/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(app(ack(),0()),y) -> app(succ(),y) 2: app(app(ack(),app(succ(),x)),y) -> app(app(ack(),x),app(succ(),0())) 3: app(app(ack(),app(succ(),x)),app(succ(),y)) -> app(app(ack(),x),app(app(ack(),app(succ(),x)),y)) 4: app(app(map(),f),nil()) -> nil() 5: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 6: app(app(filter(),f),nil()) -> nil() 7: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) 8: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) 9: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Number of strict rules: 9 Direct POLO(bPol) ... failed. Uncurrying app 1: app^2_ack(0(),y) -> app^1_succ(y) 2: app^2_ack(app^1_succ(x),y) -> app^2_ack(x,app^1_succ(0())) 3: app^2_ack(app^1_succ(x),app^1_succ(y)) -> app^2_ack(x,app^2_ack(app^1_succ(x),y)) 4: app^2_map(f,nil()) -> nil() 5: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 6: app^2_filter(f,nil()) -> nil() 7: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs) 8: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs)) 9: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs) 10: app(cons(),_1) ->= app^1_cons(_1) 11: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 12: app(succ(),_1) ->= app^1_succ(_1) 13: app(filter(),_1) ->= app^1_filter(_1) 14: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 15: app(map(),_1) ->= app^1_map(_1) 16: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 17: app(ack(),_1) ->= app^1_ack(_1) 18: app(app^1_ack(_1),_2) ->= app^2_ack(_1,_2) 19: app(filter2(),_1) ->= app^1_filter2(_1) 20: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 21: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 22: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) Number of strict rules: 9 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app^2_ack(app^1_succ(x),y) -> #app^2_ack(x,app^1_succ(0())) #2: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs) #3: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #4: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs) #5: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x) #6: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x) #7: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs) #8: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #9: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #10: #app^2_ack(app^1_succ(x),app^1_succ(y)) -> #app^2_ack(x,app^2_ack(app^1_succ(x),y)) #11: #app^2_ack(app^1_succ(x),app^1_succ(y)) -> #app^2_ack(app^1_succ(x),y) #12: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs) #13: #app(app^1_ack(_1),_2) ->? #app^2_ack(_1,_2) Number of SCCs: 2, DPs: 11 SCC { #1 #10 #11 } POLO(Sum)... succeeded. app^1_ack w: 0 app^1_cons w: 0 #app^2_map w: 0 ack w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 #app^2_ack w: x1 app^1_filter2 w: 0 true w: 0 filter2 w: 0 0 w: 1 #app^4_filter2 w: 0 succ w: 0 nil w: 0 app^1_succ w: x1 + 1 #app w: 0 map w: 0 app^1_filter w: 0 cons w: 0 filter w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^2_ack w: x1 + x2 + 2 app^2_map w: 0 #app^2_filter w: 0 app w: 0 USABLE RULES: { } Removed DPs: #1 #10 Number of SCCs: 2, DPs: 9 SCC { #11 } POLO(Sum)... POLO(max)... succeeded. app^1_ack w: 0 app^1_cons w: 0 #app^2_map w: 0 ack w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 #app^2_ack w: max(x2 + 1) app^1_filter2 w: 0 true w: 0 filter2 w: 0 0 w: 0 #app^4_filter2 w: 0 succ w: 0 nil w: 0 app^1_succ w: x1 + 1 #app w: 0 map w: 0 app^1_filter w: 0 cons w: 0 filter w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^2_ack w: 0 app^2_map w: 0 #app^2_filter w: 0 app w: 0 USABLE RULES: { } Removed DPs: #11 Number of SCCs: 1, DPs: 8 SCC { #2 #3 #5..9 #12 } POLO(Sum)... succeeded. app^1_ack w: 0 app^1_cons w: 0 #app^2_map w: x1 + 1 ack w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 1 #app^2_ack w: 0 app^1_filter2 w: 0 true w: 1 filter2 w: 0 0 w: 1 #app^4_filter2 w: x2 + 2 succ w: 0 nil w: 0 app^1_succ w: 1 #app w: x1 map w: 0 app^1_filter w: x1 + 2 cons w: 0 filter w: 0 app^3_filter2 w: x1 + x2 + x3 + 3 app^2_filter w: 0 app^1_map w: x1 + 2 app^2_cons w: 1 app^2_ack w: x2 + 3 app^2_map w: 0 #app^2_filter w: x1 + 1 app w: 0 USABLE RULES: { } Removed DPs: #2 #3 #5 #6 #8 #9 #12 Number of SCCs: 1, DPs: 1 SCC { #7 } POLO(Sum)... succeeded. app^1_ack w: 0 app^1_cons w: 0 #app^2_map w: x2 + 1 ack w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 1 #app^2_ack w: 0 app^1_filter2 w: 0 true w: 1 filter2 w: 0 0 w: 1 #app^4_filter2 w: 2 succ w: 0 nil w: 0 app^1_succ w: 1 #app w: 0 map w: 0 app^1_filter w: 2 cons w: 0 filter w: 0 app^3_filter2 w: 3 app^2_filter w: 0 app^1_map w: 2 app^2_cons w: x2 + 1 app^2_ack w: x2 + 3 app^2_map w: 0 #app^2_filter w: 1 app w: 0 USABLE RULES: { } Removed DPs: #7 Number of SCCs: 0, DPs: 0