TRS: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} DP: DP: { mark# U12 X -> mark# X, mark# U12 X -> U12# mark X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U11(X1, X2) -> U11#(mark X1, X2), mark# tt() -> active# tt(), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U21 X -> U21# mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U31(X1, X2) -> U31#(mark X1, X2), mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3), mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3), mark# s X -> mark# X, mark# s X -> active# s mark X, mark# s X -> s# mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), mark# plus(X1, X2) -> plus#(mark X1, mark X2), mark# 0() -> active# 0(), U12# mark X -> U12# X, U12# active X -> U12# X, isNat# mark X -> isNat# X, isNat# active X -> isNat# X, active# U12 tt() -> mark# tt(), active# isNat s V1 -> mark# U21 isNat V1, active# isNat s V1 -> isNat# V1, active# isNat s V1 -> U21# isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# isNat plus(V1, V2) -> isNat# V1, active# isNat plus(V1, V2) -> U11#(isNat V1, V2), active# isNat 0() -> mark# tt(), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U11(tt(), V2) -> U12# isNat V2, active# U11(tt(), V2) -> isNat# V2, active# U21 tt() -> mark# tt(), active# U31(tt(), N) -> mark# N, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U42(tt(), M, N) -> s# plus(N, M), active# U42(tt(), M, N) -> plus#(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# U41(tt(), M, N) -> isNat# N, active# U41(tt(), M, N) -> U42#(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N), active# plus(N, s M) -> isNat# M, active# plus(N, s M) -> U41#(isNat M, M, N), active# plus(N, 0()) -> mark# U31(isNat N, N), active# plus(N, 0()) -> isNat# N, active# plus(N, 0()) -> U31#(isNat N, N), U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2), U21# mark X -> U21# X, U21# active X -> U21# X, U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2), U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3), U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3), s# mark X -> s# X, s# active X -> s# X, plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(active X1, X2) -> plus#(X1, X2)} TRS: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} UR: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} EDG: { (mark# isNat X -> active# isNat X, active# plus(N, 0()) -> U31#(isNat N, N)) (mark# isNat X -> active# isNat X, active# plus(N, 0()) -> isNat# N) (mark# isNat X -> active# isNat X, active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# isNat X -> active# isNat X, active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# isNat X -> active# isNat X, active# plus(N, s M) -> isNat# M) (mark# isNat X -> active# isNat X, active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# isNat X -> active# isNat X, active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# isNat X -> active# isNat X, active# U41(tt(), M, N) -> isNat# N) (mark# isNat X -> active# isNat X, active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# isNat X -> active# isNat X, active# U42(tt(), M, N) -> plus#(N, M)) (mark# isNat X -> active# isNat X, active# U42(tt(), M, N) -> s# plus(N, M)) (mark# isNat X -> active# isNat X, active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# isNat X -> active# isNat X, active# U31(tt(), N) -> mark# N) (mark# isNat X -> active# isNat X, active# U21 tt() -> mark# tt()) (mark# isNat X -> active# isNat X, active# U11(tt(), V2) -> isNat# V2) (mark# isNat X -> active# isNat X, active# U11(tt(), V2) -> U12# isNat V2) (mark# isNat X -> active# isNat X, active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# isNat X -> active# isNat X, active# isNat 0() -> mark# tt()) (mark# isNat X -> active# isNat X, active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# isNat X -> active# isNat X, active# isNat plus(V1, V2) -> isNat# V1) (mark# isNat X -> active# isNat X, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# isNat X -> active# isNat X, active# isNat s V1 -> U21# isNat V1) (mark# isNat X -> active# isNat X, active# isNat s V1 -> isNat# V1) (mark# isNat X -> active# isNat X, active# isNat s V1 -> mark# U21 isNat V1) (mark# isNat X -> active# isNat X, active# U12 tt() -> mark# tt()) (mark# s X -> s# mark X, s# active X -> s# X) (mark# s X -> s# mark X, s# mark X -> s# X) (active# U11(tt(), V2) -> U12# isNat V2, U12# active X -> U12# X) (active# U11(tt(), V2) -> U12# isNat V2, U12# mark X -> U12# X) (U11#(X1, mark X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)) (U11#(X1, mark X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)) (U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, mark X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(X1, mark X2) -> U11#(X1, X2)) (U31#(X1, mark X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)) (U31#(X1, mark X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)) (U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)) (U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, mark X2) -> U31#(X1, X2)) (U31#(mark X1, X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)) (U31#(mark X1, X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)) (U31#(mark X1, X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)) (U31#(mark X1, X2) -> U31#(X1, X2), U31#(X1, mark X2) -> U31#(X1, X2)) (plus#(X1, mark X2) -> plus#(X1, X2), plus#(active X1, 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, active X2) -> plus#(X1, X2)) (plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (plus#(mark X1, X2) -> plus#(X1, X2), plus#(active X1, 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#(X1, active X2) -> plus#(X1, X2)) (plus#(mark X1, X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, 0()) -> U31#(isNat N, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, 0()) -> isNat# N) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, s M) -> isNat# M) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U41(tt(), M, N) -> isNat# N) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U42(tt(), M, N) -> plus#(N, M)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U42(tt(), M, N) -> s# plus(N, M)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U31(tt(), N) -> mark# N) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U21 tt() -> mark# tt()) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U11(tt(), V2) -> isNat# V2) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U11(tt(), V2) -> U12# isNat V2) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat 0() -> mark# tt()) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat plus(V1, V2) -> isNat# V1) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat s V1 -> U21# isNat V1) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat s V1 -> isNat# V1) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# isNat s V1 -> mark# U21 isNat V1) (mark# U31(X1, X2) -> active# U31(mark X1, X2), active# U12 tt() -> mark# tt()) (active# U42(tt(), M, N) -> s# plus(N, M), s# active X -> s# X) (active# U42(tt(), M, N) -> s# plus(N, M), s# mark X -> s# X) (mark# plus(X1, X2) -> plus#(mark X1, mark X2), plus#(active X1, X2) -> plus#(X1, X2)) (mark# plus(X1, X2) -> plus#(mark X1, mark X2), plus#(mark X1, X2) -> plus#(X1, X2)) (mark# plus(X1, X2) -> plus#(mark X1, mark X2), plus#(X1, active X2) -> plus#(X1, X2)) (mark# plus(X1, X2) -> plus#(mark X1, mark X2), plus#(X1, mark X2) -> plus#(X1, X2)) (mark# U11(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# U11(X1, X2) -> mark# X1, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U11(X1, X2) -> mark# X1, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U11(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2) (mark# U11(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X1) (mark# U11(X1, X2) -> mark# X1, mark# s X -> s# mark X) (mark# U11(X1, X2) -> mark# X1, mark# s X -> active# s mark X) (mark# U11(X1, X2) -> mark# X1, mark# s X -> mark# X) (mark# U11(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U11(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U11(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> mark# X1) (mark# U11(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# U11(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# U11(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> mark# X1) (mark# U11(X1, X2) -> mark# X1, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# U11(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# U11(X1, X2) -> mark# X1, mark# U31(X1, X2) -> mark# X1) (mark# U11(X1, X2) -> mark# X1, mark# U21 X -> U21# mark X) (mark# U11(X1, X2) -> mark# X1, mark# U21 X -> active# U21 mark X) (mark# U11(X1, X2) -> mark# X1, mark# U21 X -> mark# X) (mark# U11(X1, X2) -> mark# X1, mark# tt() -> active# tt()) (mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> mark# X1) (mark# U11(X1, X2) -> mark# X1, mark# isNat X -> active# isNat X) (mark# U11(X1, X2) -> mark# X1, mark# U12 X -> active# U12 mark X) (mark# U11(X1, X2) -> mark# X1, mark# U12 X -> U12# mark X) (mark# U11(X1, X2) -> mark# X1, mark# U12 X -> mark# X) (mark# U42(X1, X2, X3) -> mark# X1, mark# 0() -> active# 0()) (mark# U42(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> mark# X2) (mark# U42(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> mark# X1) (mark# U42(X1, X2, X3) -> mark# X1, mark# s X -> s# mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# s X -> active# s mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# s X -> mark# X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> mark# X1) (mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> mark# X1) (mark# U42(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> mark# X1) (mark# U42(X1, X2, X3) -> mark# X1, mark# U21 X -> U21# mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U21 X -> active# U21 mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U21 X -> mark# X) (mark# U42(X1, X2, X3) -> mark# X1, mark# tt() -> active# tt()) (mark# U42(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# U42(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> mark# X1) (mark# U42(X1, X2, X3) -> mark# X1, mark# isNat X -> active# isNat X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U12 X -> active# U12 mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U12 X -> U12# mark X) (mark# U42(X1, X2, X3) -> mark# X1, mark# U12 X -> mark# X) (mark# plus(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2) (mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X1) (mark# plus(X1, X2) -> mark# X1, mark# s X -> s# mark X) (mark# plus(X1, X2) -> mark# X1, mark# s X -> active# s mark X) (mark# plus(X1, X2) -> mark# X1, mark# s X -> mark# X) (mark# plus(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> mark# X1) (mark# plus(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> mark# X1) (mark# plus(X1, X2) -> mark# X1, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# plus(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# plus(X1, X2) -> mark# X1, mark# U31(X1, X2) -> mark# X1) (mark# plus(X1, X2) -> mark# X1, mark# U21 X -> U21# mark X) (mark# plus(X1, X2) -> mark# X1, mark# U21 X -> active# U21 mark X) (mark# plus(X1, X2) -> mark# X1, mark# U21 X -> mark# X) (mark# plus(X1, X2) -> mark# X1, mark# tt() -> active# tt()) (mark# plus(X1, X2) -> mark# X1, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# plus(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# plus(X1, X2) -> mark# X1, mark# U11(X1, X2) -> mark# X1) (mark# plus(X1, X2) -> mark# X1, mark# isNat X -> active# isNat X) (mark# plus(X1, X2) -> mark# X1, mark# U12 X -> active# U12 mark X) (mark# plus(X1, X2) -> mark# X1, mark# U12 X -> U12# mark X) (mark# plus(X1, X2) -> mark# X1, mark# U12 X -> mark# X) (active# U12 tt() -> mark# tt(), mark# tt() -> active# tt()) (active# isNat 0() -> mark# tt(), mark# tt() -> active# tt()) (active# U41(tt(), M, N) -> U42#(isNat N, M, N), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)) (active# U41(tt(), M, N) -> U42#(isNat N, M, N), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)) (mark# U12 X -> mark# X, mark# 0() -> active# 0()) (mark# U12 X -> mark# X, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U12 X -> mark# X, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U12 X -> mark# X, mark# plus(X1, X2) -> mark# X2) (mark# U12 X -> mark# X, mark# plus(X1, X2) -> mark# X1) (mark# U12 X -> mark# X, mark# s X -> s# mark X) (mark# U12 X -> mark# X, mark# s X -> active# s mark X) (mark# U12 X -> mark# X, mark# s X -> mark# X) (mark# U12 X -> mark# X, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U12 X -> mark# X, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U12 X -> mark# X, mark# U41(X1, X2, X3) -> mark# X1) (mark# U12 X -> mark# X, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# U12 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# U12 X -> mark# X, mark# U42(X1, X2, X3) -> mark# X1) (mark# U12 X -> mark# X, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# U12 X -> mark# X, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# U12 X -> mark# X, mark# U31(X1, X2) -> mark# X1) (mark# U12 X -> mark# X, mark# U21 X -> U21# mark X) (mark# U12 X -> mark# X, mark# U21 X -> active# U21 mark X) (mark# U12 X -> mark# X, mark# U21 X -> mark# X) (mark# U12 X -> mark# X, mark# tt() -> active# tt()) (mark# U12 X -> mark# X, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# U12 X -> mark# X, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# U12 X -> mark# X, mark# U11(X1, X2) -> mark# X1) (mark# U12 X -> mark# X, mark# isNat X -> active# isNat X) (mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X) (mark# U12 X -> mark# X, mark# U12 X -> U12# mark X) (mark# U12 X -> mark# X, mark# U12 X -> mark# X) (mark# s X -> mark# X, mark# 0() -> active# 0()) (mark# s X -> mark# X, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# s X -> mark# X, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# s X -> mark# X, mark# plus(X1, X2) -> mark# X2) (mark# s X -> mark# X, mark# plus(X1, X2) -> mark# X1) (mark# s X -> mark# X, mark# s X -> s# mark X) (mark# s X -> mark# X, mark# s X -> active# s mark X) (mark# s X -> mark# X, mark# s X -> mark# X) (mark# s X -> mark# X, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# s X -> mark# X, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# s X -> mark# X, mark# U41(X1, X2, X3) -> mark# X1) (mark# s X -> mark# X, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# s X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# s X -> mark# X, mark# U42(X1, X2, X3) -> mark# X1) (mark# s X -> mark# X, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# s X -> mark# X, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# s X -> mark# X, mark# U31(X1, X2) -> mark# X1) (mark# s X -> mark# X, mark# U21 X -> U21# mark X) (mark# s X -> mark# X, mark# U21 X -> active# U21 mark X) (mark# s X -> mark# X, mark# U21 X -> mark# X) (mark# s X -> mark# X, mark# tt() -> active# tt()) (mark# s X -> mark# X, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# s X -> mark# X, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# s X -> mark# X, mark# U11(X1, X2) -> mark# X1) (mark# s X -> mark# X, mark# isNat X -> active# isNat X) (mark# s X -> mark# X, mark# U12 X -> active# U12 mark X) (mark# s X -> mark# X, mark# U12 X -> U12# mark X) (mark# s X -> mark# X, mark# U12 X -> mark# X) (U12# active X -> U12# X, U12# active X -> U12# X) (U12# active X -> U12# X, U12# mark X -> U12# X) (isNat# active X -> isNat# X, isNat# active X -> isNat# X) (isNat# active X -> isNat# X, isNat# mark X -> isNat# X) (U21# active X -> U21# X, U21# active X -> U21# X) (U21# active X -> U21# X, U21# mark X -> U21# X) (s# active X -> s# X, s# active X -> s# X) (s# active X -> s# X, s# mark X -> s# X) (mark# U12 X -> active# U12 mark X, active# plus(N, 0()) -> U31#(isNat N, N)) (mark# U12 X -> active# U12 mark X, active# plus(N, 0()) -> isNat# N) (mark# U12 X -> active# U12 mark X, active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# U12 X -> active# U12 mark X, active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# U12 X -> active# U12 mark X, active# plus(N, s M) -> isNat# M) (mark# U12 X -> active# U12 mark X, active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# U12 X -> active# U12 mark X, active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# U12 X -> active# U12 mark X, active# U41(tt(), M, N) -> isNat# N) (mark# U12 X -> active# U12 mark X, active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# U12 X -> active# U12 mark X, active# U42(tt(), M, N) -> plus#(N, M)) (mark# U12 X -> active# U12 mark X, active# U42(tt(), M, N) -> s# plus(N, M)) (mark# U12 X -> active# U12 mark X, active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# U12 X -> active# U12 mark X, active# U31(tt(), N) -> mark# N) (mark# U12 X -> active# U12 mark X, active# U21 tt() -> mark# tt()) (mark# U12 X -> active# U12 mark X, active# U11(tt(), V2) -> isNat# V2) (mark# U12 X -> active# U12 mark X, active# U11(tt(), V2) -> U12# isNat V2) (mark# U12 X -> active# U12 mark X, active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# U12 X -> active# U12 mark X, active# isNat 0() -> mark# tt()) (mark# U12 X -> active# U12 mark X, active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# U12 X -> active# U12 mark X, active# isNat plus(V1, V2) -> isNat# V1) (mark# U12 X -> active# U12 mark X, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# U12 X -> active# U12 mark X, active# isNat s V1 -> U21# isNat V1) (mark# U12 X -> active# U12 mark X, active# isNat s V1 -> isNat# V1) (mark# U12 X -> active# U12 mark X, active# isNat s V1 -> mark# U21 isNat V1) (mark# U12 X -> active# U12 mark X, active# U12 tt() -> mark# tt()) (mark# s X -> active# s mark X, active# plus(N, 0()) -> U31#(isNat N, N)) (mark# s X -> active# s mark X, active# plus(N, 0()) -> isNat# N) (mark# s X -> active# s mark X, active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# s X -> active# s mark X, active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# s X -> active# s mark X, active# plus(N, s M) -> isNat# M) (mark# s X -> active# s mark X, active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# s X -> active# s mark X, active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# s X -> active# s mark X, active# U41(tt(), M, N) -> isNat# N) (mark# s X -> active# s mark X, active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# s X -> active# s mark X, active# U42(tt(), M, N) -> plus#(N, M)) (mark# s X -> active# s mark X, active# U42(tt(), M, N) -> s# plus(N, M)) (mark# s X -> active# s mark X, active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# s X -> active# s mark X, active# U31(tt(), N) -> mark# N) (mark# s X -> active# s mark X, active# U21 tt() -> mark# tt()) (mark# s X -> active# s mark X, active# U11(tt(), V2) -> isNat# V2) (mark# s X -> active# s mark X, active# U11(tt(), V2) -> U12# isNat V2) (mark# s X -> active# s mark X, active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# s X -> active# s mark X, active# isNat 0() -> mark# tt()) (mark# s X -> active# s mark X, active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# s X -> active# s mark X, active# isNat plus(V1, V2) -> isNat# V1) (mark# s X -> active# s mark X, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# s X -> active# s mark X, active# isNat s V1 -> U21# isNat V1) (mark# s X -> active# s mark X, active# isNat s V1 -> isNat# V1) (mark# s X -> active# s mark X, active# isNat s V1 -> mark# U21 isNat V1) (mark# s X -> active# s mark X, active# U12 tt() -> mark# tt()) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# plus(X1, X2) -> mark# X2) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# plus(X1, X2) -> mark# X1) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# s X -> s# mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# s X -> active# s mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# s X -> mark# X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U41(X1, X2, X3) -> mark# X1) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U42(X1, X2, X3) -> mark# X1) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U31(X1, X2) -> U31#(mark X1, X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U31(X1, X2) -> mark# X1) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U21 X -> U21# mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U21 X -> active# U21 mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U21 X -> mark# X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U11(X1, X2) -> U11#(mark X1, X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U11(X1, X2) -> mark# X1) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# isNat X -> active# isNat X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U12 X -> active# U12 mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U12 X -> U12# mark X) (active# U11(tt(), V2) -> mark# U12 isNat V2, mark# U12 X -> mark# X) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, 0()) -> U31#(isNat N, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, 0()) -> isNat# N) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, s M) -> isNat# M) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U41(tt(), M, N) -> isNat# N) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U42(tt(), M, N) -> plus#(N, M)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U42(tt(), M, N) -> s# plus(N, M)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U31(tt(), N) -> mark# N) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U21 tt() -> mark# tt()) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U11(tt(), V2) -> isNat# V2) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U11(tt(), V2) -> U12# isNat V2) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat 0() -> mark# tt()) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat plus(V1, V2) -> isNat# V1) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> U21# isNat V1) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> isNat# V1) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1) (mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# U12 tt() -> mark# tt()) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# plus(X1, X2) -> mark# X2) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# plus(X1, X2) -> mark# X1) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# s X -> s# mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# s X -> active# s mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# s X -> mark# X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U41(X1, X2, X3) -> mark# X1) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U42(X1, X2, X3) -> mark# X1) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U31(X1, X2) -> U31#(mark X1, X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U31(X1, X2) -> active# U31(mark X1, X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U31(X1, X2) -> mark# X1) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U21 X -> U21# mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U21 X -> active# U21 mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U21 X -> mark# X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U11(X1, X2) -> U11#(mark X1, X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U11(X1, X2) -> active# U11(mark X1, X2)) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U11(X1, X2) -> mark# X1) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# isNat X -> active# isNat X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U12 X -> active# U12 mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U12 X -> U12# mark X) (active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), mark# U12 X -> mark# X) (mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)) (mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3)) (U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, mark X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3)) (U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, X2, mark X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3)) (U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(X1, X2, mark X3) -> U42#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3)) (U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3)) (U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3)) (U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark X3) -> U41#(X1, X2, X3)) (mark# U11(X1, X2) -> U11#(mark X1, X2), U11#(active X1, X2) -> U11#(X1, X2)) (mark# U11(X1, X2) -> U11#(mark X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (mark# U31(X1, X2) -> 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mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U21 X -> mark# X, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U21 X -> mark# X, mark# s X -> mark# X) (mark# U21 X -> mark# X, mark# s X -> active# s mark X) (mark# U21 X -> mark# X, mark# s X -> s# mark X) (mark# U21 X -> mark# X, mark# plus(X1, X2) -> mark# X1) (mark# U21 X -> mark# X, mark# plus(X1, X2) -> mark# X2) (mark# U21 X -> mark# X, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U21 X -> mark# X, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U21 X -> mark# X, mark# 0() -> active# 0()) (active# plus(N, s M) -> U41#(isNat M, M, N), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)) (active# plus(N, s M) -> U41#(isNat M, M, N), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)) (active# U21 tt() -> mark# tt(), mark# tt() -> active# tt()) (active# isNat plus(V1, V2) -> U11#(isNat V1, V2), U11#(mark X1, X2) -> U11#(X1, X2)) (active# isNat plus(V1, V2) -> U11#(isNat V1, V2), U11#(active X1, X2) -> 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active# plus(N, s M) -> isNat# M) (mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# plus(N, 0()) -> isNat# N) (mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# plus(N, 0()) -> U31#(isNat N, N)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U12 X -> mark# X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U12 X -> U12# mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U12 X -> active# U12 mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# isNat X -> active# isNat X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> mark# X1) (mark# U41(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# tt() -> active# tt()) (mark# U41(X1, X2, X3) -> mark# X1, mark# U21 X -> mark# X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U21 X -> active# U21 mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U21 X -> U21# mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> mark# X1) (mark# U41(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> mark# X1) (mark# U41(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> mark# X1) (mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U41(X1, X2, X3) -> mark# X1, mark# s X -> mark# X) (mark# U41(X1, X2, X3) -> mark# X1, mark# s X -> active# s mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# s X -> s# mark X) (mark# U41(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> mark# X1) (mark# U41(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> mark# X2) (mark# U41(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U41(X1, X2, X3) -> mark# X1, mark# 0() -> active# 0()) (mark# U31(X1, X2) -> mark# X1, mark# U12 X -> mark# X) (mark# U31(X1, X2) -> mark# X1, mark# U12 X -> U12# mark X) (mark# U31(X1, X2) -> mark# X1, mark# U12 X -> active# U12 mark X) (mark# U31(X1, X2) -> mark# X1, mark# isNat X -> active# isNat X) (mark# U31(X1, X2) -> mark# X1, mark# U11(X1, X2) -> mark# X1) (mark# U31(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# U31(X1, X2) -> mark# X1, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# U31(X1, X2) -> mark# X1, mark# tt() -> active# tt()) (mark# U31(X1, X2) -> mark# X1, mark# U21 X -> mark# X) (mark# U31(X1, X2) -> mark# X1, mark# U21 X -> active# U21 mark X) (mark# U31(X1, X2) -> mark# X1, mark# U21 X -> U21# mark X) (mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> mark# X1) (mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# U31(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> mark# X1) (mark# U31(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# U31(X1, X2) -> mark# X1, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# U31(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> mark# X1) (mark# U31(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# U31(X1, X2) -> mark# X1, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# U31(X1, X2) -> mark# X1, mark# s X -> mark# X) (mark# U31(X1, X2) -> mark# X1, mark# s X -> active# s mark X) (mark# U31(X1, X2) -> mark# X1, mark# s X -> s# mark X) (mark# U31(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X1) (mark# U31(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2) (mark# U31(X1, X2) -> mark# X1, mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# U31(X1, X2) -> mark# X1, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U31(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (active# plus(N, 0()) -> U31#(isNat N, N), U31#(mark X1, X2) -> U31#(X1, X2)) (active# plus(N, 0()) -> U31#(isNat N, N), U31#(active X1, X2) -> U31#(X1, X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U12 X -> mark# X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U12 X -> U12# mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U12 X -> active# U12 mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# isNat X -> active# isNat X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U11(X1, X2) -> mark# X1) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U11(X1, X2) -> active# U11(mark X1, X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U11(X1, X2) -> U11#(mark X1, X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U21 X -> mark# X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U21 