/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 poly ... failed. Freezing 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 poly ... 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 } Sum... succeeded. #app❆2_map(x1,x2) w: (0) list3() w: (0) merge() w: (0) s() w: (0) app❆1_map(x1) w: (0) app❆1_plus(x1) w: (0) app❆1_if(x1) w: (0) app❆2_mult(x1,x2) w: (0) app❆2_merge(x1,x2) w: (0) #app❆3_if(x1,x2,x3) w: (0) app❆2_plus(x1,x2) w: (0) #app❆2_eq(x1,x2) w: (0) #list1() w: (0) app❆2_map(x1,x2) w: (0) eq() w: (0) list1() w: (0) false() w: (0) #hamming() w: (0) app❆2_eq(x1,x2) w: (0) app❆2_if(x1,x2) w: (0) true() w: (0) #list2() w: (0) mult() w: (0) if() w: (0) 0() w: (0) app❆1_eq(x1) w: (0) #app❆2_plus(x1,x2) w: (0) #app❆2_mult(x1,x2) w: (x1) #app❆2_lt(x1,x2) w: (0) hamming() w: (0) nil() w: (0) app❆3_if(x1,x2,x3) w: (0) #app(x1,x2) w: (0) map() w: (0) plus() w: (0) cons() w: (0) app❆2_cons(x1,x2) w: (0) #list3() w: (0) app❆2_lt(x1,x2) w: (0) #app❆2_merge(x1,x2) w: (0) app❆1_merge(x1) w: (0) list2() w: (0) app❆1_s(x1) w: (1 + x1) app❆1_mult(x1) w: (0) app❆1_cons(x1) w: (0) lt() w: (0) app❆1_lt(x1) w: (0) app(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #29 Number of SCCs: 5, DPs: 14 SCC { #18 } Sum... succeeded. #app❆2_map(x1,x2) w: (0) list3() w: (0) merge() w: (0) s() w: (0) app❆1_map(x1) w: (0) app❆1_plus(x1) w: (0) app❆1_if(x1) w: (0) app❆2_mult(x1,x2) w: (0) app❆2_merge(x1,x2) w: (0) #app❆3_if(x1,x2,x3) w: (0) app❆2_plus(x1,x2) w: (0) #app❆2_eq(x1,x2) w: (0) #list1() w: (0) app❆2_map(x1,x2) w: (0) eq() w: (0) list1() w: (0) false() w: (0) #hamming() w: (0) app❆2_eq(x1,x2) w: (0) app❆2_if(x1,x2) w: (0) true() w: (0) #list2() w: (0) mult() w: (0) if() w: (0) 0() w: (0) app❆1_eq(x1) w: (0) #app❆2_plus(x1,x2) w: (x1) #app❆2_mult(x1,x2) w: (0) #app❆2_lt(x1,x2) w: (0) hamming() w: (0) nil() w: (0) app❆3_if(x1,x2,x3) w: (0) #app(x1,x2) w: (0) map() w: (0) plus() w: (0) cons() w: (0) app❆2_cons(x1,x2) w: (0) #list3() w: (0) app❆2_lt(x1,x2) w: (0) #app❆2_merge(x1,x2) w: (0) app❆1_merge(x1) w: (0) list2() w: (0) app❆1_s(x1) w: (1 + x1) app❆1_mult(x1) w: (0) app❆1_cons(x1) w: (0) lt() w: (0) app❆1_lt(x1) w: (0) app(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #18 Number of SCCs: 4, DPs: 13 SCC { #27 } Sum... succeeded. #app❆2_map(x1,x2) w: (0) list3() w: (0) merge() w: (0) s() w: (0) app❆1_map(x1) w: (0) app❆1_plus(x1) w: (0) app❆1_if(x1) w: (0) app❆2_mult(x1,x2) w: (0) app❆2_merge(x1,x2) w: (0) #app❆3_if(x1,x2,x3) w: (0) app❆2_plus(x1,x2) w: (0) #app❆2_eq(x1,x2) w: (0) #list1() w: (0) app❆2_map(x1,x2) w: (0) eq() w: (0) list1() w: (0) false() w: (0) #hamming() w: (0) app❆2_eq(x1,x2) w: (0) app❆2_if(x1,x2) w: (0) true() w: (0) #list2() w: (0) mult() w: (0) if() w: (0) 0() w: (0) app❆1_eq(x1) w: (0) #app❆2_plus(x1,x2) w: (0) #app❆2_mult(x1,x2) w: (0) #app❆2_lt(x1,x2) w: (x2) hamming() w: (0) nil() w: (0) app❆3_if(x1,x2,x3) w: (0) #app(x1,x2) w: (0) map() w: (0) plus() w: (0) cons() w: (0) app❆2_cons(x1,x2) w: (0) #list3() w: (0) app❆2_lt(x1,x2) w: (0) #app❆2_merge(x1,x2) w: (0) app❆1_merge(x1) w: (0) list2() w: (0) app❆1_s(x1) w: (1 + x1) app❆1_mult(x1) w: (0) app❆1_cons(x1) w: (0) lt() w: (0) app❆1_lt(x1) w: (0) app(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #27 Number of SCCs: 3, DPs: 12 SCC { #15 #21 #23 #25 #26 #31 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed. Finding a loop... found. #hamming() -#25-> #list2() --->* #list2() -#21-> #hamming() --->* #hamming() Looping with: [ ]