Input TRS: 1: app'(app'(minus(),x),0()) -> x 2: app'(app'(minus(),app'(s(),x)),app'(s(),y)) -> app'(app'(minus(),x),y) 3: app'(app'(quot(),0()),app'(s(),y)) -> 0() 4: app'(app'(quot(),app'(s(),x)),app'(s(),y)) -> app'(s(),app'(app'(quot(),app'(app'(minus(),x),y)),app'(s(),y))) 5: app'(app'(le(),0()),y) -> true() 6: app'(app'(le(),app'(s(),x)),0()) -> false() 7: app'(app'(le(),app'(s(),x)),app'(s(),y)) -> app'(app'(le(),x),y) 8: app'(app'(app(),nil()),y) -> y 9: app'(app'(app(),app'(app'(add(),n),x)),y) -> app'(app'(add(),n),app'(app'(app(),x),y)) 10: app'(app'(low(),n),nil()) -> nil() 11: app'(app'(low(),n),app'(app'(add(),m),x)) -> app'(app'(app'(if_low(),app'(app'(le(),m),n)),n),app'(app'(add(),m),x)) 12: app'(app'(app'(if_low(),true()),n),app'(app'(add(),m),x)) -> app'(app'(add(),m),app'(app'(low(),n),x)) 13: app'(app'(app'(if_low(),false()),n),app'(app'(add(),m),x)) -> app'(app'(low(),n),x) 14: app'(app'(high(),n),nil()) -> nil() 15: app'(app'(high(),n),app'(app'(add(),m),x)) -> app'(app'(app'(if_high(),app'(app'(le(),m),n)),n),app'(app'(add(),m),x)) 16: app'(app'(app'(if_high(),true()),n),app'(app'(add(),m),x)) -> app'(app'(high(),n),x) 17: app'(app'(app'(if_high(),false()),n),app'(app'(add(),m),x)) -> app'(app'(add(),m),app'(app'(high(),n),x)) 18: app'(quicksort(),nil()) -> nil() 19: app'(quicksort(),app'(app'(add(),n),x)) -> app'(app'(app(),app'(quicksort(),app'(app'(low(),n),x))),app'(app'(add(),n),app'(quicksort(),app'(app'(high(),n),x)))) 20: app'(app'(map(),f),nil()) -> nil() 21: app'(app'(map(),f),app'(app'(add(),x),xs)) -> app'(app'(add(),app'(f,x)),app'(app'(map(),f),xs)) 22: app'(app'(filter(),f),nil()) -> nil() 23: app'(app'(filter(),f),app'(app'(add(),x),xs)) -> app'(app'(app'(app'(filter2(),app'(f,x)),f),x),xs) 24: app'(app'(app'(app'(filter2(),true()),f),x),xs) -> app'(app'(add(),x),app'(app'(filter(),f),xs)) 25: app'(app'(app'(app'(filter2(),false()),f),x),xs) -> app'(app'(filter(),f),xs) Number of strict rules: 25 Direct Order(PosReal,>,Poly) ... failed. Freezing app' 1: app'❆2_minus(x,0()) -> x 2: app'❆2_minus(app'❆1_s(x),app'❆1_s(y)) -> app'❆2_minus(x,y) 3: app'❆2_quot(0(),app'❆1_s(y)) -> 0() 4: app'❆2_quot(app'❆1_s(x),app'❆1_s(y)) -> app'❆1_s(app'❆2_quot(app'❆2_minus(x,y),app'❆1_s(y))) 5: app'❆2_le(0(),y) -> true() 6: app'❆2_le(app'❆1_s(x),0()) -> false() 7: app'❆2_le(app'❆1_s(x),app'❆1_s(y)) -> app'❆2_le(x,y) 8: app'❆2_app(nil(),y) -> y 9: app'❆2_app(app'❆2_add(n,x),y) -> app'❆2_add(n,app'❆2_app(x,y)) 10: app'❆2_low(n,nil()) -> nil() 11: app'❆2_low(n,app'❆2_add(m,x)) -> app'❆3_if_low(app'❆2_le(m,n),n,app'❆2_add(m,x)) 12: app'❆3_if_low(true(),n,app'❆2_add(m,x)) -> app'❆2_add(m,app'❆2_low(n,x)) 13: app'❆3_if_low(false(),n,app'❆2_add(m,x)) -> app'❆2_low(n,x) 14: app'❆2_high(n,nil()) -> nil() 15: app'❆2_high(n,app'❆2_add(m,x)) -> app'❆3_if_high(app'❆2_le(m,n),n,app'❆2_add(m,x)) 16: app'❆3_if_high(true(),n,app'❆2_add(m,x)) -> app'❆2_high(n,x) 17: app'❆3_if_high(false(),n,app'❆2_add(m,x)) -> app'❆2_add(m,app'❆2_high(n,x)) 18: app'❆1_quicksort(nil()) -> nil() 19: app'❆1_quicksort(app'❆2_add(n,x)) -> app'❆2_app(app'❆1_quicksort(app'❆2_low(n,x)),app'❆2_add(n,app'❆1_quicksort(app'❆2_high(n,x)))) 20: app'❆2_map(f,nil()) -> nil() 21: app'❆2_map(f,app'❆2_add(x,xs)) -> app'❆2_add(app'(f,x),app'❆2_map(f,xs)) 22: app'❆2_filter(f,nil()) -> nil() 23: app'❆2_filter(f,app'❆2_add(x,xs)) -> app'❆4_filter2(app'(f,x),f,x,xs) 24: app'❆4_filter2(true(),f,x,xs) -> app'❆2_add(x,app'❆2_filter(f,xs)) 25: app'❆4_filter2(false(),f,x,xs) -> app'❆2_filter(f,xs) 26: app'(le(),_1) ->= app'❆1_le(_1) 27: app'(app'❆1_le(_1),_2) ->= app'❆2_le(_1,_2) 28: app'(quot(),_1) ->= app'❆1_quot(_1) 29: app'(app'❆1_quot(_1),_2) ->= app'❆2_quot(_1,_2) 30: app'(high(),_1) ->= app'❆1_high(_1) 31: app'(app'❆1_high(_1),_2) ->= app'❆2_high(_1,_2) 32: app'(add(),_1) ->= app'❆1_add(_1) 33: app'(app'❆1_add(_1),_2) ->= app'❆2_add(_1,_2) 34: app'(s(),_1) ->= app'❆1_s(_1) 35: app'(filter(),_1) ->= app'❆1_filter(_1) 36: app'(app'❆1_filter(_1),_2) ->= app'❆2_filter(_1,_2) 37: app'(if_low(),_1) ->= app'❆1_if_low(_1) 38: app'(app'❆1_if_low(_1),_2) ->= app'❆2_if_low(_1,_2) 39: app'(app'❆2_if_low(_1,_2),_3) ->= app'❆3_if_low(_1,_2,_3) 40: app'(map(),_1) ->= app'❆1_map(_1) 41: app'(app'❆1_map(_1),_2) ->= app'❆2_map(_1,_2) 42: app'(minus(),_1) ->= app'❆1_minus(_1) 43: app'(app'❆1_minus(_1),_2) ->= app'❆2_minus(_1,_2) 44: app'(quicksort(),_1) ->= app'❆1_quicksort(_1) 45: app'(if_high(),_1) ->= app'❆1_if_high(_1) 46: app'(app'❆1_if_high(_1),_2) ->= app'❆2_if_high(_1,_2) 47: app'(app'❆2_if_high(_1,_2),_3) ->= app'❆3_if_high(_1,_2,_3) 48: app'(filter2(),_1) ->= app'❆1_filter2(_1) 49: app'(app'❆1_filter2(_1),_2) ->= app'❆2_filter2(_1,_2) 50: app'(app'❆2_filter2(_1,_2),_3) ->= app'❆3_filter2(_1,_2,_3) 51: app'(app'❆3_filter2(_1,_2,_3),_4) ->= app'❆4_filter2(_1,_2,_3,_4) 52: app'(app(),_1) ->= app'❆1_app(_1) 53: app'(app'❆1_app(_1),_2) ->= app'❆2_app(_1,_2) 54: app'(low(),_1) ->= app'❆1_low(_1) 55: app'(app'❆1_low(_1),_2) ->= app'❆2_low(_1,_2) Number of strict rules: 25 Direct Order(PosReal,>,Poly) ... failed. Dependency Pairs: #1: #app'❆2_minus(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_minus(x,y) #2: #app'(app'❆1_minus(_1),_2) ->? #app'❆2_minus(_1,_2) #3: #app'(app'❆1_quot(_1),_2) ->? #app'❆2_quot(_1,_2) #4: #app'(app'❆1_map(_1),_2) ->? #app'❆2_map(_1,_2) #5: #app'(app'❆2_if_high(_1,_2),_3) ->? #app'❆3_if_high(_1,_2,_3) #6: #app'(app'❆1_app(_1),_2) ->? #app'❆2_app(_1,_2) #7: #app'(app'❆1_low(_1),_2) ->? #app'❆2_low(_1,_2) #8: #app'(app'❆3_filter2(_1,_2,_3),_4) ->? #app'❆4_filter2(_1,_2,_3,_4) #9: #app'❆3_if_low(false(),n,app'❆2_add(m,x)) -> #app'❆2_low(n,x) #10: #app'❆2_app(app'❆2_add(n,x),y) -> #app'❆2_app(x,y) #11: #app'❆2_low(n,app'❆2_add(m,x)) -> #app'❆3_if_low(app'❆2_le(m,n),n,app'❆2_add(m,x)) #12: #app'❆2_low(n,app'❆2_add(m,x)) -> #app'❆2_le(m,n) #13: #app'❆4_filter2(true(),f,x,xs) -> #app'❆2_filter(f,xs) #14: #app'❆2_filter(f,app'❆2_add(x,xs)) -> #app'❆4_filter2(app'(f,x),f,x,xs) #15: #app'❆2_filter(f,app'❆2_add(x,xs)) -> #app'(f,x) #16: #app'❆3_if_low(true(),n,app'❆2_add(m,x)) -> #app'❆2_low(n,x) #17: #app'(app'❆1_high(_1),_2) ->? #app'❆2_high(_1,_2) #18: #app'❆4_filter2(false(),f,x,xs) -> #app'❆2_filter(f,xs) #19: #app'❆2_le(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_le(x,y) #20: #app'(app'❆2_if_low(_1,_2),_3) ->? #app'❆3_if_low(_1,_2,_3) #21: #app'(quicksort(),_1) ->? #app'❆1_quicksort(_1) #22: #app'(app'❆1_le(_1),_2) ->? #app'❆2_le(_1,_2) #23: #app'❆3_if_high(false(),n,app'❆2_add(m,x)) -> #app'❆2_high(n,x) #24: #app'❆1_quicksort(app'❆2_add(n,x)) -> #app'❆2_app(app'❆1_quicksort(app'❆2_low(n,x)),app'❆2_add(n,app'❆1_quicksort(app'❆2_high(n,x)))) #25: #app'❆1_quicksort(app'❆2_add(n,x)) -> #app'❆1_quicksort(app'❆2_low(n,x)) #26: #app'❆1_quicksort(app'❆2_add(n,x)) -> #app'❆2_low(n,x) #27: #app'❆1_quicksort(app'❆2_add(n,x)) -> #app'❆1_quicksort(app'❆2_high(n,x)) #28: #app'❆1_quicksort(app'❆2_add(n,x)) -> #app'❆2_high(n,x) #29: #app'(app'❆1_filter(_1),_2) ->? #app'❆2_filter(_1,_2) #30: #app'❆2_map(f,app'❆2_add(x,xs)) -> #app'(f,x) #31: #app'❆2_map(f,app'❆2_add(x,xs)) -> #app'❆2_map(f,xs) #32: #app'❆3_if_high(true(),n,app'❆2_add(m,x)) -> #app'❆2_high(n,x) #33: #app'❆2_high(n,app'❆2_add(m,x)) -> #app'❆3_if_high(app'❆2_le(m,n),n,app'❆2_add(m,x)) #34: #app'❆2_high(n,app'❆2_add(m,x)) -> #app'❆2_le(m,n) #35: #app'❆2_quot(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_quot(app'❆2_minus(x,y),app'❆1_s(y)) #36: #app'❆2_quot(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_minus(x,y) Number of SCCs: 8, DPs: 21, edges: 36 SCC { #19 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: 0 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: 0 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: x2 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: 0 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: 0 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: 0 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: 0 app'❆1_s(x1) weight: (/ 1 2) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #19 Number of SCCs: 7, DPs: 20, edges: 35 SCC { #1 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: 0 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: 0 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: x2 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: 0 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: 0 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: 0 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: 0 app'❆1_s(x1) weight: (/ 1 2) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #1 Number of SCCs: 6, DPs: 19, edges: 34 SCC { #10 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: 0 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: 0 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: x1 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: 0 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: 0 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: 0 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x2 app'❆1_s(x1) weight: (/ 1 2) app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #10 Number of SCCs: 5, DPs: 18, edges: 33 SCC { #35 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: 0 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: (/ 1 4) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: 0 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: 0 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: x1 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: 0 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 4) app'❆1_s(x1) weight: (/ 1 2) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: 0 app() weight: 0 Usable rules: { 1 2 } Removed DPs: #35 Number of SCCs: 4, DPs: 17, edges: 32 SCC { #25 #27 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: (/ 1 4) + x3 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: (/ 1 4) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: (/ 1 4) + x2 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: (/ 1 4) app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: (/ 1 4) + x3 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: x1 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: 0 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: x1 app() weight: 0 Usable rules: { 10..17 } Removed DPs: #25 #27 Number of SCCs: 3, DPs: 15, edges: 28 SCC { #9 #11 #16 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: 0 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: (/ 1 4) + x3 #app'❆3_if_low(x1,x2,x3) weight: x2 + x3 app'❆2_minus(x1,x2) weight: (/ 1 4) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: (/ 1 4) + x2 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: (/ 1 4) app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: (/ 1 4) + x3 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: x1 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: (/ 1 4) + x1 + x2 filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: x1 app() weight: 0 Usable