Input TRS: 1: app'(app'(eq(),0()),0()) -> true() 2: app'(app'(eq(),0()),app'(s(),x)) -> false() 3: app'(app'(eq(),app'(s(),x)),0()) -> false() 4: app'(app'(eq(),app'(s(),x)),app'(s(),y)) -> app'(app'(eq(),x),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'(min(),app'(app'(add(),n),nil())) -> n 11: app'(min(),app'(app'(add(),n),app'(app'(add(),m),x))) -> app'(app'(if_min(),app'(app'(le(),n),m)),app'(app'(add(),n),app'(app'(add(),m),x))) 12: app'(app'(if_min(),true()),app'(app'(add(),n),app'(app'(add(),m),x))) -> app'(min(),app'(app'(add(),n),x)) 13: app'(app'(if_min(),false()),app'(app'(add(),n),app'(app'(add(),m),x))) -> app'(min(),app'(app'(add(),m),x)) 14: app'(app'(rm(),n),nil()) -> nil() 15: app'(app'(rm(),n),app'(app'(add(),m),x)) -> app'(app'(app'(if_rm(),app'(app'(eq(),n),m)),n),app'(app'(add(),m),x)) 16: app'(app'(app'(if_rm(),true()),n),app'(app'(add(),m),x)) -> app'(app'(rm(),n),x) 17: app'(app'(app'(if_rm(),false()),n),app'(app'(add(),m),x)) -> app'(app'(add(),m),app'(app'(rm(),n),x)) 18: app'(app'(minsort(),nil()),nil()) -> nil() 19: app'(app'(minsort(),app'(app'(add(),n),x)),y) -> app'(app'(app'(if_minsort(),app'(app'(eq(),n),app'(min(),app'(app'(add(),n),x)))),app'(app'(add(),n),x)),y) 20: app'(app'(app'(if_minsort(),true()),app'(app'(add(),n),x)),y) -> app'(app'(add(),n),app'(app'(minsort(),app'(app'(app(),app'(app'(rm(),n),x)),y)),nil())) 21: app'(app'(app'(if_minsort(),false()),app'(app'(add(),n),x)),y) -> app'(app'(minsort(),x),app'(app'(add(),n),y)) 22: app'(app'(map(),f),nil()) -> nil() 23: app'(app'(map(),f),app'(app'(add(),x),xs)) -> app'(app'(add(),app'(f,x)),app'(app'(map(),f),xs)) 24: app'(app'(filter(),f),nil()) -> nil() 25: app'(app'(filter(),f),app'(app'(add(),x),xs)) -> app'(app'(app'(app'(filter2(),app'(f,x)),f),x),xs) 26: app'(app'(app'(app'(filter2(),true()),f),x),xs) -> app'(app'(add(),x),app'(app'(filter(),f),xs)) 27: app'(app'(app'(app'(filter2(),false()),f),x),xs) -> app'(app'(filter(),f),xs) Number of strict rules: 27 Direct Order(PosReal,>,Poly) ... failed. Freezing app'❆1_min app' 1: app'❆2_eq(0(),0()) -> true() 2: app'❆2_eq(0(),app'❆1_s(x)) -> false() 3: app'❆2_eq(app'❆1_s(x),0()) -> false() 4: app'❆2_eq(app'❆1_s(x),app'❆1_s(y)) -> app'❆2_eq(x,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'❆1_min❆1_app'❆2_add(n,nil()) -> n 11: app'❆1_min❆1_app'❆2_add(n,app'❆2_add(m,x)) -> app'❆2_if_min(app'❆2_le(n,m),app'❆2_add(n,app'❆2_add(m,x))) 12: app'❆2_if_min(true(),app'❆2_add(n,app'❆2_add(m,x))) -> app'❆1_min❆1_app'❆2_add(n,x) 13: app'❆2_if_min(false(),app'❆2_add(n,app'❆2_add(m,x))) -> app'❆1_min❆1_app'❆2_add(m,x) 14: app'❆2_rm(n,nil()) -> nil() 15: app'❆2_rm(n,app'❆2_add(m,x)) -> app'❆3_if_rm(app'❆2_eq(n,m),n,app'❆2_add(m,x)) 16: app'❆3_if_rm(true(),n,app'❆2_add(m,x)) -> app'❆2_rm(n,x) 17: app'❆3_if_rm(false(),n,app'❆2_add(m,x)) -> app'❆2_add(m,app'❆2_rm(n,x)) 18: app'❆2_minsort(nil(),nil()) -> nil() 19: app'❆2_minsort(app'❆2_add(n,x),y) -> app'❆3_if_minsort(app'❆2_eq(n,app'❆1_min❆1_app'❆2_add(n,x)),app'❆2_add(n,x),y) 20: app'❆3_if_minsort(true(),app'❆2_add(n,x),y) -> app'❆2_add(n,app'❆2_minsort(app'❆2_app(app'❆2_rm(n,x),y),nil())) 21: