/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO Input TRS: 1: app(app(app(if(),true()),xs),ys) -> xs 2: app(app(app(if(),false()),xs),ys) -> ys 3: app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y) 4: app(app(lt(),0()),app(s(),y)) -> true() 5: app(app(lt(),y),0()) -> false() 6: app(app(eq(),x),x) -> true() 7: app(app(eq(),app(s(),x)),0()) -> false() 8: app(app(eq(),0()),app(s(),x)) -> false() 9: app(app(merge(),xs),nil()) -> xs 10: app(app(merge(),nil()),ys) -> ys 11: app(app(merge(),app(app(cons(),x),xs)),app(app(cons(),y),ys)) -> app(app(app(if(),app(app(lt(),x),y)),app(app(cons(),x),app(app(merge(),xs),app(app(cons(),y),ys)))),app(app(app(if(),app(app(eq(),x),y)),app(app(cons(),x),app(app(merge(),xs),ys))),app(app(cons(),y),app(app(merge(),app(app(cons(),x),xs)),ys)))) 12: app(app(map(),f),nil()) -> nil() 13: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 14: app(app(mult(),0()),x) -> 0() 15: app(app(mult(),app(s(),x)),y) -> app(app(plus(),y),app(app(mult(),x),y)) 16: app(app(plus(),0()),x) -> 0() 17: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) 18: list1() -> app(app(map(),app(mult(),app(s(),app(s(),0())))),hamming()) 19: list2() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),0()))))),hamming()) 20: list3() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),app(s(),app(s(),0()))))))),hamming()) 21: hamming() -> app(app(cons(),app(s(),0())),app(app(merge(),list1()),app(app(merge(),list2()),list3()))) Number of strict rules: 21 Direct POLO(bPol) ... failed. Uncurrying app 1: app^3_if(true(),xs,ys) -> xs 2: app^3_if(false(),xs,ys) -> ys 3: app^2_lt(app^1_s(x),app^1_s(y)) -> app^2_lt(x,y) 4: app^2_lt(0(),app^1_s(y)) -> true() 5: app^2_lt(y,0()) -> false() 6: app^2_eq(x,x) -> true() 7: app^2_eq(app^1_s(x),0()) -> false() 8: app^2_eq(0(),app^1_s(x)) -> false() 9: app^2_merge(xs,nil()) -> xs 10: app^2_merge(nil(),ys) -> ys 11: app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> app^3_if(app^2_lt(x,y),app^2_cons(x,app^2_merge(xs,app^2_cons(y,ys))),app^3_if(app^2_eq(x,y),app^2_cons(x,app^2_merge(xs,ys)),app^2_cons(y,app^2_merge(app^2_cons(x,xs),ys)))) 12: app^2_map(f,nil()) -> nil() 13: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 14: app^2_mult(0(),x) -> 0() 15: app^2_mult(app^1_s(x),y) -> app^2_plus(y,app^2_mult(x,y)) 16: app^2_plus(0(),x) -> 0() 17: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y)) 18: list1() -> app^2_map(app^1_mult(app^1_s(app^1_s(0()))),hamming()) 19: list2() -> app^2_map(app^1_mult(app^1_s(app^1_s(app^1_s(0())))),hamming()) 20: list3() -> app^2_map(app^1_mult(app^1_s(app^1_s(app^1_s(app^1_s(app^1_s(0())))))),hamming()) 21: hamming() -> app^2_cons(app^1_s(0()),app^2_merge(list1(),app^2_merge(list2(),list3()))) 22: app(eq(),_1) ->= app^1_eq(_1) 23: app(app^1_eq(_1),_2) ->= app^2_eq(_1,_2) 24: app(plus(),_1) ->= app^1_plus(_1) 25: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2) 26: app(if(),_1) ->= app^1_if(_1) 27: app(app^1_if(_1),_2) ->= app^2_if(_1,_2) 28: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3) 29: app(cons(),_1) ->= app^1_cons(_1) 30: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 31: app(merge(),_1) ->= app^1_merge(_1) 32: app(app^1_merge(_1),_2) ->= app^2_merge(_1,_2) 33: app(s(),_1) ->= app^1_s(_1) 34: app(map(),_1) ->= app^1_map(_1) 35: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 36: app(lt(),_1) ->= app^1_lt(_1) 37: app(app^1_lt(_1),_2) ->= app^2_lt(_1,_2) 38: app(mult(),_1) ->= app^1_mult(_1) 39: app(app^1_mult(_1),_2) ->= app^2_mult(_1,_2) Number of strict rules: 21 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #2: #app(app^1_lt(_1),_2) ->? #app^2_lt(_1,_2) #3: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x) #4: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs) #5: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^3_if(app^2_lt(x,y),app^2_cons(x,app^2_merge(xs,app^2_cons(y,ys))),app^3_if(app^2_eq(x,y),app^2_cons(x,app^2_merge(xs,ys)),app^2_cons(y,app^2_merge(app^2_cons(x,xs),ys)))) #6: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^2_lt(x,y) #7: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^2_merge(xs,app^2_cons(y,ys)) #8: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^3_if(app^2_eq(x,y),app^2_cons(x,app^2_merge(xs,ys)),app^2_cons(y,app^2_merge(app^2_cons(x,xs),ys))) #9: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^2_eq(x,y) #10: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^2_merge(xs,ys) #11: #app^2_merge(app^2_cons(x,xs),app^2_cons(y,ys)) -> #app^2_merge(app^2_cons(x,xs),ys) #12: #app(app^1_eq(_1),_2) ->? #app^2_eq(_1,_2) #13: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2) #14: #list3() -> #app^2_map(app^1_mult(app^1_s(app^1_s(app^1_s(app^1_s(app^1_s(0())))))),hamming()) #15: #list3() -> #hamming() #16: #app(app^1_mult(_1),_2) ->? #app^2_mult(_1,_2) #17: #app(app^2_if(_1,_2),_3) ->? #app^3_if(_1,_2,_3) #18: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y) #19: #app(app^1_merge(_1),_2) ->? #app^2_merge(_1,_2) #20: #list2() -> #app^2_map(app^1_mult(app^1_s(app^1_s(app^1_s(0())))),hamming()) #21: #list2() -> #hamming() #22: #hamming() -> #app^2_merge(list1(),app^2_merge(list2(),list3())) #23: #hamming() -> #list1() #24: #hamming() -> #app^2_merge(list2(),list3()) #25: #hamming() -> #list2() #26: #hamming() -> #list3() #27: #app^2_lt(app^1_s(x),app^1_s(y)) -> #app^2_lt(x,y) #28: #app^2_mult(app^1_s(x),y) -> #app^2_plus(y,app^2_mult(x,y)) #29: #app^2_mult(app^1_s(x),y) -> #app^2_mult(x,y) #30: #list1() -> #app^2_map(app^1_mult(app^1_s(app^1_s(0()))),hamming()) #31: #list1() -> #hamming() Number of SCCs: 6, DPs: 15 SCC { #29 } POLO(Sum)... succeeded. #app^3_if w: 0 list3 w: 0 #app^2_mult w: x1 merge w: 0 app^1_lt w: 0 s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 app^1_merge w: 0 #app^2_lt w: 0 #list1 w: 0 eq w: 0 list1 w: 0 false w: 0 #hamming w: 0 app^2_merge w: 0 #app^2_merge w: 0 true w: 0 #app^2_plus w: 0 #list2 w: 0 mult w: 0 app^2_plus w: 0 if w: 0 0 w: 0 hamming w: 0 nil w: 0 #app w: 0 app^1_mult w: 0 map w: 0 app^2_lt w: 0 #app^2_eq w: 0 plus w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #list3 w: 0 app^2_mult w: 0 app^2_eq w: 0 list2 w: 0 app^1_map w: 0 lt w: 0 app^2_cons w: 0 app^1_eq w: 0 app^1_if w: 0 app^1_s w: x1 + 1 app^2_map w: 0 app w: 0 USABLE RULES: { } Removed DPs: #29 Number of SCCs: 5, DPs: 14 SCC { #18 } POLO(Sum)... succeeded. #app^3_if w: 0 list3 w: 0 #app^2_mult w: 0 merge w: 0 app^1_lt w: 0 s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 app^1_merge w: 0 #app^2_lt w: 0 #list1 w: 0 eq w: 0 list1 w: 0 false w: 0 #hamming w: 0 app^2_merge w: 0 #app^2_merge w: 0 true w: 0 #app^2_plus w: x1 #list2 w: 0 mult w: 0 app^2_plus w: 0 if w: 0 0 w: 0 hamming w: 0 nil w: 0 #app w: 0 app^1_mult w: 0 map w: 0 app^2_lt w: 0 #app^2_eq w: 0 plus w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #list3 w: 0 app^2_mult w: 0 app^2_eq w: 0 list2 w: 0 app^1_map w: 0 lt w: 0 app^2_cons w: 0 app^1_eq w: 0 app^1_if w: 0 app^1_s w: x1 + 1 app^2_map w: 0 app w: 0 USABLE RULES: { } Removed DPs: #18 Number of SCCs: 4, DPs: 13 SCC { #27 } POLO(Sum)... succeeded. #app^3_if w: 0 list3 w: 0 #app^2_mult w: 0 merge w: 0 app^1_lt w: 0 s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 app^1_merge w: 0 #app^2_lt w: x2 #list1 w: 0 eq w: 0 list1 w: 0 false w: 0 #hamming w: 0 app^2_merge w: 0 #app^2_merge w: 0 true w: 0 #app^2_plus w: 0 #list2 w: 0 mult w: 0 app^2_plus w: 0 if w: 0 0 w: 0 hamming w: 0 nil w: 0 #app w: 0 app^1_mult w: 0 map w: 0 app^2_lt w: 0 #app^2_eq w: 0 plus w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #list3 w: 0 app^2_mult w: 0 app^2_eq w: 0 list2 w: 0 app^1_map w: 0 lt w: 0 app^2_cons w: 0 app^1_eq w: 0 app^1_if w: 0 app^1_s w: x1 + 1 app^2_map w: 0 app w: 0 USABLE RULES: { } Removed DPs: #27 Number of SCCs: 3, DPs: 12 SCC { #15 #21 #23 #25 #26 #31 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... found. #hamming() -#25-> #list2() --->* #list2() -#21-> #hamming() --->* #hamming() Looping with: [ ]