/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Proof: DP Processor: DPs: Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s TDG Processor: DPs: Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s graph: Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) Term_sub#(Case(m,xi,n),s) -> Sum_sub#(xi,s) -> Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) SCC Processor: #sccs: 2 #rules: 22 #arcs: 203/529 DPs: Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s EDG Processor: DPs: Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s graph: Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Concat(s,t),u) -> Concat#(t,u) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(t,u) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) -> Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) -> Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) -> Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) SCC Processor: #sccs: 2 #rules: 20 #arcs: 165/400 DPs: Concat#(Concat(s,t),u) -> Concat#(t,u) Concat#(Cons_sum(xi,k,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Term_sub#(m,t) Term_sub#(Term_sub(m,s),t) -> Term_sub#(m,Concat(s,t)) Term_sub#(Term_sub(m,s),t) -> Concat#(s,t) Concat#(Cons_usual(x,m,s),t) -> Concat#(s,t) Concat#(Concat(s,t),u) -> Concat#(s,Concat(t,u)) Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_pair(m,n),s) -> Term_sub#(n,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(m,s) Term_sub#(Term_app(m,n),s) -> Term_sub#(n,s) Term_sub#(Case(m,xi,n),s) -> Frozen#(m,Sum_sub(xi,s),n,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(m,s) Frozen#(m,Sum_term_var(xi),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Right()),n,s) -> Term_sub#(n,s) Frozen#(m,Sum_constant(Left()),n,s) -> Term_sub#(m,s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Subterm Criterion Processor: simple projection: pi(Case) = [0,2,2] pi(Sum_sub) = [0,1,1,1] pi(Sum_constant) = [0,0] pi(Sum_term_var) = 0 pi(Term_app) = [0,1,1] pi(Term_pair) = [0,0,1] pi(Term_inl) = 0 pi(Term_inr) = 0 pi(Term_sub#) = [0,0] pi(Frozen#) = [0,0,2,2] pi(Concat#) = [0,0] problem: DPs: Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Size-Change Termination Processor: DPs: TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s The DP: Term_sub#(Term_inr(m),s) -> Term_sub#(m,s) has the edges: 0 > 0 1 >= 1 The DP: Term_sub#(Term_inl(m),s) -> Term_sub#(m,s) has the edges: 0 > 0 1 >= 1 Qed DPs: Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Size-Change Termination Processor: DPs: TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s The DP: Term_sub#(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub#(Term_var(x),s) has the edges: 0 >= 0 1 > 1 The DP: Term_sub#(Term_var(x),Cons_usual(y,m,s)) -> Term_sub#(Term_var(x),s) has the edges: 0 >= 0 1 > 1 Qed DPs: Sum_sub#(xi,Cons_sum(psi,k,s)) -> Sum_sub#(xi,s) Sum_sub#(xi,Cons_usual(y,m,s)) -> Sum_sub#(xi,s) TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Subterm Criterion Processor: simple projection: pi(Sum_sub#) = 1 problem: DPs: TRS: Term_sub(Case(m,xi,n),s) -> Frozen(m,Sum_sub(xi,s),n,s) Frozen(m,Sum_constant(Left()),n,s) -> Term_sub(m,s) Frozen(m,Sum_constant(Right()),n,s) -> Term_sub(n,s) Frozen(m,Sum_term_var(xi),n,s) -> Case(Term_sub(m,s),xi,Term_sub(n,s)) Term_sub(Term_app(m,n),s) -> Term_app(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_pair(m,n),s) -> Term_pair(Term_sub(m,s),Term_sub(n,s)) Term_sub(Term_inl(m),s) -> Term_inl(Term_sub(m,s)) Term_sub(Term_inr(m),s) -> Term_inr(Term_sub(m,s)) Term_sub(Term_var(x),Id()) -> Term_var(x) Term_sub(Term_var(x),Cons_usual(y,m,s)) -> m Term_sub(Term_var(x),Cons_usual(y,m,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_var(x),Cons_sum(xi,k,s)) -> Term_sub(Term_var(x),s) Term_sub(Term_sub(m,s),t) -> Term_sub(m,Concat(s,t)) Sum_sub(xi,Id()) -> Sum_term_var(xi) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_constant(k) Sum_sub(xi,Cons_sum(psi,k,s)) -> Sum_sub(xi,s) Sum_sub(xi,Cons_usual(y,m,s)) -> Sum_sub(xi,s) Concat(Concat(s,t),u) -> Concat(s,Concat(t,u)) Concat(Cons_usual(x,m,s),t) -> Cons_usual(x,Term_sub(m,t),Concat(s,t)) Concat(Cons_sum(xi,k,s),t) -> Cons_sum(xi,k,Concat(s,t)) Concat(Id(),s) -> s Qed