/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'(minus(),x),0()) -> x 2: app'(app'(minus(),app'(s(),x)),app'(s(),y)) -> app'(app'(minus(),x),y) 3: app'(app'(minus(),app'(app'(minus(),x),y)),z) -> app'(app'(minus(),x),app'(app'(plus(),y),z)) 4: app'(app'(quot(),0()),app'(s(),y)) -> 0() 5: app'(app'(quot(),app'(s(),x)),app'(s(),y)) -> app'(s(),app'(app'(quot(),app'(app'(minus(),x),y)),app'(s(),y))) 6: app'(app'(plus(),0()),y) -> y 7: app'(app'(plus(),app'(s(),x)),y) -> app'(s(),app'(app'(plus(),x),y)) 8: app'(app'(app(),nil()),k) -> k 9: app'(app'(app(),l),nil()) -> l 10: app'(app'(app(),app'(app'(cons(),x),l)),k) -> app'(app'(cons(),x),app'(app'(app(),l),k)) 11: app'(sum(),app'(app'(cons(),x),nil())) -> app'(app'(cons(),x),nil()) 12: app'(sum(),app'(app'(cons(),x),app'(app'(cons(),y),l))) -> app'(sum(),app'(app'(cons(),app'(app'(plus(),x),y)),l)) 13: app'(sum(),app'(app'(app(),l),app'(app'(cons(),x),app'(app'(cons(),y),k)))) -> app'(sum(),app'(app'(app(),l),app'(sum(),app'(app'(cons(),x),app'(app'(cons(),y),k))))) 14: app'(app'(map(),f),nil()) -> nil() 15: app'(app'(map(),f),app'(app'(cons(),x),xs)) -> app'(app'(cons(),app'(f,x)),app'(app'(map(),f),xs)) 16: app'(app'(filter(),f),nil()) -> nil() 17: app'(app'(filter(),f),app'(app'(cons(),x),xs)) -> app'(app'(app'(app'(filter2(),app'(f,x)),f),x),xs) 18: app'(app'(app'(app'(filter2(),true()),f),x),xs) -> app'(app'(cons(),x),app'(app'(filter(),f),xs)) 19: app'(app'(app'(app'(filter2(),false()),f),x),xs) -> app'(app'(filter(),f),xs) Number of strict rules: 19 Direct POLO(bPol) ... failed. Uncurrying 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_minus(app'^2_minus(x,y),z) -> app'^2_minus(x,app'^2_plus(y,z)) 4: app'^2_quot(0(),app'^1_s(y)) -> 0() 5: 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))) 6: app'^2_plus(0(),y) -> y 7: app'^2_plus(app'^1_s(x),y) -> app'^1_s(app'^2_plus(x,y)) 8: app'^2_app(nil(),k) -> k 9: app'^2_app(l,nil()) -> l 10: app'^2_app(app'^2_cons(x,l),k) -> app'^2_cons(x,app'^2_app(l,k)) 11: app'^1_sum(app'^2_cons(x,nil())) -> app'^2_cons(x,nil()) 12: app'^1_sum(app'^2_cons(x,app'^2_cons(y,l))) -> app'^1_sum(app'^2_cons(app'^2_plus(x,y),l)) 13: app'^1_sum(app'^2_app(l,app'^2_cons(x,app'^2_cons(y,k)))) -> app'^1_sum(app'^2_app(l,app'^1_sum(app'^2_cons(x,app'^2_cons(y,k))))) 14: app'^2_map(f,nil()) -> nil() 15: app'^2_map(f,app'^2_cons(x,xs)) -> app'^2_cons(app'(f,x),app'^2_map(f,xs)) 16: app'^2_filter(f,nil()) -> nil() 17: app'^2_filter(f,app'^2_cons(x,xs)) -> app'^4_filter2(app'(f,x),f,x,xs) 18: app'^4_filter2(true(),f,x,xs) -> app'^2_cons(x,app'^2_filter(f,xs)) 19: app'^4_filter2(false(),f,x,xs) -> app'^2_filter(f,xs) 20: app'(plus(),_1) ->= app'^1_plus(_1) 21: app'(app'^1_plus(_1),_2) ->= app'^2_plus(_1,_2) 22: app'(cons(),_1) ->= app'^1_cons(_1) 23: app'(app'^1_cons(_1),_2) ->= app'^2_cons(_1,_2) 24: app'(quot(),_1) ->= app'^1_quot(_1) 25: app'(app'^1_quot(_1),_2) ->= app'^2_quot(_1,_2) 26: app'(s(),_1) ->= app'^1_s(_1) 27: app'(filter(),_1) ->= app'^1_filter(_1) 28: app'(app'^1_filter(_1),_2) ->= app'^2_filter(_1,_2) 29: app'(map(),_1) ->= app'^1_map(_1) 30: app'(app'^1_map(_1),_2) ->= app'^2_map(_1,_2) 31: app'(minus(),_1) ->= app'^1_minus(_1) 32: app'(app'^1_minus(_1),_2) ->= app'^2_minus(_1,_2) 33: app'(filter2(),_1) ->= app'^1_filter2(_1) 34: app'(app'^1_filter2(_1),_2) ->= app'^2_filter2(_1,_2) 35: app'(app'^2_filter2(_1,_2),_3) ->= app'^3_filter2(_1,_2,_3) 