YES

Proof:
This system is quasi-decreasing.
By \cite{O02}, p. 214, Proposition 7.2.50.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to U(R).
Call external tool:
ttt2 - trs 30
Input:
  plus(0, X) -> X
  plus(s(X), Y) -> plus(X, s(Y))
  fib(0) -> pair(s(0), 0)
  ?2(W, X, Y, Z) -> pair(W, Y)
  ?1(pair(Y, Z), X) -> ?2(plus(Y, Z), X, Y, Z)
  fib(s(X)) -> ?1(fib(X), X)

 DP Processor:
  DPs:
   plus#(s(X),Y) -> plus#(X,s(Y))
   ?1#(pair(Y,Z),X) -> plus#(Y,Z)
   ?1#(pair(Y,Z),X) -> ?2#(plus(Y,Z),X,Y,Z)
   fib#(s(X)) -> fib#(X)
   fib#(s(X)) -> ?1#(fib(X),X)
  TRS:
   plus(0(),X) -> X
   plus(s(X),Y) -> plus(X,s(Y))
   fib(0()) -> pair(s(0()),0())
   ?2(W,X,Y,Z) -> pair(W,Y)
   ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
   fib(s(X)) -> ?1(fib(X),X)
  TDG Processor:
   DPs:
    plus#(s(X),Y) -> plus#(X,s(Y))
    ?1#(pair(Y,Z),X) -> plus#(Y,Z)
    ?1#(pair(Y,Z),X) -> ?2#(plus(Y,Z),X,Y,Z)
    fib#(s(X)) -> fib#(X)
    fib#(s(X)) -> ?1#(fib(X),X)
   TRS:
    plus(0(),X) -> X
    plus(s(X),Y) -> plus(X,s(Y))
    fib(0()) -> pair(s(0()),0())
    ?2(W,X,Y,Z) -> pair(W,Y)
    ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
    fib(s(X)) -> ?1(fib(X),X)
   graph:
    ?1#(pair(Y,Z),X) -> plus#(Y,Z) -> plus#(s(X),Y) -> plus#(X,s(Y))
    fib#(s(X)) -> ?1#(fib(X),X) ->
    ?1#(pair(Y,Z),X) -> ?2#(plus(Y,Z),X,Y,Z)
    fib#(s(X)) -> ?1#(fib(X),X) -> ?1#(pair(Y,Z),X) -> plus#(Y,Z)
    fib#(s(X)) -> fib#(X) -> fib#(s(X)) -> ?1#(fib(X),X)
    fib#(s(X)) -> fib#(X) -> fib#(s(X)) -> fib#(X)
    plus#(s(X),Y) -> plus#(X,s(Y)) -> plus#(s(X),Y) -> plus#(X,s(Y))
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 6/25
    DPs:
     fib#(s(X)) -> fib#(X)
    TRS:
     plus(0(),X) -> X
     plus(s(X),Y) -> plus(X,s(Y))
     fib(0()) -> pair(s(0()),0())
     ?2(W,X,Y,Z) -> pair(W,Y)
     ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
     fib(s(X)) -> ?1(fib(X),X)
    Subterm Criterion Processor:
     simple projection:
      pi(fib#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),X) -> X
       plus(s(X),Y) -> plus(X,s(Y))
       fib(0()) -> pair(s(0()),0())
       ?2(W,X,Y,Z) -> pair(W,Y)
       ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
       fib(s(X)) -> ?1(fib(X),X)
     Qed
    
    DPs:
     plus#(s(X),Y) -> plus#(X,s(Y))
    TRS:
     plus(0(),X) -> X
     plus(s(X),Y) -> plus(X,s(Y))
     fib(0()) -> pair(s(0()),0())
     ?2(W,X,Y,Z) -> pair(W,Y)
     ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
     fib(s(X)) -> ?1(fib(X),X)
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),X) -> X
       plus(s(X),Y) -> plus(X,s(Y))
       fib(0()) -> pair(s(0()),0())
       ?2(W,X,Y,Z) -> pair(W,Y)
       ?1(pair(Y,Z),X) -> ?2(plus(Y,Z),X,Y,Z)
       fib(s(X)) -> ?1(fib(X),X)
     Qed