app'❆3_if_minsort(false(),app'❆2_add(n,x),y) -> app'❆2_minsort(x,app'❆2_add(n,y)) 22: app'❆2_map(f,nil()) -> nil() 23: app'❆2_map(f,app'❆2_add(x,xs)) -> app'❆2_add(app'(f,x),app'❆2_map(f,xs)) 24: app'❆2_filter(f,nil()) -> nil() 25: app'❆2_filter(f,app'❆2_add(x,xs)) -> app'❆4_filter2(app'(f,x),f,x,xs) 26: app'❆4_filter2(true(),f,x,xs) -> app'❆2_add(x,app'❆2_filter(f,xs)) 27: app'❆4_filter2(false(),f,x,xs) -> app'❆2_filter(f,xs) 28: app'(eq(),_1) ->= app'❆1_eq(_1) 29: app'(app'❆1_eq(_1),_2) ->= app'❆2_eq(_1,_2) 30: app'(min(),_1) ->= app'❆1_min(_1) 31: app'(le(),_1) ->= app'❆1_le(_1) 32: app'(app'❆1_le(_1),_2) ->= app'❆2_le(_1,_2) 33: app'(if_rm(),_1) ->= app'❆1_if_rm(_1) 34: app'(app'❆1_if_rm(_1),_2) ->= app'❆2_if_rm(_1,_2) 35: app'(app'❆2_if_rm(_1,_2),_3) ->= app'❆3_if_rm(_1,_2,_3) 36: app'(add(),_1) ->= app'❆1_add(_1) 37: app'(app'❆1_add(_1),_2) ->= app'❆2_add(_1,_2) 38: app'(if_min(),_1) ->= app'❆1_if_min(_1) 39: app'(app'❆1_if_min(_1),_2) ->= app'❆2_if_min(_1,_2) 40: app'(s(),_1) ->= app'❆1_s(_1) 41: app'(if_minsort(),_1) ->= app'❆1_if_minsort(_1) 42: app'(app'❆1_if_minsort(_1),_2) ->= app'❆2_if_minsort(_1,_2) 43: app'(app'❆2_if_minsort(_1,_2),_3) ->= app'❆3_if_minsort(_1,_2,_3) 44: app'(filter(),_1) ->= app'❆1_filter(_1) 45: app'(app'❆1_filter(_1),_2) ->= app'❆2_filter(_1,_2) 46: app'(minsort(),_1) ->= app'❆1_minsort(_1) 47: app'(app'❆1_minsort(_1),_2) ->= app'❆2_minsort(_1,_2) 48: app'(map(),_1) ->= app'❆1_map(_1) 49: app'(app'❆1_map(_1),_2) ->= app'❆2_map(_1,_2) 50: app'(filter2(),_1) ->= app'❆1_filter2(_1) 51: app'(app'❆1_filter2(_1),_2) ->= app'❆2_filter2(_1,_2) 52: app'(app'❆2_filter2(_1,_2),_3) ->= app'❆3_filter2(_1,_2,_3) 53: app'(app'❆3_filter2(_1,_2,_3),_4) ->= app'❆4_filter2(_1,_2,_3,_4) 54: app'(rm(),_1) ->= app'❆1_rm(_1) 55: app'(app'❆1_rm(_1),_2) ->= app'❆2_rm(_1,_2) 56: app'(app(),_1) ->= app'❆1_app(_1) 57: app'(app'❆1_app(_1),_2) ->= app'❆2_app(_1,_2) 58: app'❆1_min(app'❆2_add(_1,_2)) ->= app'❆1_min❆1_app'❆2_add(_1,_2) Number of strict rules: 27 Direct Order(PosReal,>,Poly) ... failed. Dependency Pairs: #1: #app'(app'❆2_if_minsort(_1,_2),_3) ->? #app'❆3_if_minsort(_1,_2,_3) #2: #app'(app'❆1_eq(_1),_2) ->? #app'❆2_eq(_1,_2) #3: #app'(app'❆2_if_rm(_1,_2),_3) ->? #app'❆3_if_rm(_1,_2,_3) #4: #app'(app'❆1_minsort(_1),_2) ->? #app'❆2_minsort(_1,_2) #5: #app'(app'❆3_filter2(_1,_2,_3),_4) ->? #app'❆4_filter2(_1,_2,_3,_4) #6: #app'❆1_min(app'❆2_add(_1,_2)) ->? #app'❆1_min❆1_app'❆2_add(_1,_2) #7: #app'(app'❆1_rm(_1),_2) ->? #app'❆2_rm(_1,_2) #8: #app'❆2_if_min(false(),app'❆2_add(n,app'❆2_add(m,x))) -> #app'❆1_min❆1_app'❆2_add(m,x) #9: #app'❆2_app(app'❆2_add(n,x),y) -> #app'❆2_app(x,y) #10: #app'❆1_min❆1_app'❆2_add(n,app'❆2_add(m,x)) -> #app'❆2_if_min(app'❆2_le(n,m),app'❆2_add(n,app'❆2_add(m,x))) #11: #app'❆1_min❆1_app'❆2_add(n,app'❆2_add(m,x)) -> #app'❆2_le(n,m) #12: #app'(app'❆1_app(_1),_2) ->? #app'❆2_app(_1,_2) #13: #app'❆2_map(f,app'❆2_add(x,xs)) -> #app'(f,x) #14: #app'❆2_map(f,app'❆2_add(x,xs)) -> #app'❆2_map(f,xs) #15: #app'(app'❆1_filter(_1),_2) ->? #app'❆2_filter(_1,_2) #16: #app'❆2_if_min(true(),app'❆2_add(n,app'❆2_add(m,x))) -> #app'❆1_min❆1_app'❆2_add(n,x) #17: #app'(min(),_1) ->? #app'❆1_min(_1) #18: #app'(app'❆1_map(_1),_2) ->? #app'❆2_map(_1,_2) #19: #app'❆2_filter(f,app'❆2_add(x,xs)) -> #app'❆4_filter2(app'(f,x),f,x,xs) #20: #app'❆2_filter(f,app'❆2_add(x,xs)) -> #app'(f,x) #21: #app'❆3_if_minsort(true(),app'❆2_add(n,x),y) -> #app'❆2_minsort(app'❆2_app(app'❆2_rm(n,x),y),nil()) #22: #app'❆3_if_minsort(true(),app'❆2_add(n,x),y) -> #app'❆2_app(app'❆2_rm(n,x),y) #23: #app'❆3_if_minsort(true(),app'❆2_add(n,x),y) -> #app'❆2_rm(n,x) #24: #app'❆2_le(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_le(x,y) #25: #app'(app'❆1_if_min(_1),_2) ->? #app'❆2_if_min(_1,_2) #26: #app'❆4_filter2(false(),f,x,xs) -> #app'❆2_filter(f,xs) #27: #app'❆3_if_rm(false(),n,app'❆2_add(m,x)) -> #app'❆2_rm(n,x) #28: #app'(app'❆1_le(_1),_2) ->? #app'❆2_le(_1,_2) #29: #app'❆2_minsort(app'❆2_add(n,x),y) -> #app'❆3_if_minsort(app'❆2_eq(n,app'❆1_min❆1_app'❆2_add(n,x)),app'❆2_add(n,x),y) #30: #app'❆2_minsort(app'❆2_add(n,x),y) -> #app'❆2_eq(n,app'❆1_min❆1_app'❆2_add(n,x)) #31: #app'❆2_minsort(app'❆2_add(n,x),y) -> #app'❆1_min❆1_app'❆2_add(n,x) #32: #app'❆4_filter2(true(),f,x,xs) -> #app'❆2_filter(f,xs) #33: #app'❆3_if_minsort(false(),app'❆2_add(n,x),y) -> #app'❆2_minsort(x,app'❆2_add(n,y)) #34: #app'❆3_if_rm(true(),n,app'❆2_add(m,x)) -> #app'❆2_rm(n,x) #35: #app'❆2_rm(n,app'❆2_add(m,x)) -> #app'❆3_if_rm(app'❆2_eq(n,m),n,app'❆2_add(m,x)) #36: #app'❆2_rm(n,app'❆2_add(m,x)) -> #app'❆2_eq(n,m) #37: #app'❆2_eq(app'❆1_s(x),app'❆1_s(y)) -> #app'❆2_eq(x,y) Number of SCCs: 7, DPs: 21, edges: 35 SCC { #24 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: 0 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: 0 #app'❆2_minsort(x1,x2) weight: 0 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: x2 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 nil() weight: 0 app'❆2_eq(x1,x2) weight: 0 #app'❆2_rm(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: 0 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆2_add(x1,x2) weight: 0 app'❆1_s(x1) weight: (/ 1 2) + x1 app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #24 Number of SCCs: 6, DPs: 20, edges: 34 SCC { #9 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: 0 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: 0 #app'❆2_minsort(x1,x2) weight: 0 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: x1 app'❆2_app(x1,x2) weight: 0 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 nil() weight: 0 app'❆2_eq(x1,x2) weight: 0 #app'❆2_rm(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: 0 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x2 app'❆1_s(x1) weight: (/ 1 2) app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #9 Number of SCCs: 5, DPs: 19, edges: 33 SCC { #37 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: x1 app'❆3_if_rm(x1,x2,x3) weight: 0 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: 0 #app'❆2_minsort(x1,x2) weight: 0 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 nil() weight: 0 app'❆2_eq(x1,x2) weight: 0 #app'❆2_rm(x1,x2) weight: 0 map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: 0 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) app'❆1_s(x1) weight: (/ 1 2) + x1 app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #37 