YES Time: 0.024273 TRS: { h(x, c(y, z)) -> h(c(s y, x), z), h(c(s x, c(s 0(), y)), z) -> h(y, c(s 0(), c(x, z)))} DP: DP: { h#(x, c(y, z)) -> h#(c(s y, x), z), h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z)))} TRS: { h(x, c(y, z)) -> h(c(s y, x), z), h(c(s x, c(s 0(), y)), z) -> h(y, c(s 0(), c(x, z)))} UR: {} EDG: {(h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z)))) (h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))))} EDG: {(h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z)))) (h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))))} EDG: {(h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(x, c(y, z)) -> h#(c(s y, x), z))} EDG: {(h#(c(s x, c(s 0(), y)), z) -> h#(y, c(s 0(), c(x, z))), h#(x, c(y, z)) -> h#(c(s y, x), z)) (h#(x, c(y, z)) -> h#(c(s y, x), z), h#(x, c(y, z)) -> h#(c(s y, x), z))} STATUS: arrows: 0.500000 SCCS (1): Scc: {h#(x, c(y, z)) -> h#(c(s y, x), z)} SCC (1): Strict: {h#(x, c(y, z)) -> h#(c(s y, x), z)} Weak: { h(x, c(y, z)) -> h(c(s y, x), z), h(c(s x, c(s 0(), y)), z) -> h(y, c(s 0(), c(x, z)))} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [h](x0, x1) = 0, [c](x0, x1) = x0 + 1, [s](x0) = 0, [0] = 0, [h#](x0, x1) = x0 Strict: h#(x, c(y, z)) -> h#(c(s y, x), z) 1 + 0y + 0x + 1z >= 0 + 0y + 0x + 1z Weak: h(c(s x, c(s 0(), y)), z) -> h(y, c(s 0(), c(x, z))) 0 + 0y + 0x + 0z >= 0 + 0y + 0x + 0z h(x, c(y, z)) -> h(c(s y, x), z) 0 + 0y + 0x + 0z >= 0 + 0y + 0x + 0z Qed