YES Time: 0.039703 TRS: { a c d x -> c x, u b d d x -> b x, v c x -> b x, v a c x -> u b d x, v a a x -> u v x, w c x -> b x, w a c x -> u b d x, w a a x -> u w x} DP: DP: {v# a c x -> u# b d x, v# a a x -> u# v x, v# a a x -> v# x, w# a c x -> u# b d x, w# a a x -> u# w x, w# a a x -> w# x} TRS: { a c d x -> c x, u b d d x -> b x, v c x -> b x, v a c x -> u b d x, v a a x -> u v x, w c x -> b x, w a c x -> u b d x, w a a x -> u w x} UR: {u b d d x -> b x, v c x -> b x, v a c x -> u b d x, v a a x -> u v x, w c x -> b x, w a c x -> u b d x, w a a x -> u w x} EDG: {(w# a a x -> w# x, w# a a x -> w# x) (w# a a x -> w# x, w# a a x -> u# w x) (w# a a x -> w# x, w# a c x -> u# b d x) (v# a a x -> v# x, v# a c x -> u# b d x) (v# a a x -> v# x, v# a a x -> u# v x) (v# a a x -> v# x, v# a a x -> v# x)} STATUS: arrows: 0.833333 SCCS (2): Scc: {w# a a x -> w# x} Scc: {v# a a x -> v# x} SCC (1): Strict: {w# a a x -> w# x} Weak: { a c d x -> c x, u b d d x -> b x, v c x -> b x, v a c x -> u b d x, v a a x -> u v x, w c x -> b x, w a c x -> u b d x, w a a x -> u w x} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [c](x0) = 1, [a](x0) = x0 + 1, [d](x0) = x0 + 1, [b](x0) = 0, [u](x0) = 0, [v](x0) = x0 + 1, [w](x0) = x0 + 1, [w#](x0) = x0 Strict: w# a a x -> w# x 2 + 1x >= 0 + 1x Weak: w a a x -> u w x 3 + 1x >= 0 + 0x w a c x -> u b d x 3 + 0x >= 0 + 0x w c x -> b x 2 + 0x >= 0 + 0x v a a x -> u v x 3 + 1x >= 0 + 0x v a c x -> u b d x 3 + 0x >= 0 + 0x v c x -> b x 2 + 0x >= 0 + 0x u b d d x -> b x 0 + 0x >= 0 + 0x a c d x -> c x 2 + 0x >= 1 + 0x Qed SCC (1): Strict: {v# a a x -> v# x} Weak: { a c d x -> c x, u b d d x -> b x, v c x -> b x, v a c x -> u b d x, v a a x -> u v x, w c x -> b x, w a c x -> u b d x, w a a x -> u w x} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [c](x0) = 1, [a](x0) = x0 + 1, [d](x0) = x0 + 1, [b](x0) = 0, [u](x0) = 0, [v](x0) = x0 + 1, [w](x0) = x0 + 1, [v#](x0) = x0 Strict: v# a a x -> v# x 2 + 1x >= 0 + 1x Weak: w a a x -> u w x 3 + 1x >= 0 + 0x w a c x -> u b d x 3 + 0x >= 0 + 0x w c x -> b x 2 + 0x >= 0 + 0x v a a x -> u v x 3 + 1x >= 0 + 0x v a c x -> u b d x 3 + 0x >= 0 + 0x v c x -> b x 2 + 0x >= 0 + 0x u b d d x -> b x 0 + 0x >= 0 + 0x a c d x -> c x 2 + 0x >= 1 + 0x Qed