X -> active# U21 mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U21 X -> U21# mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U31(X1, X2) -> mark# X1) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U31(X1, X2) -> active# U31(mark X1, X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U31(X1, X2) -> U31#(mark X1, X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U42(X1, X2, X3) -> mark# X1) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U41(X1, X2, X3) -> mark# X1) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# s X -> mark# X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# s X -> active# s mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# s X -> s# mark X) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# plus(X1, X2) -> mark# X1) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# plus(X1, X2) -> mark# X2) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (active# plus(N, 0()) -> mark# U31(isNat N, N), mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U12 X -> mark# X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U12 X -> U12# mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U12 X -> active# U12 mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# isNat X -> active# isNat X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U11(X1, X2) -> mark# X1) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U11(X1, X2) -> active# U11(mark X1, X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U11(X1, X2) -> U11#(mark X1, X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U21 X -> mark# X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U21 X -> active# U21 mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U21 X -> U21# mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U31(X1, X2) -> mark# X1) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U31(X1, X2) -> active# U31(mark X1, X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U31(X1, X2) -> U31#(mark X1, X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U42(X1, X2, X3) -> mark# X1) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U41(X1, X2, X3) -> mark# X1) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# s X -> mark# X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# s X -> active# s mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# s X -> s# mark X) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# plus(X1, X2) -> mark# X1) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# plus(X1, X2) -> mark# X2) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# plus(X1, X2) -> active# plus(mark X1, mark X2)) (active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U12 tt() -> mark# tt()) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat s V1 -> mark# U21 isNat V1) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat s V1 -> isNat# V1) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat s V1 -> U21# isNat V1) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat plus(V1, V2) -> isNat# V1) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat plus(V1, V2) -> U11#(isNat V1, V2)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat 0() -> mark# tt()) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U11(tt(), V2) -> mark# U12 isNat V2) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U11(tt(), V2) -> U12# isNat V2) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U11(tt(), V2) -> isNat# V2) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U21 tt() -> mark# tt()) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U31(tt(), N) -> mark# N) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U42(tt(), M, N) -> mark# s plus(N, M)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U42(tt(), M, N) -> s# plus(N, M)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U42(tt(), M, N) -> plus#(N, M)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U41(tt(), M, N) -> isNat# N) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# U41(tt(), M, N) -> U42#(isNat N, M, N)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, s M) -> mark# U41(isNat M, M, N)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, s M) -> isNat# M) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, s M) -> U41#(isNat M, M, N)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, 0()) -> mark# U31(isNat N, N)) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, 0()) -> isNat# N) (mark# U11(X1, X2) -> active# U11(mark X1, X2), active# plus(N, 0()) -> U31#(isNat N, N)) (plus#(active 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)) (plus#(active X1, X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (plus#(active X1, X2) -> plus#(X1, X2), plus#(active X1, X2) -> plus#(X1, X2)) (plus#(X1, active X2) -> plus#(X1, X2), plus#(X1, mark X2) -> plus#(X1, X2)) (plus#(X1, active X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2)) (plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)) (plus#(X1, active X2) -> plus#(X1, X2), plus#(active X1, X2) -> plus#(X1, X2)) (U31#(active X1, X2) -> U31#(X1, X2), U31#(X1, mark X2) -> U31#(X1, X2)) (U31#(active X1, X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)) (U31#(active X1, X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)) (U31#(active X1, X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)) (U31#(X1, active X2) -> U31#(X1, X2), U31#(X1, mark X2) -> U31#(X1, X2)) (U31#(X1, active X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)) (U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)) (U31#(X1, active X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)) (U11#(active X1, X2) -> U11#(X1, X2), U11#(X1, mark X2) -> U11#(X1, X2)) (U11#(active X1, X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)) (U11#(active X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(active X1, X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)) (U11#(X1, active X2) -> U11#(X1, X2), U11#(X1, mark X2) -> U11#(X1, X2)) (U11#(X1, active X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)) (U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(X1, active X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)) (mark# plus(X1, X2) -> mark# X2, mark# U12 X -> mark# X) (mark# plus(X1, X2) -> mark# X2, mark# U12 X -> U12# mark X) (mark# plus(X1, X2) -> mark# X2, mark# U12 X -> active# U12 mark X) (mark# plus(X1, X2) -> mark# X2, mark# isNat X -> active# isNat X) (mark# plus(X1, X2) -> mark# X2, mark# U11(X1, X2) -> mark# X1) (mark# plus(X1, X2) -> mark# X2, mark# U11(X1, X2) -> active# U11(mark X1, X2)) (mark# plus(X1, X2) -> mark# X2, mark# U11(X1, X2) -> U11#(mark X1, X2)) (mark# plus(X1, X2) -> mark# X2, mark# tt() -> active# tt()) (mark# plus(X1, X2) -> mark# X2, mark# U21 X -> mark# X) (mark# plus(X1, X2) -> mark# X2, mark# U21 X -> active# U21 mark X) (mark# plus(X1, X2) -> mark# X2, mark# U21 X -> U21# mark X) (mark# plus(X1, X2) -> mark# X2, mark# U31(X1, X2) -> mark# X1) (mark# plus(X1, X2) -> mark# X2, mark# U31(X1, X2) -> active# U31(mark X1, X2)) (mark# plus(X1, X2) -> mark# X2, mark# U31(X1, X2) -> U31#(mark X1, X2)) (mark# plus(X1, X2) -> mark# X2, mark# U42(X1, X2, X3) -> mark# X1) (mark# plus(X1, X2) -> mark# X2, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X2, mark# U42(X1, X2, X3) -> U42#(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X2, mark# U41(X1, X2, X3) -> mark# X1) (mark# plus(X1, X2) -> mark# X2, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X2, mark# U41(X1, X2, X3) -> U41#(mark X1, X2, X3)) (mark# plus(X1, X2) -> mark# X2, mark# s X -> mark# X) (mark# plus(X1, X2) -> mark# X2, mark# s X -> active# s mark X) (mark# plus(X1, X2) -> mark# X2, mark# s X -> s# mark X) (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# plus(X1, X2) -> active# plus(mark X1, mark X2)) (mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> plus#(mark X1, mark X2)) (mark# plus(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (active# isNat s V1 -> U21# isNat V1, U21# mark X -> U21# X) (active# isNat s V1 -> U21# isNat V1, U21# active X -> U21# X) (mark# U21 X -> U21# mark X, U21# mark X -> U21# X) (mark# U21 X -> U21# mark X, U21# active X -> U21# X) (mark# U12 X -> U12# mark X, U12# mark X -> U12# X) (mark# U12 X -> U12# mark X, U12# active X -> U12# X) } STATUS: arrows: 0.881246 SCCS (10): Scc: { isNat# mark X -> isNat# X, isNat# active X -> isNat# X} Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> mark# X, mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U31(tt(), N) -> mark# N, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N), active# plus(N, 0()) -> mark# U31(isNat N, N)} Scc: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(active X1, X2) -> plus#(X1, X2)} Scc: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)} Scc: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)} Scc: { s# mark X -> s# X, s# active X -> s# X} Scc: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)} Scc: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)} Scc: { U21# mark X -> U21# X, U21# active X -> U21# X} Scc: { U12# mark X -> U12# X, U12# active X -> U12# X} SCC (2): Strict: { isNat# mark X -> isNat# X, isNat# active X -> isNat# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [isNat#](x0) = x0 Strict: isNat# active X -> isNat# X 1 + 1X >= 0 + 1X isNat# mark X -> isNat# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {isNat# mark X -> isNat# X} SCC (1): Strict: {isNat# mark X -> isNat# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [isNat#](x0) = x0 Strict: isNat# mark X -> isNat# X 1 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (26): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> mark# X1, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> mark# X1, mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> mark# X, mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U31(tt(), N) -> mark# N, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N), active# plus(N, 0()) -> mark# U31(isNat N, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + x2 + 1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# plus(N, 0()) -> mark# U31(isNat N, N) 1 + 1N >= 0 + 1N active# plus(N, s M) -> mark# U41(isNat M, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 1N + 1M >= 1 + 1N + 1M active# U31(tt(), N) -> mark# N 0 + 1N >= 0 + 1N active# U11(tt(), V2) -> mark# U12 isNat V2 0 + 0V2 >= 0 + 0V2 active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# plus(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 1 + 1X >= 1 + 1X mark# s X -> mark# X 1 + 1X >= 0 + 1X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark# U41(X1, X2, X3) -> mark# X1 1 + 1X1 + 1X2 + 1X3 >= 0 + 1X1 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark# U42(X1, X2, X3) -> mark# X1 1 + 1X1 + 1X2 + 1X3 >= 0 + 1X1 mark# U31(X1, X2) -> active# U31(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# U31(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 1X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 1X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 1 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 U31(active X1, X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 1N + 1M >= 1 + 1N + 1M active U31(tt(), N) -> mark N 0 + 1N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 1 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 1 + 1X >= 1 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U31(tt(), N) -> mark# N, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} SCC (22): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U31(tt(), N) -> mark# N, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = 1, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 1, [tt] = 1, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# plus(N, s M) -> mark# U41(isNat M, M, N) 1 + 1N + 0M >= 1 + 0N + 0M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active# U31(tt(), N) -> mark# N 1 + 1N >= 0 + 1N active# U11(tt(), V2) -> mark# U12 isNat V2 1 + 0V2 >= 1 + 0V2 active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 1 + 0V1 >= 1 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# plus(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 1 + 0X >= 1 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 mark# U31(X1, X2) -> active# U31(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# U31(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 1X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 1 + 0X >= 1 + 0X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 1X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 1 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 0M >= 1 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active U31(tt(), N) -> mark N 1 + 1N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 1 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 1 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 0X >= 1 + 0X isNat mark X -> isNat X 1 + 0X >= 1 + 0X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 1 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 1 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 1 >= 1 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 1 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} SCC (21): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + x1 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 1, [tt] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# plus(N, s M) -> mark# U41(isNat M, M, N) 1 + 1N + 0M >= 1 + 0N + 0M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active# U11(tt(), V2) -> mark# U12 isNat V2 0 + 0V2 >= 0 + 0V2 active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# plus(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 1 + 0X >= 1 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U31(X1, X2) -> active# U31(mark X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# U31(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 1X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 1X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 1 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 0M >= 1 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active U31(tt(), N) -> mark N 1 + 1N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 1 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 1 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} SCC (20): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U31(X1, X2) -> active# U31(mark X1, X2), mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = x0, [U31](x0, x1) = 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 0, [tt] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# plus(N, s M) -> mark# U41(isNat M, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active# U11(tt(), V2) -> mark# U12 isNat V2 0 + 0V2 >= 0 + 0V2 active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark# plus(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 0 + 0X >= 0 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U31(X1, X2) -> active# U31(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 0X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 0X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 1 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 1N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} SCC (19): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U11(tt(), V2) -> mark# U12 isNat V2, active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1, [U41](x0, x1, x2) = x0 + x1, [U11](x0, x1) = x0 + x1, [U31](x0, x1) = x0, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = x0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = x0, [tt] = 1, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# plus(N, s M) -> mark# U41(isNat M, M, N) 0 + 1N + 1M >= 0 + 1N + 1M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 0 + 1N + 1M >= 0 + 1N + 1M active# U42(tt(), M, N) -> mark# s plus(N, M) 0 + 1N + 1M >= 0 + 1N + 1M active# U11(tt(), V2) -> mark# U12 isNat V2 1 + 1V2 >= 0 + 1V2 active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 1V2 + 1V1 >= 0 + 1V2 + 1V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 1V1 >= 0 + 1V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# plus(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 0 + 1X >= 0 + 1X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 1X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 1X >= 0 + 1X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 1X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 0 + 1X >= 0 + 1X s mark X -> s X 0 + 1X >= 0 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 1N + 1M >= 0 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 1N + 1M >= 0 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 1N + 1M >= 0 + 1N + 1M active U31(tt(), N) -> mark N 0 + 1N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 0 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 1V2 + 1V1 >= 0 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 0 + 1V1 >= 0 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 1 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 0 + 1X >= 0 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 1 >= 1 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark isNat X -> active isNat X 0 + 1X >= 0 + 1X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} SCC (18): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> mark# X1, mark# plus(X1, X2) -> mark# X2, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N), active# plus(N, s M) -> mark# U41(isNat M, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0, [plus](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [U12](x0) = x0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 1, [tt] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# plus(N, s M) -> mark# U41(isNat M, M, N) 2 + 1N + 0M >= 1 + 0N + 0M active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# plus(X1, X2) -> mark# X2 1 + 1X1 + 1X2 >= 0 + 1X2 mark# plus(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# s X -> active# s mark X 1 + 0X >= 1 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U21 X -> active# U21 mark X 0 + 1X >= 0 + 1X mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X mark# U12 X -> active# U12 mark X 0 + 1X >= 0 + 1X mark# U12 X -> mark# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 1N + 0M >= 1 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active U31(tt(), N) -> mark N 0 + 1N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 1X >= 0 + 1X U12 mark X -> U12 X 0 + 1X >= 0 + 1X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark s X -> active s mark X 1 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 1X >= 0 + 1X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (15): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U21 X -> active# U21 mark X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, mark# plus(X1, X2) -> active# plus(mark X1, mark X2), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U11](x0, x1) = 1, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = 0, [U12](x0) = 1, [isNat](x0) = 1, [active](x0) = 0, [U21](x0) = 0, [s](x0) = 1, [tt] = 0, [0] = 0, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 1 + 0V1 >= 1 + 0V1 mark# plus(X1, X2) -> active# plus(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# s X -> active# s mark X 1 + 0X >= 1 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U21 X -> active# U21 mark X 1 + 0X >= 0 + 0X mark# U21 X -> mark# X 1 + 0X >= 1 + 0X mark# U11(X1, X2) -> active# U11(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# isNat X -> active# isNat X 1 + 0X >= 1 + 0X mark# U12 X -> active# U12 mark X 1 + 0X >= 1 + 0X mark# U12 X -> mark# X 1 + 0X >= 1 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 0 + 0N >= 0 + 0N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 1 + 0X >= 1 + 0X isNat mark X -> isNat X 1 + 0X >= 1 + 0X U12 active X -> U12 X 1 + 0X >= 1 + 0X U12 mark X -> U12 X 1 