YES Time: 0.007272 TRS: { minus(X, 0()) -> X, minus(s X, s Y) -> p minus(X, Y), p s X -> X, div(0(), s Y) -> 0(), div(s X, s Y) -> s div(minus(X, Y), s Y)} DP: DP: {minus#(s X, s Y) -> minus#(X, Y), minus#(s X, s Y) -> p# minus(X, Y), div#(s X, s Y) -> minus#(X, Y), div#(s X, s Y) -> div#(minus(X, Y), s Y)} TRS: { minus(X, 0()) -> X, minus(s X, s Y) -> p minus(X, Y), p s X -> X, div(0(), s Y) -> 0(), div(s X, s Y) -> s div(minus(X, Y), s Y)} EDG: {(minus#(s X, s Y) -> minus#(X, Y), minus#(s X, s Y) -> p# minus(X, Y)) (minus#(s X, s Y) -> minus#(X, Y), minus#(s X, s Y) -> minus#(X, Y)) (div#(s X, s Y) -> minus#(X, Y), minus#(s X, s Y) -> minus#(X, Y)) (div#(s X, s Y) -> minus#(X, Y), minus#(s X, s Y) -> p# minus(X, Y)) (div#(s X, s Y) -> div#(minus(X, Y), s Y), div#(s X, s Y) -> minus#(X, Y)) (div#(s X, s Y) -> div#(minus(X, Y), s Y), div#(s X, s Y) -> div#(minus(X, Y), s Y))} SCCS (2): Scc: {div#(s X, s Y) -> div#(minus(X, Y), s Y)} Scc: {minus#(s X, s Y) -> minus#(X, Y)} SCC (1): Strict: {div#(s X, s Y) -> div#(minus(X, Y), s Y)} Weak: { minus(X, 0()) -> X, minus(s X, s Y) -> p minus(X, Y), p s X -> X, div(0(), s Y) -> 0(), div(s X, s Y) -> s div(minus(X, Y), s Y)} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [minus](x0, x1) = x0, [div](x0, x1) = x0 + x1, [p](x0) = x0 + 1, [s](x0) = x0 + 1, [0] = 0, [div#](x0, x1) = x0 + 1 Strict: div#(s X, s Y) -> div#(minus(X, Y), s Y) 2 + 1X + 0Y >= 1 + 1X + 0Y Weak: Qed SCC (1): Strict: {minus#(s X, s Y) -> minus#(X, Y)} Weak: { minus(X, 0()) -> X, minus(s X, s Y) -> p minus(X, Y), p s X -> X, div(0(), s Y) -> 0(), div(s X, s Y) -> s div(minus(X, Y), s Y)} SPSC: Simple Projection: pi(minus#) = 1 Strict: {} Qed