36: app'(app'^3_filter2(_1,_2,_3),_4) ->= app'^4_filter2(_1,_2,_3,_4) 37: app'(sum(),_1) ->= app'^1_sum(_1) 38: app'(app(),_1) ->= app'^1_app(_1) 39: app'(app'^1_app(_1),_2) ->= app'^2_app(_1,_2) Number of strict rules: 19 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app'^2_minus(app'^1_s(x),app'^1_s(y)) -> #app'^2_minus(x,y) #2: #app'(sum(),_1) ->? #app'^1_sum(_1) #3: #app'^1_sum(app'^2_app(l,app'^2_cons(x,app'^2_cons(y,k)))) -> #app'^1_sum(app'^2_app(l,app'^1_sum(app'^2_cons(x,app'^2_cons(y,k))))) #4: #app'^1_sum(app'^2_app(l,app'^2_cons(x,app'^2_cons(y,k)))) -> #app'^2_app(l,app'^1_sum(app'^2_cons(x,app'^2_cons(y,k)))) #5: #app'^1_sum(app'^2_app(l,app'^2_cons(x,app'^2_cons(y,k)))) -> #app'^1_sum(app'^2_cons(x,app'^2_cons(y,k))) #6: #app'^1_sum(app'^2_cons(x,app'^2_cons(y,l))) -> #app'^1_sum(app'^2_cons(app'^2_plus(x,y),l)) #7: #app'^1_sum(app'^2_cons(x,app'^2_cons(y,l))) -> #app'^2_plus(x,y) #8: #app'(app'^1_map(_1),_2) ->? #app'^2_map(_1,_2) #9: #app'(app'^1_quot(_1),_2) ->? #app'^2_quot(_1,_2) #10: #app'^2_plus(app'^1_s(x),y) -> #app'^2_plus(x,y) #11: #app'(app'^1_app(_1),_2) ->? #app'^2_app(_1,_2) #12: #app'^2_app(app'^2_cons(x,l),k) -> #app'^2_app(l,k) #13: #app'^2_quot(app'^1_s(x),app'^1_s(y)) -> #app'^2_quot(app'^2_minus(x,y),app'^1_s(y)) #14: #app'^2_quot(app'^1_s(x),app'^1_s(y)) -> #app'^2_minus(x,y) #15: #app'(app'^1_filter(_1),_2) ->? #app'^2_filter(_1,_2) #16: #app'^2_filter(f,app'^2_cons(x,xs)) -> #app'^4_filter2(app'(f,x),f,x,xs) #17: #app'^2_filter(f,app'^2_cons(x,xs)) -> #app'(f,x) #18: #app'(app'^1_minus(_1),_2) ->? #app'^2_minus(_1,_2) #19: #app'^4_filter2(false(),f,x,xs) -> #app'^2_filter(f,xs) #20: #app'(app'^3_filter2(_1,_2,_3),_4) ->? #app'^4_filter2(_1,_2,_3,_4) #21: #app'(app'^1_plus(_1),_2) ->? #app'^2_plus(_1,_2) #22: #app'^2_minus(app'^2_minus(x,y),z) -> #app'^2_minus(x,app'^2_plus(y,z)) #23: #app'^2_minus(app'^2_minus(x,y),z) -> #app'^2_plus(y,z) #24: #app'^2_map(f,app'^2_cons(x,xs)) -> #app'(f,x) #25: #app'^2_map(f,app'^2_cons(x,xs)) -> #app'^2_map(f,xs) #26: #app'^4_filter2(true(),f,x,xs) -> #app'^2_filter(f,xs) Number of SCCs: 7, DPs: 16 SCC { #10 } POLO(Sum)... succeeded. app'^1_s w: x1 + 1 app'^2_minus w: 0 #app'^2_plus w: x1 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: 0 app'^1_sum w: 0 #app' w: 0 false w: 0 app'^2_app w: 0 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: 0 app'^1_filter2 w: 0 0 w: 0 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: 0 #app'^4_filter2 w: 0 nil w: 0 #app'^2_quot w: 0 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: 0 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: 0 USABLE RULES: { } Removed DPs: #10 Number of SCCs: 6, DPs: 15 SCC { #12 } POLO(Sum)... succeeded. app'^1_s w: 1 app'^2_minus w: 0 #app'^2_plus w: 0 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: x1 app'^1_sum w: 0 #app' w: 0 false w: 0 app'^2_app w: 0 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: 0 app'^1_filter2 w: 0 0 w: 0 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: x2 + 1 #app'^4_filter2 w: 0 nil w: 0 #app'^2_quot w: 0 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: 0 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: 0 USABLE RULES: { } Removed DPs: #12 Number of SCCs: 5, DPs: 14 SCC { #13 } POLO(Sum)... succeeded. app'^1_s w: x1 + 2 app'^2_minus w: x1 + 1 #app'^2_plus w: 0 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: 