ceta_equiv: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.3: 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(#) -> # 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(#, 0(x)) -> ge(#, x) ge(#, 1(x)) -> false if(true, x, y) -> x if(false, x, y) -> y log(x) -> -(log'(x), 1(#)) log'(#) -> # log'(1(x)) -> +(log'(x), 1(#)) log'(0(x)) -> if(ge(x, 1(#)), +(log'(x), 1(#)), #) not(true) -> false not(false) -> true 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