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 0 + 0X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 0 + 0X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (13): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), mark# s X -> active# s mark X, active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U11](x0, x1) = 1, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = 0, [U12](x0) = 1, [isNat](x0) = 1, [active](x0) = 0, [U21](x0) = 0, [s](x0) = 0, [tt] = 0, [0] = 0, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 0N + 0M >= 1 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 0N + 0M >= 1 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 1 + 0V1 >= 1 + 0V1 mark# s X -> active# s mark X 1 + 0X >= 0 + 0X mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# U21 X -> mark# X 1 + 0X >= 1 + 0X mark# U11(X1, X2) -> active# U11(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# isNat X -> active# isNat X 1 + 0X >= 1 + 0X mark# U12 X -> active# U12 mark X 1 + 0X >= 1 + 0X mark# U12 X -> mark# X 1 + 0X >= 1 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 0 + 0N >= 0 + 0N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 1 + 0X >= 1 + 0X isNat mark X -> isNat X 1 + 0X >= 1 + 0X U12 active X -> U12 X 1 + 0X >= 1 + 0X U12 mark X -> U12 X 1 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 0 + 0X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 0 + 0X SCCS (1): Scc: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (12): Strict: { mark# U12 X -> mark# X, mark# U12 X -> active# U12 mark X, mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = x0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = x0 + 1, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 0, [tt] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X mark# U12 X -> active# U12 mark X 1 + 1X >= 0 + 0X mark# U12 X -> mark# X 1 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 0 + 0N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 1 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 1 + 1X >= 1 + 1X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 1 + 1X >= 1 + 1X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (10): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U42(tt(), M, N) -> mark# s plus(N, M), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1, [U41](x0, x1, x2) = x0 + x1, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0, [U12](x0) = 1, [isNat](x0) = 1, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 0, [tt] = 1, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 1N + 0M >= 1 + 1N + 0M active# U42(tt(), M, N) -> mark# s plus(N, M) 1 + 1N + 0M >= 0 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 1 + 0V1 >= 1 + 0V1 mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 1 + 0X >= 1 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 U31(active X1, X2) -> U31(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 1 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 0M >= 1 + 1N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 1 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 1N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 1N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 1 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 1 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 0X >= 1 + 0X isNat mark X -> isNat X 1 + 0X >= 1 + 0X U12 active X -> U12 X 1 + 0X >= 1 + 0X U12 mark X -> U12 X 1 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 1X1 + 0X2 + 1X3 >= 0 + 1X1 + 0X2 + 1X3 mark U31(X1, X2) -> active U31(mark X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 1 >= 1 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 1 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 1 + 0X >= 1 + 0X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (9): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 1, [U11](x0, x1) = x0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 0, [tt] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# U41(X1, X2, X3) -> active# U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 0N + 0M >= 1 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 0 + 0N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 0 + 0X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} SCC (8): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2), active# U41(tt(), M, N) -> mark# U42(isNat N, M, N)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = 0, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = 0, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = 0, [active#](x0) = x0 Strict: active# U41(tt(), M, N) -> mark# U42(isNat N, M, N) 1 + 1N + 0M >= 0 + 0N + 0M active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U21 X -> mark# X 0 + 0X >= 0 + 0X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 0X1 + 0X2 >= 0 + 0X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 2 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 2 + 1N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 1 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 0 + 0N + 0M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 0 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 2 + 0V2 active isNat 0() -> mark tt() 0 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 1 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 1 + 0X >= 0 + 0X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark isNat X -> active isNat X 1 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} SCC (7): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3), active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 0, [U11](x0, x1) = x0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = 0, [tt] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active# isNat s V1 -> mark# U21 isNat V1 0 + 0V1 >= 0 + 0V1 mark# U42(X1, X2, X3) -> active# U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 0 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 0 + 0N + 0M >= 1 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 0 + 0N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 0 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 0 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 0 + 0X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} SCC (6): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, active# isNat s V1 -> mark# U21 isNat V1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0, [plus](x0, x1) = x0 + x1, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = x0, [active](x0) = x0, [U21](x0) = x0, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 1V2 + 1V1 >= 0 + 0V2 + 1V1 active# isNat s V1 -> mark# U21 isNat V1 1 + 1V1 >= 0 + 1V1 mark# U21 X -> mark# X 0 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 1 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U21 active X -> U21 X 0 + 1X >= 0 + 1X U21 mark X -> U21 X 0 + 1X >= 0 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 1M >= 1 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 1N + 1M >= 1 + 1N + 1M active U31(tt(), N) -> mark N 0 + 1N >= 0 + 1N active U21 tt() -> mark tt() 0 >= 0 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 0 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 1V2 + 1V1 >= 0 + 0V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 1 + 1V1 >= 0 + 1V1 active U12 tt() -> mark tt() 0 >= 0 isNat active X -> isNat X 0 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 1 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark s X -> active s mark X 1 + 1X >= 1 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 0X1 + 1X2 + 1X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark U21 X -> active U21 mark X 0 + 1X >= 0 + 1X mark tt() -> active tt() 0 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark isNat X -> active isNat X 0 + 1X >= 0 + 1X mark U12 X -> active U12 mark X 0 + 0X >= 0 + 0X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} SCC (5): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), mark# U21 X -> mark# X, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + x1 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = 0, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 mark# U21 X -> mark# X 1 + 1X >= 0 + 1X mark# U11(X1, X2) -> active# U11(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 0X >= 0 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 2 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 2 + 1N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 2 + 0N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 1N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 2 + 0V2 active isNat 0() -> mark tt() 0 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 0 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 0 + 0V1 >= 2 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 0X1 + 0X2 + 1X3 >= 1 + 0X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark isNat X -> active isNat X 1 + 0X >= 0 + 0X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} SCC (4): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, mark# U11(X1, X2) -> active# U11(mark X1, X2), active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = 0, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 mark# U11(X1, X2) -> active# U11(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# U11(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# isNat X -> active# isNat X 1 + 0X >= 1 + 0X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 3 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 0N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 3 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 1 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 3 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 0X >= 1 + 0X isNat mark X -> isNat X 1 + 0X >= 1 + 0X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark isNat X -> active isNat X 2 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} SCC (3): Strict: { mark# isNat X -> active# isNat