0 app'^1_sum w: 0 #app' w: 0 false w: 0 app'^2_app w: 0 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: x1 + x2 + 1 app'^1_filter2 w: 0 0 w: 1 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: 1 #app'^4_filter2 w: 0 nil w: 0 #app'^2_quot w: x1 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: 0 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: 0 USABLE RULES: { 1..3 6 7 } Removed DPs: #13 Number of SCCs: 4, DPs: 13 SCC { #6 } POLO(Sum)... succeeded. app'^1_s w: x1 + 2 app'^2_minus w: x1 + 1 #app'^2_plus w: 0 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: 0 app'^1_sum w: 0 #app' w: 0 false w: 0 app'^2_app w: 0 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: x1 + x2 + 1 app'^1_filter2 w: 0 0 w: 1 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: x1 + x2 + 2 #app'^4_filter2 w: 0 nil w: 0 #app'^2_quot w: x1 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: 0 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: x1 USABLE RULES: { 1..3 6 7 } Removed DPs: #6 Number of SCCs: 3, DPs: 12 SCC { #3 } POLO(Sum)... succeeded. app'^1_s w: x1 + 2 app'^2_minus w: x1 + 1 #app'^2_plus w: 0 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: 0 app'^1_sum w: 3 #app' w: 0 false w: 0 app'^2_app w: x1 + x2 + 1 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: x1 + x2 + 1 app'^1_filter2 w: 0 0 w: 1 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: x2 + 2 #app'^4_filter2 w: 0 nil w: 1 #app'^2_quot w: x1 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: 0 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: x1 USABLE RULES: { 1..3 6..12 } Removed DPs: #3 Number of SCCs: 2, DPs: 11 SCC { #1 #22 } POLO(Sum)... succeeded. app'^1_s w: x1 + 2 app'^2_minus w: x1 + x2 + 2 #app'^2_plus w: 0 s w: 0 app'^4_filter2 w: 0 app'^2_map w: 0 minus w: 0 #app'^2_app w: 0 app'^1_sum w: 3 #app' w: 0 false w: 0 app'^2_app w: x1 + x2 + 1 app'^1_filter w: 0 app'^2_quot w: 0 #app'^2_filter w: 0 app'^1_plus w: 0 true w: 0 filter2 w: 0 sum w: 0 app'^2_plus w: x1 + x2 + 1 app'^1_filter2 w: 0 0 w: 1 app' w: 0 quot w: 0 app'^1_map w: 0 app'^2_cons w: x2 + 2 #app'^4_filter2 w: 0 nil w: 1 #app'^2_quot w: x1 app'^2_filter w: 0 map w: 0 app'^1_quot w: 0 app'^1_cons w: 0 #app'^2_minus w: x1 + x2 app'^3_filter2 w: 0 plus w: 0 app'^2_filter2 w: 0 cons w: 0 filter w: 0 #app'^2_map w: 0 app w: 0 app'^1_minus w: 0 app'^1_app w: 0 #app'^1_sum w: x1 USABLE RULES: { 1..3 6..12 } Removed DPs: #1 #22 Number of SCCs: 1, DPs: 9 SCC { #8 #15..17 #19 #20 #24..26 } POLO(Sum)... succeeded. app'^1_s w: x1 app'^2_minus w: x1 + x2 + 2 #app'^2_plus w: 0 s w: 1 app'^4_filter2 w: x1 + x2 + x3 + x4 + 3 app'^2_map w: x1 + 2 minus w: 1 #app'^2_app w: 0 app'^1_sum w: 1 #app' w: x1 + x2 false w: 1 app'^2_app w: x1 + x2 + 2 app'^1_filter w: x1 + 1 app'^2_quot w: x2 + 1 #app'^2_filter w: x1 + x2 app'^1_plus w: 1 true w: 1 filter2 w: 1 sum w: 1 app'^2_plus w: x2 + 1 app'^1_filter2 w: 1 0 w: 0 app' w: x2 + 1 quot w: 1 app'^1_map w: x1 + 1 app'^2_cons w: x1 + x2 + 2 #app'^4_filter2 w: x2 + x3 + x4 + 1 nil w: 3 #app'^2_quot w: x1 app'^2_filter w: x2 + 1 map w: 1 app'^1_quot w: 1 app'^1_cons w: 1 #app'^2_minus w: x2 app'^3_filter2 w: x1 + x2 + x3 + 2 plus w: 1 app'^2_filter2 w: 1 cons w: 1 filter w: 1 #app'^2_map w: x1 + x2 app w: 1 app'^1_minus w: 1 app'^1_app w: 1 #app'^1_sum w: 0 USABLE RULES: { 1..10 } Removed DPs: #8 #15..17 #19 #20 #24..26 Number of SCCs: 0, DPs: 0