/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: app(f(),0()) -> true() 2: app(f(),1()) -> false() 3: app(f(),app(s(),x)) -> app(f(),x) 4: app(app(app(if(),true()),app(s(),x)),app(s(),y)) -> app(s(),x) 5: app(app(app(if(),false()),app(s(),x)),app(s(),y)) -> app(s(),y) 6: app(app(g(),x),app(c(),y)) -> app(c(),app(app(g(),x),y)) 7: app(app(g(),x),app(c(),y)) -> app(app(g(),x),app(app(app(if(),app(f(),x)),app(c(),app(app(g(),app(s(),x)),y))),app(c(),y))) 8: app(app(map(),fun),nil()) -> nil() 9: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs)) 10: app(app(filter(),fun),nil()) -> nil() 11: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs) 12: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs)) 13: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs) Number of strict rules: 13 Direct POLO(bPol) ... failed. Uncurrying app 1: app^1_f(0()) -> true() 2: app^1_f(1()) -> false() 3: app^1_f(app^1_s(x)) -> app^1_f(x) 4: app^3_if(true(),app^1_s(x),app^1_s(y)) -> app^1_s(x) 5: app^3_if(false(),app^1_s(x),app^1_s(y)) -> app^1_s(y) 6: app^2_g(x,app^1_c(y)) -> app^1_c(app^2_g(x,y)) 7: app^2_g(x,app^1_c(y)) -> app^2_g(x,app^3_if(app^1_f(x),app^1_c(app^2_g(app^1_s(x),y)),app^1_c(y))) 8: app^2_map(fun,nil()) -> nil() 9: app^2_map(fun,app^2_cons(x,xs)) -> app^2_cons(app(fun,x),app^2_map(fun,xs)) 10: app^2_filter(fun,nil()) -> nil() 11: app^2_filter(fun,app^2_cons(x,xs)) -> app^4_filter2(app(fun,x),fun,x,xs) 12: app^4_filter2(true(),fun,x,xs) -> app^2_cons(x,app^2_filter(fun,xs)) 13: app^4_filter2(false(),fun,x,xs) -> app^2_filter(fun,xs) 14: app(if(),_1) ->= app^1_if(_1) 15: app(app^1_if(_1),_2) ->= app^2_if(_1,_2) 16: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3) 17: app(cons(),_1) ->= app^1_cons(_1) 18: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 19: app(s(),_1) ->= app^1_s(_1) 20: app(filter(),_1) ->= app^1_filter(_1) 21: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 22: app(c(),_1) ->= app^1_c(_1) 23: app(map(),_1) ->= app^1_map(_1) 24: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 25: app(g(),_1) ->= app^1_g(_1) 26: app(app^1_g(_1),_2) ->= app^2_g(_1,_2) 27: app(f(),_1) ->= app^1_f(_1) 28: app(filter2(),_1) ->= app^1_filter2(_1) 29: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 30: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 31: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) Number of strict rules: 13 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app^2_g(x,app^1_c(y)) -> #app^2_g(x,y) #2: #app^4_filter2(false(),fun,x,xs) -> #app^2_filter(fun,xs) #3: #app^2_map(fun,app^2_cons(x,xs)) -> #app(fun,x) #4: #app^2_map(fun,app^2_cons(x,xs)) -> #app^2_map(fun,xs) #5: #app^2_filter(fun,app^2_cons(x,xs)) -> #app^4_filter2(app(fun,x),fun,x,xs) #6: #app^2_filter(fun,app^2_cons(x,xs)) -> #app(fun,x) #7: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #8: #app^4_filter2(true(),fun,x,xs) -> #app^2_filter(fun,xs) #9: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #10: #app^2_g(x,app^1_c(y)) -> #app^2_g(x,app^3_if(app^1_f(x),app^1_c(app^2_g(app^1_s(x),y)),app^1_c(y))) #11: #app^2_g(x,app^1_c(y)) -> #app^3_if(app^1_f(x),app^1_c(app^2_g(app^1_s(x),y)),app^1_c(y)) #12: #app^2_g(x,app^1_c(y)) -> #app^1_f(x) #13: #app^2_g(x,app^1_c(y)) -> #app^2_g(app^1_s(x),y) #14: #app(f(),_1) ->? #app^1_f(_1) #15: #app(app^1_g(_1),_2) ->? #app^2_g(_1,_2) #16: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #17: #app(app^2_if(_1,_2),_3) ->? #app^3_if(_1,_2,_3) #18: #app^1_f(app^1_s(x)) -> #app^1_f(x) Number of SCCs: 3, DPs: 12 SCC { #18 } POLO(Sum)... succeeded. #app^3_if w: 0 1 w: 0 s w: 0 app^1_cons w: 0 #app^2_map w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 #app^2_g w: 0 c w: 0 #app^1_f w: x1 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 0 if w: 0 #app^4_filter2 w: 0 nil w: 0 #app w: 0 map w: 0 app^1_filter w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 app^1_c w: 0 app^3_filter2 w: 0 app^2_filter w: 0 g w: 0 app^2_g w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app w: 0 app^1_g w: 0 USABLE RULES: { } Removed DPs: #18 Number of SCCs: 2, DPs: 11 SCC { #1 #13 } POLO(Sum)... succeeded. #app^3_if w: 0 1 w: 0 s w: 0 app^1_cons w: 0 #app^2_map w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 #app^2_g w: x2 c w: 0 #app^1_f w: 0 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 0 if w: 0 #app^4_filter2 w: 0 nil w: 0 #app w: 0 map w: 0 app^1_filter w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 app^1_c w: x1 + 1 app^3_filter2 w: 0 app^2_filter w: 0 g w: 0 app^2_g w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_s w: 1 app^2_map w: 0 #app^2_filter w: 0 app w: 0 app^1_g w: 0 USABLE RULES: { } Removed DPs: #1 #13 Number of SCCs: 1, DPs: 9 SCC { #2..9 #16 } POLO(Sum)... succeeded. #app^3_if w: 0 1 w: 1 s w: 1 app^1_cons w: 1 #app^2_map w: x1 + x2 app^2_filter2 w: 1 app^4_filter2 w: x1 + 4 false w: 4 #app^2_g w: 0 c w: 1 #app^1_f w: 0 app^1_filter2 w: x1 + 2 true w: 4 f w: 1 filter2 w: 1 0 w: 1 if w: 1 #app^4_filter2 w: x2 + x3 + x4 + 1 nil w: 6 #app w: x1 + x2 map w: 1 app^1_filter w: x1 + 2 cons w: 1 app^2_if w: x1 + 2 app^3_if w: x1 + x2 + 2 app^1_f w: x1 + 2 filter w: 1 app^1_c w: x1 + 2 app^3_filter2 w: x1 + x2 + x3 + 2 app^2_filter w: 5 g w: 1 app^2_g w: x1 + 2 app^1_map w: x1 + 2 app^2_cons w: x1 + x2 + 4 app^1_if w: x1 + 2 app^1_s w: 1 app^2_map w: x2 + 2 #app^2_filter w: x1 + x2 app w: 1 app^1_g w: 1 USABLE RULES: { } Removed DPs: #2..9 #16 Number of SCCs: 0, DPs: 0