X, mark# U11(X1, X2) -> mark# X1, active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0, [U31](x0, x1) = x0 + x1 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# isNat plus(V1, V2) -> mark# U11(isNat V1, V2) 1 + 0V2 + 1V1 >= 0 + 0V2 + 1V1 mark# U11(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# isNat X -> active# isNat X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U31(X1, mark X2) -> U31(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 2 + 2N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 0M >= 2 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 2 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 3 + 1N + 0M active U31(tt(), N) -> mark N 1 + 1N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 0 + 0V2 >= 2 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 1V1 >= 1 + 0V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 1 + 1V1 >= 2 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 1X >= 0 + 1X isNat mark X -> isNat X 1 + 1X >= 0 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark isNat X -> active isNat X 1 + 1X >= 0 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: {mark# U11(X1, X2) -> mark# X1} SCC (1): Strict: {mark# U11(X1, X2) -> mark# X1} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [mark#](x0) = x0 Strict: mark# U11(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (4): Strict: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2), plus#(active X1, X2) -> plus#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [plus#](x0, x1) = x0 Strict: plus#(active X1, X2) -> plus#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 plus#(mark X1, X2) -> plus#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 plus#(X1, active X2) -> plus#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 plus#(X1, mark X2) -> plus#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)} SCC (3): Strict: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2), plus#(mark X1, X2) -> plus#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 0, [plus#](x0, x1) = x0 Strict: plus#(mark X1, X2) -> plus#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 plus#(X1, active X2) -> plus#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 plus#(X1, mark X2) -> plus#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2)} SCC (2): Strict: { plus#(X1, mark X2) -> plus#(X1, X2), plus#(X1, active X2) -> plus#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [plus#](x0, x1) = x0 Strict: plus#(X1, active X2) -> plus#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 plus#(X1, mark X2) -> plus#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {plus#(X1, mark X2) -> plus#(X1, X2)} SCC (1): Strict: {plus#(X1, mark X2) -> plus#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [plus#](x0, x1) = x0 Strict: plus#(X1, mark X2) -> plus#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (6): Strict: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(active X1, X2, X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = x0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 1, [U41#](x0, x1, x2) = x0 Strict: U41#(active X1, X2, X3) -> U41#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(mark X1, X2, X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, active X2, X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, mark X2, X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, X2, active X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 1 >= 2 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)} SCC (5): Strict: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(X1, active X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = x0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = x0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U41#](x0, x1, x2) = x0 Strict: U41#(mark X1, X2, X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, active X2, X3) -> U41#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, mark X2, X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, X2, active X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 2 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)} SCC (4): Strict: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U41#](x0, x1, x2) = x0 Strict: U41#(mark X1, X2, X3) -> U41#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, mark X2, X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, X2, active X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 2 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 0 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3)} SCC (3): Strict: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3), U41#(X1, mark X2, X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 0, [U41#](x0, x1, x2) = x0 Strict: U41#(X1, mark X2, X3) -> U41#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, X2, active X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3)} SCC (2): Strict: { U41#(X1, X2, mark X3) -> U41#(X1, X2, X3), U41#(X1, X2, active X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U41#](x0, x1, x2) = x0 Strict: U41#(X1, X2, active X3) -> U41#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 0 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U41#(X1, X2, mark X3) -> U41#(X1, X2, X3)} SCC (1): Strict: {U41#(X1, X2, mark X3) -> U41#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U41#](x0, x1, x2) = x0 Strict: U41#(X1, X2, mark X3) -> U41#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (6): Strict: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3), U42#(active X1, X2, X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = x0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 1, [U42#](x0, x1, x2) = x0 Strict: U42#(active X1, X2, X3) -> U42#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(mark X1, X2, X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, active X2, X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, mark X2, X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, X2, active X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 1 >= 2 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)} SCC (5): Strict: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(X1, active X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = x0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = x0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U42#](x0, x1, x2) = x0 Strict: U42#(mark X1, X2, X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, active X2, X3) -> U42#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, mark X2, X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, X2, active X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 2 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 0 + 1X isNat mark X -> isNat X 0 + 1X >= 0 + 1X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)} SCC (4): Strict: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3), U42#(mark X1, X2, X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U42#](x0, x1, x2) = x0 Strict: U42#(mark X1, X2, X3) -> U42#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, mark X2, X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, X2, active X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 1N >= 2 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 0 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3)} SCC (3): Strict: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3), U42#(X1, mark X2, X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 0, [U42#](x0, x1, x2) = x0 Strict: U42#(X1, mark X2, X3) -> U42#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, X2, active X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3)} SCC (2): Strict: { U42#(X1, X2, mark X3) -> U42#(X1, X2, X3), U42#(X1, X2, active X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U42#](x0, x1, x2) = x0 Strict: U42#(X1, X2, active X3) -> U42#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 0 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U42#(X1, X2, mark X3) -> U42#(X1, X2, X3)} SCC (1): Strict: {U42#(X1, X2, mark X3) -> U42#(X1, X2, X3)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U42#](x0, x1, x2) = x0 Strict: U42#(X1, X2, mark X3) -> U42#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (2): Strict: { s# mark X -> s# X, s# active X -> s# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [s#](x0) = x0 Strict: s# active X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (4): Strict: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2), U31#(active X1, X2) -> U31#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U31#](x0, x1) = x0 Strict: U31#(active X1, X2) -> U31#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31#(mark X1, X2) -> U31#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31#(X1, active X2) -> U31#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31#(X1, mark X2) -> U31#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)} SCC (3): Strict: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 0, [U31#](x0, x1) = x0 Strict: U31#(mark X1, X2) -> U31#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31#(X1, active X2) -> U31#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U31#(X1, mark X2) -> U31#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)} SCC (2): Strict: { U31#(X1, mark X2) -> U31#(X1, X2), U31#(X1, active X2) -> U31#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U31#](x0, x1) = x0 Strict: U31#(X1, active X2) -> U31#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U31#(X1, mark X2) -> U31#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U31#(X1, mark X2) -> U31#(X1, X2)} SCC (1): Strict: {U31#(X1, mark X2) -> U31#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U31#](x0, x1) = x0 Strict: U31#(X1, mark X2) -> U31#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (4): Strict: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2), U11#(active