/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N))) 2: sqr(0()) -> 0() 3: sqr(s(X)) -> s(add(sqr(X),dbl(X))) 4: dbl(0()) -> 0() 5: dbl(s(X)) -> s(s(dbl(X))) 6: add(0(),X) -> X 7: add(s(X),Y) -> s(add(X,Y)) 8: first(0(),X) -> nil() 9: first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) 10: half(0()) -> 0() 11: half(s(0())) -> 0() 12: half(s(s(X))) -> s(half(X)) 13: half(dbl(X)) -> X 14: terms(X) -> n__terms(X) 15: s(X) -> n__s(X) 16: first(X1,X2) -> n__first(X1,X2) 17: activate(n__terms(X)) -> terms(activate(X)) 18: activate(n__s(X)) -> s(activate(X)) 19: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) 20: activate(X) -> X Number of strict rules: 20 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #first(s(X),cons(Y,Z)) -> #activate(Z) #2: #half(s(s(X))) -> #s(half(X)) #3: #half(s(s(X))) -> #half(X) #4: #add(s(X),Y) -> #s(add(X,Y)) #5: #add(s(X),Y) -> #add(X,Y) #6: #dbl(s(X)) -> #s(s(dbl(X))) #7: #dbl(s(X)) -> #s(dbl(X)) #8: #dbl(s(X)) -> #dbl(X) #9: #activate(n__terms(X)) -> #terms(activate(X)) #10: #activate(n__terms(X)) -> #activate(X) #11: #activate(n__first(X1,X2)) -> #first(activate(X1),activate(X2)) #12: #activate(n__first(X1,X2)) -> #activate(X1) #13: #activate(n__first(X1,X2)) -> #activate(X2) #14: #sqr(s(X)) -> #s(add(sqr(X),dbl(X))) #15: #sqr(s(X)) -> #add(sqr(X),dbl(X)) #16: #sqr(s(X)) -> #sqr(X) #17: #sqr(s(X)) -> #dbl(X) #18: #terms(N) -> #sqr(N) #19: #activate(n__s(X)) -> #s(activate(X)) #20: #activate(n__s(X)) -> #activate(X) Number of SCCs: 5, DPs: 10 SCC { #16 } POLO(Sum)... succeeded. s w: x1 + 1 n__first w: 0 recip w: 0 activate w: 0 dbl w: 0 #dbl w: 0 #terms w: 0 #activate w: 0 #half w: 0 half w: 0 n__s w: 0 #sqr w: x1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 first w: 0 n__terms w: 0 cons w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #16 Number of SCCs: 4, DPs: 9 SCC { #8 } POLO(Sum)... succeeded. s w: x1 + 1 n__first w: 0 recip w: 0 activate w: 0 dbl w: 0 #dbl w: x1 #terms w: 0 #activate w: 0 #half w: 0 half w: 0 n__s w: 0 #sqr w: 0 0 w: 0 #s w: 0 #first w: 0 nil w: 0 first w: 0 n__terms w: 0 cons w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #8 Number of SCCs: 3, DPs: 8 SCC { #3 } POLO(Sum)... succeeded. s w: x1 + 1 n__first w: 0 recip w: 0 activate w: 0 dbl w: 0 #dbl w: 0 #terms w: 0 #activate w: 0 #half w: x1 half w: 0 n__s w: 0 #sqr w: 0 0 w: 0 #s w: 0 #first w: 0 nil w: 0 first w: 0 n__terms w: 0 cons w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 2, DPs: 7 SCC { #5 } POLO(Sum)... succeeded. s w: x1 + 1 n__first w: 0 recip w: 0 activate w: 0 dbl w: 0 #dbl w: 0 #terms w: 0 #activate w: 0 #half w: 0 half w: 0 n__s w: 0 #sqr w: 0 0 w: 0 #s w: 0 #first w: 0 nil w: 0 first w: 0 n__terms w: 0 cons w: 0 #add w: x1 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #5 Number of SCCs: 1, DPs: 6 SCC { #1 #10..13 #20 } POLO(Sum)... succeeded. s w: x1 n__first w: x1 + x2 + 2 recip w: x1 activate w: x1 dbl w: 1 #dbl w: 0 #terms w: 0 #activate w: x1 #half w: 0 half w: 0 n__s w: x1 #sqr w: 0 0 w: 1 #s w: 0 #first w: x2 + 1 nil w: 0 first w: x1 + x2 + 2 n__terms w: x1 + 1 cons w: x2 #add w: 0 add w: x2 + 1 sqr w: 2 terms w: x1 + 1 USABLE RULES: { 1..9 14..20 } Removed DPs: #1 #10..13 Number of SCCs: 1, DPs: 1 SCC { #20 } POLO(Sum)... succeeded. s w: 2 n__first w: 1 recip w: x1 activate w: 1 dbl w: x1 + 1 #dbl w: 0 #terms w: 0 #activate w: x1 #half w: 0 half w: 0 n__s w: x1 + 3 #sqr w: 0 0 w: 0 #s w: 0 #first w: 1 nil w: 1 first w: x1 + x2 n__terms w: x1 + 1 cons w: x2 #add w: 0 add w: x2 + 2 sqr w: x1 + 1 terms w: x1 + 4 USABLE RULES: { 2 4 6 } Removed DPs: #20 Number of SCCs: 0, DPs: 0