YES Time: 0.014751 TRS: { quot(x, 0(), s z) -> s quot(x, s z, s z), quot(0(), s y, s z) -> 0(), quot(s x, s y, z) -> quot(x, y, z)} DP: DP: {quot#(x, 0(), s z) -> quot#(x, s z, s z), quot#(s x, s y, z) -> quot#(x, y, z)} TRS: { quot(x, 0(), s z) -> s quot(x, s z, s z), quot(0(), s y, s z) -> 0(), quot(s x, s y, z) -> quot(x, y, z)} EDG: {(quot#(x, 0(), s z) -> quot#(x, s z, s z), quot#(s x, s y, z) -> quot#(x, y, z)) (quot#(s x, s y, z) -> quot#(x, y, z), quot#(x, 0(), s z) -> quot#(x, s z, s z)) (quot#(s x, s y, z) -> quot#(x, y, z), quot#(s x, s y, z) -> quot#(x, y, z))} STATUS: arrows: 0.250000 SCCS (1): Scc: {quot#(x, 0(), s z) -> quot#(x, s z, s z), quot#(s x, s y, z) -> quot#(x, y, z)} SCC (2): Strict: {quot#(x, 0(), s z) -> quot#(x, s z, s z), quot#(s x, s y, z) -> quot#(x, y, z)} Weak: { quot(x, 0(), s z) -> s quot(x, s z, s z), quot(0(), s y, s z) -> 0(), quot(s x, s y, z) -> quot(x, y, z)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [quot](x0, x1, x2) = x0 + x1, [s](x0) = x0 + 1, [0] = 1, [quot#](x0, x1, x2) = x0 + 1 Strict: quot#(s x, s y, z) -> quot#(x, y, z) 2 + 0y + 0z + 1x >= 1 + 0y + 0z + 1x quot#(x, 0(), s z) -> quot#(x, s z, s z) 1 + 0z + 1x >= 1 + 0z + 1x Weak: quot(s x, s y, z) -> quot(x, y, z) 2 + 1y + 0z + 1x >= 0 + 1y + 0z + 1x quot(0(), s y, s z) -> 0() 2 + 1y + 0z >= 1 quot(x, 0(), s z) -> s quot(x, s z, s z) 1 + 0z + 1x >= 2 + 1z + 1x SCCS (0):