ceta_equiv: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.4: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: -#(0(x), 0(y)) -> -#(x, y) -#(0(x), 1(y)) -> -#(-(x, y), 1(#)) -#(0(x), 1(y)) -> -#(x, y) -#(1(x), 0(y)) -> -#(x, y) -#(1(x), 1(y)) -> -#(x, y) rules: +(x, #) -> x +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 0(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) +(x, +(y, z)) -> +(+(x, y), z) -(x, #) -> x -(#, x) -> # -(0(x), 0(y)) -> 0(-(x, y)) -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) -(1(x), 0(y)) -> 1(-(x, y)) -(1(x), 1(y)) -> 0(-(x, y)) 0(#) -> # and(x, true) -> x and(x, false) -> false bs(l(x)) -> true bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))) ge(0(x), 0(y)) -> ge(x, y) ge(0(x), 1(y)) -> not(ge(y, x)) ge(1(x), 0(y)) -> ge(x, y) ge(1(x), 1(y)) -> ge(x, y) ge(x, #) -> true ge(#, 1(x)) -> false ge(#, 0(x)) -> ge(#, x) if(true, x, y) -> x if(false, x, y) -> y max(l(x)) -> x max(n(x, y, z)) -> max(z) min(l(x)) -> x min(n(x, y, z)) -> min(y) not(false) -> true not(true) -> false size(l(x)) -> 1(#) size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#)) val(l(x)) -> x val(n(x, y, z)) -> x wb(l(x)) -> true wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z))) the pairs -#(0(x), 0(y)) -> -#(x, y) -#(0(x), 1(y)) -> -#(-(x, y), 1(#)) -#(0(x), 1(y)) -> -#(x, y) -#(1(x), 0(y)) -> -#(x, y) -#(1(x), 1(y)) -> -#(x, y) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(-#) = [(epsilon,0),(1,0),(2,0)] polynomial interpretration over naturals with negative constants Pol(-#(x_1, x_2)) = 1 Pol(0(x_1)) = 1 + x_1 Pol(1(x_1)) = 1 + x_1 Pol(-(x_1, x_2)) = x_1 Pol(#) = 0 problem when orienting DPs cannot orient pair -#(0(x), 1(y)) -> -#(-(x, y), 1(#)) strictly: [(-#(0(x), 1(y)),0),(0(x),0),(1(y),0)] >mu [(-#(-(x, y), 1(#)),0),(-(x, y),0),(1(#),0)] could not be ensured