(VAR x y ) (STRATEGY INNERMOST) (RULES g(s(x),s(y)) -> if(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0))),k(n(s(x),s(y)),s(s(0))))),g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) n(0,y) -> 0 n(x,0) -> 0 n(s(x),s(y)) -> s(n(x,y)) m(0,y) -> y m(x,0) -> x m(s(x),s(y)) -> s(m(x,y)) k(0,s(y)) -> 0 k(s(x),s(y)) -> s(k(minus(x,y),s(y))) t(x) -> p(x,x) p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x)) p(0,y) -> y p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y)))) minus(x,0) -> x minus(s(x),s(y)) -> minus(x,y) id(x) -> x if(true,x,y) -> x if(false,x,y) -> y not(x) -> if(x,false,true) and(x,false) -> false and(true,true) -> true f(0) -> true f(s(x)) -> h(x) h(0) -> false h(s(x)) -> f(x) gt(s(x),0) -> true gt(0,y) -> false gt(s(x),s(y)) -> gt(x,y) )