(GOAL COMPLEXITY) (STARTTERM CONSTRUCTOR-BASED) (STRATEGY INNERMOST) (STRATEGY INNERMOST) (VAR b x y z) (DATATYPES A = µX.< s(X), 0, false, true, baseError, logZeroError >) (SIGNATURES le :: [A x A] -> A plus :: [A x A] -> A times :: [A x A] -> A log :: [A x A] -> A loop :: [A x A x A x A] -> A if :: [A x A x A x A x A] -> A) (RULES le(s(x),0()) -> false() le(0(),y) -> true() le(s(x),s(y)) -> le(x,y) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> plus(y ,times(x,y)) log(x,0()) -> baseError() log(x,s(0())) -> baseError() log(0(),s(s(b))) -> logZeroError() log(s(x),s(s(b))) -> loop(s(x) ,s(s(b)) ,s(0()) ,0()) loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z) if(true(),x,b,y,z) -> z if(false(),x,b,y,z) -> loop(x ,b ,times(b,y) ,s(z)))