Number of SCCs: 4, DPs: 18, edges: 32 SCC { #27 #34 #35 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: 0 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: 0 #app'❆2_minsort(x1,x2) weight: 0 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: x3 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: 0 app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 nil() weight: 0 app'❆2_eq(x1,x2) weight: (/ 1 4) + x1 #app'❆2_rm(x1,x2) weight: (/ 1 4) + x2 map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: 0 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 2) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #27 #34 #35 Number of SCCs: 3, DPs: 15, edges: 28 SCC { #8 #10 #16 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: 0 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: 0 #app'❆2_minsort(x1,x2) weight: 0 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: 0 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: x2 app'❆1_minsort(x1) weight: 0 0() weight: 0 app'❆2_le(x1,x2) weight: (/ 1 8) app'(x1,x2) weight: 0 app'❆2_map(x1,x2) weight: 0 nil() weight: 0 app'❆2_eq(x1,x2) weight: (/ 1 8) + x1 #app'❆2_rm(x1,x2) weight: (/ 1 8) map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 3 8) + x2 app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: 0 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: 0 app'❆2_add(x1,x2) weight: (/ 1 4) + x2 app'❆1_s(x1) weight: (/ 1 8) app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #8 #10 #16 Number of SCCs: 2, DPs: 12, edges: 24 SCC { #21 #29 #33 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: x2 + x3 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: (/ 1 4) + x3 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: x2 #app'❆2_minsort(x1,x2) weight: x1 + x2 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: (/ 1 4) + x1 + x2 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) 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 nil() weight: 0 app'❆2_eq(x1,x2) weight: (/ 1 4) + x1 #app'❆2_rm(x1,x2) weight: (/ 1 4) map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 3 4) app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 5 4) app'❆2_add(x1,x2) weight: (/ 3 4) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { 8 9 14..17 } Removed DPs: #21 Number of SCCs: 2, DPs: 11, edges: 22 SCC { #29 #33 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: x2 app'❆2_filter(x1,x2) weight: 0 app'❆4_filter2(x1,x2,x3,x4) weight: 0 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: (/ 1 4) + x3 if_rm() weight: 0 app'❆1_filter2(x1) weight: 0 s() weight: 0 app'❆1_map(x1) weight: 0 app'❆1_min(x1) weight: 0 #app'❆2_map(x1,x2) weight: 0 #app'❆2_filter(x1,x2) weight: 0 app'❆2_if_min(x1,x2) weight: x2 #app'❆2_minsort(x1,x2) weight: (/ 1 4) + x1 app'❆1_if_minsort(x1) weight: 0 eq() weight: 0 app'❆2_if_rm(x1,x2) weight: 0 app'❆2_if_minsort(x1,x2) weight: 0 #app'❆4_filter2(x1,x2,x3,x4) weight: 0 #app'(x1,x2) weight: 0 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: 0 #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: (/ 1 4) + x1 + x2 app'❆1_if_rm(x1) weight: 0 #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: 0 app'❆1_eq(x1) weight: 0 true() weight: 0 app'❆1_le(x1) weight: 0 filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) 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 nil() weight: 0 app'❆2_eq(x1,x2) weight: (/ 1 4) + x1 #app'❆2_rm(x1,x2) weight: (/ 1 4) map() weight: 0 app'❆1_app(x1) weight: 0 #app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 3 4) app'❆3_filter2(x1,x2,x3) weight: 0 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_minsort(x1,x2) weight: 0 app'❆2_filter2(x1,x2) weight: 0 add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: (/ 1 4) + x2 app'❆1_if_min(x1) weight: 0 app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 1 4) app'❆2_add(x1,x2) weight: (/ 3 4) + x1 + x2 app'❆1_s(x1) weight: (/ 1 4) + x1 app'❆1_filter(x1) weight: 0 rm() weight: 0 app() weight: 0 Usable rules: { } Removed DPs: #29 #33 Number of SCCs: 1, DPs: 9, edges: 20 SCC { #5 #13..15 #18..20 #26 #32 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #app'❆3_if_minsort(x1,x2,x3) weight: 0 app'❆2_filter(x1,x2) weight: (/ 1 2) + x1 app'❆4_filter2(x1,x2,x3,x4) weight: (/ 3 8) + x1 + x3 + x4 le() weight: 0 #app'❆2_eq(x1,x2) weight: 0 app'❆3_if_rm(x1,x2,x3) weight: (/ 3 8) + x3 if_rm() weight: 0 app'❆1_filter2(x1) weight: (/ 3 8) s() weight: 0 app'❆1_map(x1) weight: (/ 3 8) app'❆1_min(x1) weight: (/ 3 8) #app'❆2_map(x1,x2) weight: x2 #app'❆2_filter(x1,x2) weight: x2 app'❆2_if_min(x1,x2) weight: (/ 3 8) + x2 #app'❆2_minsort(x1,x2) weight: (/ 1 8) + x1 app'❆1_if_minsort(x1) weight: (/ 3 8) eq() weight: 0 app'❆2_if_rm(x1,x2) weight: (/ 3 8) + x1 app'❆2_if_minsort(x1,x2) weight: (/ 3 8) + x1 #app'❆4_filter2(x1,x2,x3,x4) weight: (/ 1 8) + x4 #app'(x1,x2) weight: (/ 1 4) + x2 false() weight: 0 #app'❆1_min(x1) weight: 0 app'❆1_rm(x1) weight: (/ 3 8) #app'❆2_app(x1,x2) weight: 0 app'❆2_app(x1,x2) weight: (/ 3 8) + x1 + x2 app'❆1_if_rm(x1) weight: (/ 3 8) #app'❆3_if_rm(x1,x2,x3) weight: 0 app'❆1_add(x1) weight: (/ 3 8) app'❆1_eq(x1) weight: (/ 3 8) true() weight: 0 app'❆1_le(x1) weight: (/ 3 8) filter2() weight: 0 #app'❆2_le(x1,x2) weight: 0 #app'❆2_if_min(x1,x2) weight: 0 app'❆1_minsort(x1) weight: (/ 3 8) 0() weight: 0 app'❆2_le(x1,x2) weight: (/ 3 8) app'(x1,x2) weight: (/ 1 4) + x2 app'❆2_map(x1,x2) weight: (/ 3 8) + x1 nil() weight: 0 app'❆2_eq(x1,x2) weight: (/ 3 8) + x1 #app'❆2_rm(x1,x2) weight: (/ 1 8) map() weight: 0 app'❆1_app(x1) weight: (/ 3 8) #app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 3 8) app'❆3_filter2(x1,x2,x3) weight: (/ 3 8) + x1 min() weight: 0 app'❆3_if_minsort(x1,x2,x3) weight: (/ 3 8) + x2 + x3 app'❆2_minsort(x1,x2) weight: (/ 5 8) app'❆2_filter2(x1,x2) weight: (/ 3 8) add() weight: 0 if_min() weight: 0 if_minsort() weight: 0 filter() weight: 0 minsort() weight: 0 app'❆2_rm(x1,x2) weight: (/ 3 8) + x2 app'❆1_if_min(x1) weight: (/ 3 8) app'❆1_min❆1_app'❆2_add(x1,x2) weight: (/ 1 2) app'❆2_add(x1,x2) weight: (/ 3 8) + x1 + x2 app'❆1_s(x1) weight: (/ 3 8) + x1 app'❆1_filter(x1) weight: (/ 3 8) rm() weight: 0 app() weight: 0 Usable rules: { 8 9 14..17 } Removed DPs: #5 #13..15 #18..20 #26 #32 Number of SCCs: 1, DPs: 0, edges: 0 YES