YES Time: 0.007391 TRS: {dfib(s s x, y) -> dfib(s x, dfib(x, y))} DP: DP: {dfib#(s s x, y) -> dfib#(x, y), dfib#(s s x, y) -> dfib#(s x, dfib(x, y))} TRS: {dfib(s s x, y) -> dfib(s x, dfib(x, y))} EDG: {(dfib#(s s x, y) -> dfib#(x, y), dfib#(s s x, y) -> dfib#(s x, dfib(x, y))) (dfib#(s s x, y) -> dfib#(x, y), dfib#(s s x, y) -> dfib#(x, y)) (dfib#(s s x, y) -> dfib#(s x, dfib(x, y)), dfib#(s s x, y) -> dfib#(x, y)) (dfib#(s s x, y) -> dfib#(s x, dfib(x, y)), dfib#(s s x, y) -> dfib#(s x, dfib(x, y)))} STATUS: arrows: 0.000000 SCCS (1): Scc: {dfib#(s s x, y) -> dfib#(x, y), dfib#(s s x, y) -> dfib#(s x, dfib(x, y))} SCC (2): Strict: {dfib#(s s x, y) -> dfib#(x, y), dfib#(s s x, y) -> dfib#(s x, dfib(x, y))} Weak: {dfib(s s x, y) -> dfib(s x, dfib(x, y))} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [dfib](x0, x1) = 1, [s](x0) = x0 + 1, [dfib#](x0, x1) = x0 + x1 Strict: dfib#(s s x, y) -> dfib#(s x, dfib(x, y)) 2 + 1x + 1y >= 2 + 1x + 0y dfib#(s s x, y) -> dfib#(x, y) 2 + 1x + 1y >= 0 + 1x + 1y Weak: dfib(s s x, y) -> dfib(s x, dfib(x, y)) 1 + 0x + 0y >= 1 + 0x + 0y SCCS (1): Scc: {dfib#(s s x, y) -> dfib#(s x, dfib(x, y))} SCC (1): Strict: {dfib#(s s x, y) -> dfib#(s x, dfib(x, y))} Weak: {dfib(s s x, y) -> dfib(s x, dfib(x, y))} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [dfib](x0, x1) = 0, [s](x0) = x0 + 1, [dfib#](x0, x1) = x0 Strict: dfib#(s s x, y) -> dfib#(s x, dfib(x, y)) 2 + 1x + 0y >= 1 + 1x + 0y Weak: dfib(s s x, y) -> dfib(s x, dfib(x, y)) 0 + 0x + 0y >= 0 + 0x + 0y Qed