YES
Input TRS:
AC symbols: plus app
      1: if(true(),x,y) -> x
      2: if(false(),x,y) -> y
      3: eq(0(),0()) -> true()
      4: eq(0(),s(x)) -> false()
      5: eq(s(x),s(y)) -> eq(x,y)
      6: plus(empty(),x) -> x
      7: app(x,empty()) -> empty()
      8: app(x,app(empty(),z)) -> app(empty(),z)
      9: app(x,plus(y,z)) -> plus(app(x,y),app(x,z))
      10: app(x,app(plus(y,z),t)) -> app(plus(app(x,y),app(x,z)),t)
      11: app(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty())
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #app(x,app(y,z)) ->= #app(app(x,y),z)
     #2: #app(x,app(y,z)) ->= #app(x,y)
     #3: #app(x,plus(y,z)) -> #plus(app(x,y),app(x,z))
     #4: #app(x,plus(y,z)) -> #app(x,y)
     #5: #app(x,plus(y,z)) -> #app(x,z)
     #6: #app(singl(x),singl(y)) -> #if(eq(x,y),singl(x),empty())
     #7: #app(singl(x),singl(y)) -> #eq(x,y)
     #8: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #9: #plus(x,plus(y,z)) ->= #plus(x,y)
     #10: #app(x,app(plus(y,z),t)) -> #app(plus(app(x,y),app(x,z)),t)
     #11: #app(x,app(plus(y,z),t)) -> #plus(app(x,y),app(x,z))
     #12: #app(x,app(plus(y,z),t)) -> #app(x,y)
     #13: #app(x,app(plus(y,z),t)) -> #app(x,z)
     #14: #eq(s(x),s(y)) -> #eq(x,y)
Number of SCCs: 3, DPs: 10
  SCC { #14 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: 0
      eq	w: 0
      false	w: 0
      true	w: 0
      #eq	w: x2
      if	w: 0
      0 	w: 0
      #app	w: 0
      singl	w: 0
      plus	w: 0
      #if	w: 0
      empty	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #14
Number of SCCs: 2, DPs: 9
  SCC { #8 #9 }
only weak rules.
Number of SCCs: 1, DPs: 7
  SCC { #1 #2 #4 #5 #10 #12 #13 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 0
      eq	s: []	p: 1
      false	s: []	p: 1
      true	s: []	p: 1
      #eq	s: [1,2]	p: 0
      if	s: [3,2,1]	p: 2
      0 	s: []	p: 0
      #app	s: {1,2}	p: 3
      singl	s: []	p: 1
      plus	s: {1,2}	p: 0
      #if	s: [3,2,1]	p: 0
      empty	s: []	p: 1
      app	s: {1,2}	p: 3
    USABLE RULES: { 1..13 }
    Removed DPs: #2 #4 #5 #10 #12 #13
Number of SCCs: 1, DPs: 1
  SCC { #1 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #15: #plus(plus(empty(),x),_1) -> #plus(x,_1)
     #16: #app(x,app(y,z)) ->= #app(app(x,y),z)
     #17: #app(x,app(y,z)) ->= #app(x,y)
     #18: #app(app(x,plus(y,z)),_1) -> #app(plus(app(x,y),app(x,z)),_1)
     #19: #app(app(singl(x),singl(y)),_1) -> #app(if(eq(x,y),singl(x),empty()),_1)
     #20: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #21: #plus(x,plus(y,z)) ->= #plus(x,y)
     #22: #app(app(x,empty()),_1) -> #app(empty(),_1)
     #23: #app(app(x,app(plus(y,z),t)),_1) -> #app(app(plus(app(x,y),app(x,z)),t),_1)
     #24: #app(app(x,app(empty(),z)),_1) -> #app(app(empty(),z),_1)
Number of SCCs: 2, DPs: 10
  SCC { #16..19 #22..24 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: []	p: 0
      #plus	s: {}	p: 0
      eq	s: 1
      false	s: []	p: 3
      true	s: []	p: 2
      #eq	s: [1,2]	p: 0
      if	s: [3,2]	p: 2
      0 	s: []	p: 3
      #app	s: {1,2}	p: 3
      singl	s: []	p: 1
      plus	s: {1,2}	p: 0
      #if	s: [3,2,1]	p: 0
      empty	s: []	p: 0
      app	s: {1,2}	p: 3
    USABLE RULES: { 1..4 6..13 }
    Removed DPs: #17..19 #22..24
Number of SCCs: 2, DPs: 4
  SCC { #16 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #15 #20 #21 }
POLO(Sum)... succeeded.
      s 	w: 1
      #plus	w: x1 + x2
      eq	w: x1 + 1
      false	w: 3
      true	w: 3
      #eq	w: 0
      if	w: 3
      0 	w: 1
      #app	w: 0
      singl	w: 1
      plus	w: x1 + x2 + 1
      #if	w: 0
      empty	w: 3
      app	w: 2
    USABLE RULES: { 6 12 }
    Removed DPs: #15 #21
Number of SCCs: 1, DPs: 1
  SCC { #20 }
only weak rules.
Number of SCCs: 0, DPs: 0