TRS: {a__f(f(X)) -> a__c(f(g(f(X)))), a__c(X) -> d(X), a__h(X) -> a__c(d(X)), mark(f(X)) -> a__f(mark(X)), mark(c(X)) -> a__c(X), mark(h(X)) -> a__h(mark(X)), mark(g(X)) -> g(X), mark(d(X)) -> d(X), a__f(X) -> f(X), a__c(X) -> c(X), a__h(X) -> h(X)} POP*: Quasi-Precedence: a__h > a__c, a__h > d, a__h > h, a__f > a__c, a__f > f, a__f > g, a__c > c, a__c > d, mark > a__h, mark > a__f, mark > a__c empty Normal: pi(mark) = [1] Safe: pi(h) = [1], pi(c) = [1], pi(a__h) = [1], pi(d) = [1], pi(a__f) = [1], pi(g) = [1], pi(f) = [1], pi(a__c) = [1] Predicative System: {a__f(;f(;X)) -> a__c(;f(;g(;f(;X)))), a__c(;X) -> d(;X), a__h(;X) -> a__c(;d(;X)), mark(f(;X);) -> a__f(;mark(X;)), mark(c(;X);) -> a__c(;X), mark(h(;X);) -> a__h(;mark(X;)), mark(g(;X);) -> g(;X), mark(d(;X);) -> d(;X), a__f(;X) -> f(;X), a__c(;X) -> c(;X), a__h(;X) -> h(;X)} Qed