rules: { 5..7 } Removed DPs: #9 #11 #16 Number of SCCs: 2, DPs: 12, edges: 24 SCC { #23 #32 #33 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 app'❆1_quicksort(x1) weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 minus() weight: 0 #app'❆2_high(x1,x2) weight: (/ 1 4) + x2 if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: (/ 1 4) + x3 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: (/ 1 4) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 app'❆2_high(x1,x2) weight: (/ 1 4) + x2 #app'(x1,x2) weight: 0 false() weight: 0 app'❆1_if_high(x1) weight: 0 app'❆2_low(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_low(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 #app'❆3_if_high(x1,x2,x3) weight: x3 app'❆1_quot(x1) weight: 0 app'❆1_add(x1) weight: 0 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: (/ 1 4) app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: 0 nil() weight: 0 app'❆1_low(x1) weight: 0 #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 app'❆3_if_high(x1,x2,x3) weight: (/ 1 4) + x3 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 app'❆1_minus(x1) weight: 0 app'❆2_filter2(x1,x2) weight: 0 #app'❆2_quot(x1,x2) weight: x1 app'❆2_if_low(x1,x2) weight: 0 add() weight: 0 app'❆2_quot(x1,x2) weight: 0 #app'❆2_low(x1,x2) weight: (/ 1 4) filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: 0 #app'❆1_quicksort(x1) weight: x1 app() weight: 0 Usable rules: { } Removed DPs: #23 #32 #33 Number of SCCs: 1, DPs: 9, edges: 20 SCC { #4 #8 #13..15 #18 #29..31 } Removing DPs: Order(PosReal,>,Sum)... succeeded. app'❆2_filter(x1,x2) weight: (/ 1 4) + x2 app'❆4_filter2(x1,x2,x3,x4) weight: (/ 1 2) + x3 + x4 le() weight: 0 app'❆1_quicksort(x1) weight: (/ 1 4) + x1 app'❆1_filter2(x1) weight: (/ 1 4) s() weight: 0 app'❆1_map(x1) weight: (/ 1 4) + x1 #app'❆2_map(x1,x2) weight: x1 + x2 #app'❆2_filter(x1,x2) weight: x1 + x2 minus() weight: 0 #app'❆2_high(x1,x2) weight: (/ 1 8) if_high() weight: 0 app'❆3_if_low(x1,x2,x3) weight: (/ 1 4) + x1 + x3 #app'❆3_if_low(x1,x2,x3) weight: 0 app'❆2_minus(x1,x2) weight: (/ 1 4) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: (/ 1 8) + x2 + x3 + x4 app'❆2_high(x1,x2) weight: (/ 1 4) + x2 #app'(x1,x2) weight: x1 + x2 false() weight: 0 app'❆1_if_high(x1) weight: (/ 1 4) + x1 app'❆2_low(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_low(x1) weight: (/ 1 4) + x1 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: (/ 1 4) + x2 #app'❆3_if_high(x1,x2,x3) weight: 0 app'❆1_quot(x1) weight: (/ 1 4) + x1 app'❆1_add(x1) weight: (/ 1 4) + x1 quicksort() weight: 0 true() weight: 0 app'❆1_le(x1) weight: (/ 1 4) + x1 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: (/ 1 8) app'❆2_map(x1,x2) weight: (/ 1 4) quot() weight: 0 high() weight: 0 app'❆2_if_high(x1,x2) weight: (/ 1 4) + x1 + x2 nil() weight: 0 app'❆1_low(x1) weight: (/ 1 4) #app'❆2_minus(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: (/ 1 4) + x1 app'❆3_if_high(x1,x2,x3) weight: (/ 1 4) + x1 + x3 low() weight: 0 app'❆3_filter2(x1,x2,x3) weight: (/ 1 4) + x2 + x3 app'❆1_minus(x1) weight: (/ 1 4) + x1 app'❆2_filter2(x1,x2) weight: (/ 1 4) + x1 + x2 #app'❆2_quot(x1,x2) weight: x1 app'❆2_if_low(x1,x2) weight: (/ 1 4) + x1 add() weight: 0 app'❆2_quot(x1,x2) weight: (/ 1 4) + x2 #app'❆2_low(x1,x2) weight: (/ 1 8) filter() weight: 0 if_low() weight: 0 app'❆1_high(x1) weight: (/ 1 4) + x1 app'❆2_add(x1,x2) weight: (/ 1 4) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: (/ 1 4) + x1 #app'❆1_quicksort(x1) weight: x1 app() weight: 0 Usable rules: { 1..3 5..7 10..17 22..25 } Removed DPs: #4 #8 #13..15 #18 #29..31 Number of SCCs: 0, DPs: 0, edges: 0 YES