X1, X2) -> U11#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U11#](x0, x1) = x0 Strict: U11#(active X1, X2) -> U11#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11#(mark X1, X2) -> U11#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11#(X1, active X2) -> U11#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11#(X1, mark X2) -> U11#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)} SCC (3): Strict: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 0, [U11#](x0, x1) = x0 Strict: U11#(mark X1, X2) -> U11#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11#(X1, active X2) -> U11#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 U11#(X1, mark X2) -> U11#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 0 + 1N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 1N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 1M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 1M >= 2 + 1N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 1V2 + 1V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark plus(X1, X2) -> active plus(mark X1, mark X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X SCCS (1): Scc: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)} SCC (2): Strict: { U11#(X1, mark X2) -> U11#(X1, X2), U11#(X1, active X2) -> U11#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U11#](x0, x1) = x0 Strict: U11#(X1, active X2) -> U11#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 U11#(X1, mark X2) -> U11#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U11#(X1, mark X2) -> U11#(X1, X2)} SCC (1): Strict: {U11#(X1, mark X2) -> U11#(X1, X2)} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U11#](x0, x1) = x0 Strict: U11#(X1, mark X2) -> U11#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (2): Strict: { U21# mark X -> U21# X, U21# active X -> U21# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U21#](x0) = x0 Strict: U21# active X -> U21# X 1 + 1X >= 0 + 1X U21# mark X -> U21# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U21# mark X -> U21# X} SCC (1): Strict: {U21# mark X -> U21# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U21#](x0) = x0 Strict: U21# mark X -> U21# X 1 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed SCC (2): Strict: { U12# mark X -> U12# X, U12# active X -> U12# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U31](x0, x1) = 0, [plus](x0, x1) = 0, [mark](x0) = x0, [U12](x0) = 0, [isNat](x0) = 0, [active](x0) = x0 + 1, [U21](x0) = 0, [s](x0) = 0, [tt] = 1, [0] = 0, [U12#](x0) = x0 Strict: U12# active X -> U12# X 1 + 1X >= 0 + 1X U12# mark X -> U12# X 0 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(mark X1, X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, active X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 plus(X1, mark X2) -> plus(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X U41(active X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U21 active X -> U21 X 0 + 0X >= 0 + 0X U21 mark X -> U21 X 0 + 0X >= 0 + 0X U11(active X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(mark X1, X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, active X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 U11(X1, mark X2) -> U11(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active plus(N, 0()) -> mark U31(isNat N, N) 1 + 0N >= 0 + 0N active plus(N, s M) -> mark U41(isNat M, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 0N + 0M >= 0 + 0N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 0 + 0N + 0M active U31(tt(), N) -> mark N 1 + 0N >= 0 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 0V2 >= 0 + 0V2 active isNat 0() -> mark tt() 1 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 1 + 0V2 + 0V1 >= 0 + 0V2 + 0V1 active isNat s V1 -> mark U21 isNat V1 1 + 0V1 >= 0 + 0V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 0 + 0X >= 0 + 0X isNat mark X -> isNat X 0 + 0X >= 0 + 0X U12 active X -> U12 X 0 + 0X >= 0 + 0X U12 mark X -> U12 X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark s X -> active s mark X 0 + 0X >= 1 + 0X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark U21 X -> active U21 mark X 0 + 0X >= 1 + 0X mark tt() -> active tt() 1 >= 2 mark U11(X1, X2) -> active U11(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark isNat X -> active isNat X 0 + 0X >= 1 + 0X mark U12 X -> active U12 mark X 0 + 0X >= 1 + 0X SCCS (1): Scc: {U12# mark X -> U12# X} SCC (1): Strict: {U12# mark X -> U12# X} Weak: { mark U12 X -> active U12 mark X, mark isNat X -> active isNat X, mark U11(X1, X2) -> active U11(mark X1, X2), mark tt() -> active tt(), mark U21 X -> active U21 mark X, mark U31(X1, X2) -> active U31(mark X1, X2), mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3), mark U41(X1, X2, X3) -> active U41(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(), U12 mark X -> U12 X, U12 active X -> U12 X, isNat mark X -> isNat X, isNat active X -> isNat X, active U12 tt() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat plus(V1, V2) -> mark U11(isNat V1, V2), active isNat 0() -> mark tt(), active U11(tt(), V2) -> mark U12 isNat V2, active U21 tt() -> mark tt(), active U31(tt(), N) -> mark N, active U42(tt(), M, N) -> mark s plus(N, M), active U41(tt(), M, N) -> mark U42(isNat N, M, N), active plus(N, s M) -> mark U41(isNat M, M, N), active plus(N, 0()) -> mark U31(isNat N, N), U11(X1, mark X2) -> U11(X1, X2), U11(X1, active X2) -> U11(X1, X2), U11(mark X1, X2) -> U11(X1, X2), U11(active X1, X2) -> U11(X1, X2), U21 mark X -> U21 X, U21 active X -> U21 X, U31(X1, mark X2) -> U31(X1, X2), U31(X1, active X2) -> U31(X1, X2), U31(mark X1, X2) -> U31(X1, X2), U31(active X1, X2) -> U31(X1, X2), U42(X1, X2, mark X3) -> U42(X1, X2, X3), U42(X1, X2, active X3) -> U42(X1, X2, X3), U42(X1, mark X2, X3) -> U42(X1, X2, X3), U42(X1, active X2, X3) -> U42(X1, X2, X3), U42(mark X1, X2, X3) -> U42(X1, X2, X3), U42(active X1, X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark X3) -> U41(X1, X2, X3), U41(X1, X2, active X3) -> U41(X1, X2, X3), U41(X1, mark X2, X3) -> U41(X1, X2, X3), U41(X1, active X2, X3) -> U41(X1, X2, X3), U41(mark X1, X2, X3) -> U41(X1, X2, X3), U41(active X1, X2, X3) -> U41(X1, X2, X3), s mark X -> s X, s active X -> s X, plus(X1, mark X2) -> plus(X1, X2), plus(X1, active X2) -> plus(X1, X2), plus(mark X1, X2) -> plus(X1, X2), plus(active X1, X2) -> plus(X1, X2)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 1, [plus](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [U12](x0) = x0 + 1, [isNat](x0) = x0 + 1, [active](x0) = x0, [U21](x0) = x0 + 1, [s](x0) = x0 + 1, [tt] = 0, [0] = 1, [U12#](x0) = x0 Strict: U12# mark X -> U12# X 1 + 1X >= 0 + 1X Weak: plus(active X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(mark X1, X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, active X2) -> plus(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 plus(X1, mark X2) -> plus(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X U41(active X1, X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(mark X1, X2, X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, active X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, mark X2, X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, active X3) -> U41(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U41(X1, X2, mark X3) -> U41(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 0X2 + 1X3 U42(active X1, X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(mark X1, X2, X3) -> U42(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, active X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, mark X2, X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, active X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U42(X1, X2, mark X3) -> U42(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 0X2 + 0X3 U31(active X1, X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(mark X1, X2) -> U31(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, active X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U31(X1, mark X2) -> U31(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 U21 active X -> U21 X 1 + 1X >= 1 + 1X U21 mark X -> U21 X 2 + 1X >= 1 + 1X U11(active X1, X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(mark X1, X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, active X2) -> U11(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 U11(X1, mark X2) -> U11(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active plus(N, 0()) -> mark U31(isNat N, N) 2 + 0N >= 3 + 1N active plus(N, s M) -> mark U41(isNat M, M, N) 2 + 0N + 1M >= 3 + 1N + 1M active U41(tt(), M, N) -> mark U42(isNat N, M, N) 1 + 1N + 0M >= 3 + 1N + 0M active U42(tt(), M, N) -> mark s plus(N, M) 1 + 0N + 0M >= 3 + 0N + 1M active U31(tt(), N) -> mark N 1 + 0N >= 1 + 1N active U21 tt() -> mark tt() 1 >= 1 active U11(tt(), V2) -> mark U12 isNat V2 1 + 1V2 >= 3 + 1V2 active isNat 0() -> mark tt() 2 >= 1 active isNat plus(V1, V2) -> mark U11(isNat V1, V2) 2 + 1V2 + 0V1 >= 3 + 1V2 + 1V1 active isNat s V1 -> mark U21 isNat V1 2 + 1V1 >= 3 + 1V1 active U12 tt() -> mark tt() 1 >= 1 isNat active X -> isNat X 1 + 1X >= 1 + 1X isNat mark X -> isNat X 2 + 1X >= 1 + 1X U12 active X -> U12 X 1 + 1X >= 1 + 1X U12 mark X -> U12 X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark plus(X1, X2) -> active plus(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark s X -> active s mark X 2 + 1X >= 2 + 1X mark U41(X1, X2, X3) -> active U41(mark X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 2 + 1X1 + 0X2 + 1X3 mark U42(X1, X2, X3) -> active U42(mark X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 2 + 1X1 + 0X2 + 0X3 mark U31(X1, X2) -> active U31(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark U21 X -> active U21 mark X 2 + 1X >= 2 + 1X mark tt() -> active tt() 1 >= 0 mark U11(X1, X2) -> active U11(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark isNat X -> active isNat X 2 + 1X >= 1 + 1X mark U12 X -> active U12 mark X 2 + 1X >= 2 + 1X Qed