/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: isEmpty(cons(x,xs)) -> false() 2: isEmpty(nil()) -> true() 3: isZero(0()) -> true() 4: isZero(s(x)) -> false() 5: head(cons(x,xs)) -> x 6: tail(cons(x,xs)) -> xs 7: tail(nil()) -> nil() 8: append(nil(),x) -> cons(x,nil()) 9: append(cons(y,ys),x) -> cons(y,append(ys,x)) 10: p(s(s(x))) -> s(p(s(x))) 11: p(s(0())) -> 0() 12: p(0()) -> 0() 13: inc(s(x)) -> s(inc(x)) 14: inc(0()) -> s(0()) 15: addLists(xs,ys,zs) -> if(isEmpty(xs),isEmpty(ys),isZero(head(xs)),tail(xs),tail(ys),cons(p(head(xs)),tail(xs)),cons(inc(head(ys)),tail(ys)),zs,append(zs,head(ys))) 16: if(true(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> zs 17: if(true(),false(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError() 18: if(false(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError() 19: if(false(),false(),false(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs2,ys2,zs) 20: if(false(),false(),true(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs,ys,zs2) 21: addList(xs,ys) -> addLists(xs,ys,nil()) Number of strict rules: 21 Direct POLO(bPol) ... failed. Uncurrying p 1: isEmpty(cons(x,xs)) -> false() 2: isEmpty(nil()) -> true() 3: isZero(0()) -> true() 4: isZero(s(x)) -> false() 5: head(cons(x,xs)) -> x 6: tail(cons(x,xs)) -> xs 7: tail(nil()) -> nil() 8: append(nil(),x) -> cons(x,nil()) 9: append(cons(y,ys),x) -> cons(y,append(ys,x)) 10: p^1_s(s(x)) -> s(p^1_s(x)) 11: p^1_s(0()) -> 0() 12: p^1_0() -> 0() 13: inc(s(x)) -> s(inc(x)) 14: inc(0()) -> s(0()) 15: addLists(xs,ys,zs) -> if(isEmpty(xs),isEmpty(ys),isZero(head(xs)),tail(xs),tail(ys),cons(p(head(xs)),tail(xs)),cons(inc(head(ys)),tail(ys)),zs,append(zs,head(ys))) 16: if(true(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> zs 17: if(true(),false(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError() 18: if(false(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError() 19: if(false(),false(),false(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs2,ys2,zs) 20: if(false(),false(),true(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs,ys,zs2) 21: addList(xs,ys) -> addLists(xs,ys,nil()) 22: p(0()) ->= p^1_0() 23: p(s(_1)) ->= p^1_s(_1) Number of strict rules: 21 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #inc(s(x)) -> #inc(x) #2: #append(cons(y,ys),x) -> #append(ys,x) #3: #p(s(_1)) ->? #p^1_s(_1) #4: #if(false(),false(),true(),xs,ys,xs2,ys2,zs,zs2) -> #addLists(xs,ys,zs2) #5: #p^1_s(s(x)) -> #p^1_s(x) #6: #p(0()) ->? #p^1_0() #7: #if(false(),false(),false(),xs,ys,xs2,ys2,zs,zs2) -> #addLists(xs2,ys2,zs) #8: #addList(xs,ys) -> #addLists(xs,ys,nil()) #9: #addLists(xs,ys,zs) -> #if(isEmpty(xs),isEmpty(ys),isZero(head(xs)),tail(xs),tail(ys),cons(p(head(xs)),tail(xs)),cons(inc(head(ys)),tail(ys)),zs,append(zs,head(ys))) #10: #addLists(xs,ys,zs) -> #isEmpty(xs) #11: #addLists(xs,ys,zs) -> #isEmpty(ys) #12: #addLists(xs,ys,zs) -> #isZero(head(xs)) #13: #addLists(xs,ys,zs) -> #head(xs) #14: #addLists(xs,ys,zs) -> #tail(xs) #15: #addLists(xs,ys,zs) -> #tail(ys) #16: #addLists(xs,ys,zs) -> #p(head(xs)) #17: #addLists(xs,ys,zs) -> #head(xs) #18: #addLists(xs,ys,zs) -> #tail(xs) #19: #addLists(xs,ys,zs) -> #inc(head(ys)) #20: #addLists(xs,ys,zs) -> #head(ys) #21: #addLists(xs,ys,zs) -> #tail(ys) #22: #addLists(xs,ys,zs) -> #append(zs,head(ys)) #23: #addLists(xs,ys,zs) -> #head(ys) Number of SCCs: 4, DPs: 6 SCC { #5 } POLO(Sum)... succeeded. s w: x1 + 1 #p^1_0 w: 0 #append w: 0 #isZero w: 0 #p^1_s w: x1 #isEmpty w: 0 p^1_0 w: 0 false w: 0 #head w: 0 isEmpty w: 0 p^1_s w: 0 addList w: 0 #inc w: 0 #p w: 0 inc w: 0 true w: 0 differentLengthError w: 0 p w: 0 tail w: 0 append w: 0 0 w: 0 if w: 0 nil w: 0 #tail w: 0 addLists w: 0 head w: 0 cons w: 0 #if w: 0 isZero w: 0 #addList w: 0 #addLists w: 0 USABLE RULES: { } Removed DPs: #5 Number of SCCs: 3, DPs: 5 SCC { #1 } POLO(Sum)... succeeded. s w: x1 + 1 #p^1_0 w: 0 #append w: 0 #isZero w: 0 #p^1_s w: 0 #isEmpty w: 0 p^1_0 w: 0 false w: 0 #head w: 0 isEmpty w: 0 p^1_s w: 0 addList w: 0 #inc w: x1 #p w: 0 inc w: 0 true w: 0 differentLengthError w: 0 p w: 0 tail w: 0 append w: 0 0 w: 0 if w: 0 nil w: 0 #tail w: 0 addLists w: 0 head w: 0 cons w: 0 #if w: 0 isZero w: 0 #addList w: 0 #addLists w: 0 USABLE RULES: { } Removed DPs: #1 Number of SCCs: 2, DPs: 4 SCC { #2 } POLO(Sum)... succeeded. s w: 1 #p^1_0 w: 0 #append w: x1 #isZero w: 0 #p^1_s w: 0 #isEmpty w: 0 p^1_0 w: 0 false w: 0 #head w: 0 isEmpty w: 0 p^1_s w: 0 addList w: 0 #inc w: 0 #p w: 0 inc w: 0 true w: 0 differentLengthError w: 0 p w: 0 tail w: 0 append w: 0 0 w: 0 if w: 0 nil w: 0 #tail w: 0 addLists w: 0 head w: 0 cons w: x2 + 1 #if w: 0 isZero w: 0 #addList w: 0 #addLists w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 1, DPs: 3 SCC { #4 #7 #9 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. s w: max(x1 + 3, 0) #p^1_0 w: 0 #append w: 0 #isZero w: 0 #p^1_s w: max(x1 - 1, 0) #isEmpty w: 0 p^1_0 w: 3 false w: 2 #head w: max(x1 - 1, 0) isEmpty w: 1 p^1_s w: max(x1 + 1, 0) addList w: max(x1 - 1, 0) #inc w: 0 #p w: max(x1 - 1, 0) inc w: 1 true w: 2 differentLengthError w: 0 p w: max(x1, 0) tail w: max(x1 - 4, 0) append w: max(x1 - 5, 0) 0 w: 3 if w: 0 nil w: 0 #tail w: 0 addLists w: max(x2 - 1, 0) head w: max(x1 - 4, 0) cons w: max(x1 + 4, x2 + 4, 0) #if w: max(x3 - 1, x4, x6 - 4, 0) isZero w: max(x1 - 1, 0) #addList w: max(x1 - 1, 0) #addLists w: max(x1 - 4, 0) USABLE RULES: { 3..7 10..12 22 23 } Removed DPs: #4 Number of SCCs: 1, DPs: 2 SCC { #7 #9 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. s w: max(x1 + 5, 0) #p^1_0 w: 0 #append w: 0 #isZero w: 0 #p^1_s w: max(x1 - 1, 0) #isEmpty w: 0 p^1_0 w: 0 false w: 4 #head w: max(x1 - 1, 0) isEmpty w: 2 p^1_s w: max(x1 + 1, 0) addList w: max(x1 - 1, 0) #inc w: 0 #p w: max(x1 - 1, 0) inc w: max(x1 + 5, 0) true w: 0 differentLengthError w: 0 p w: max(x1 - 1, 0) tail w: max(x1 - 2, 0) append w: max(x1 - 8, 0) 0 w: 0 if w: 0 nil w: 0 #tail w: 0 addLists w: max(x2 - 1, 0) head w: max(x1 - 2, 0) cons w: max(x1 + 2, 0) #if w: max(x3 - 2, x6 - 3, 0) isZero w: max(x1 - 1, 0) #addList w: max(x1 - 1, 0) #addLists w: max(x1 - 4, 0) USABLE RULES: { 3..5 10..14 22 23 } Removed DPs: #7 Number of SCCs: 0, DPs: 0