/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__dbl(0()) -> 0() 2: a__dbl(s(X)) -> s(s(dbl(X))) 3: a__dbls(nil()) -> nil() 4: a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y)) 5: a__sel(0(),cons(X,Y)) -> mark(X) 6: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z)) 7: a__indx(nil(),X) -> nil() 8: a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z)) 9: a__from(X) -> cons(X,from(s(X))) 10: a__dbl1(0()) -> 01() 11: a__dbl1(s(X)) -> s1(s1(a__dbl1(mark(X)))) 12: a__sel1(0(),cons(X,Y)) -> mark(X) 13: a__sel1(s(X),cons(Y,Z)) -> a__sel1(mark(X),mark(Z)) 14: a__quote(0()) -> 01() 15: a__quote(s(X)) -> s1(a__quote(mark(X))) 16: a__quote(dbl(X)) -> a__dbl1(mark(X)) 17: a__quote(sel(X,Y)) -> a__sel1(mark(X),mark(Y)) 18: mark(dbl(X)) -> a__dbl(mark(X)) 19: mark(dbls(X)) -> a__dbls(mark(X)) 20: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) 21: mark(indx(X1,X2)) -> a__indx(mark(X1),X2) 22: mark(from(X)) -> a__from(X) 23: mark(dbl1(X)) -> a__dbl1(mark(X)) 24: mark(sel1(X1,X2)) -> a__sel1(mark(X1),mark(X2)) 25: mark(quote(X)) -> a__quote(mark(X)) 26: mark(0()) -> 0() 27: mark(s(X)) -> s(X) 28: mark(nil()) -> nil() 29: mark(cons(X1,X2)) -> cons(X1,X2) 30: mark(01()) -> 01() 31: mark(s1(X)) -> s1(mark(X)) 32: a__dbl(X) -> dbl(X) 33: a__dbls(X) -> dbls(X) 34: a__sel(X1,X2) -> sel(X1,X2) 35: a__indx(X1,X2) -> indx(X1,X2) 36: a__from(X) -> from(X) 37: a__dbl1(X) -> dbl1(X) 38: a__sel1(X1,X2) -> sel1(X1,X2) 39: a__quote(X) -> quote(X) Number of strict rules: 39 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z)) #2: #a__sel(s(X),cons(Y,Z)) -> #mark(X) #3: #a__sel(s(X),cons(Y,Z)) -> #mark(Z) #4: #a__sel1(s(X),cons(Y,Z)) -> #a__sel1(mark(X),mark(Z)) #5: #a__sel1(s(X),cons(Y,Z)) -> #mark(X) #6: #a__sel1(s(X),cons(Y,Z)) -> #mark(Z) #7: #a__dbl1(s(X)) -> #a__dbl1(mark(X)) #8: #a__dbl1(s(X)) -> #mark(X) #9: #mark(sel1(X1,X2)) -> #a__sel1(mark(X1),mark(X2)) #10: #mark(sel1(X1,X2)) -> #mark(X1) #11: #mark(sel1(X1,X2)) -> #mark(X2) #12: #mark(dbl1(X)) -> #a__dbl1(mark(X)) #13: #mark(dbl1(X)) -> #mark(X) #14: #a__sel1(0(),cons(X,Y)) -> #mark(X) #15: #mark(s1(X)) -> #mark(X) #16: #mark(quote(X)) -> #a__quote(mark(X)) #17: #mark(quote(X)) -> #mark(X) #18: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2)) #19: #mark(sel(X1,X2)) -> #mark(X1) #20: #mark(sel(X1,X2)) -> #mark(X2) #21: #a__sel(0(),cons(X,Y)) -> #mark(X) #22: #mark(from(X)) -> #a__from(X) #23: #a__quote(sel(X,Y)) -> #a__sel1(mark(X),mark(Y)) #24: #a__quote(sel(X,Y)) -> #mark(X) #25: #a__quote(sel(X,Y)) -> #mark(Y) #26: #mark(dbls(X)) -> #a__dbls(mark(X)) #27: #mark(dbls(X)) -> #mark(X) #28: #mark(indx(X1,X2)) -> #a__indx(mark(X1),X2) #29: #mark(indx(X1,X2)) -> #mark(X1) #30: #a__quote(dbl(X)) -> #a__dbl1(mark(X)) #31: #a__quote(dbl(X)) -> #mark(X) #32: #a__quote(s(X)) -> #a__quote(mark(X)) #33: #a__quote(s(X)) -> #mark(X) #34: #mark(dbl(X)) -> #a__dbl(mark(X)) #35: #mark(dbl(X)) -> #mark(X) Number of SCCs: 1, DPs: 31 SCC { #1..21 #23..25 #27 #29..33 #35 } POLO(Sum)... POLO(max)... succeeded. #a__quote w: x1 + 1 a__dbl1 w: x1 + 2 01 w: 1 s w: x1 #a__from w: 0 dbls w: x1 + 1 a__indx w: max(x1 + 5, x2 + 4) a__from w: x1 + 1 #a__indx w: 0 dbl w: x1 + 1 indx w: max(x1 + 5, x2 + 4) #a__dbl1 w: x1 + 1 a__dbl w: x1 + 1 a__sel1 w: max(x1 + 6, x2 + 4) #a__dbls w: 0 #mark w: x1 0 w: 1 a__quote w: x1 + 2 sel w: max(x1 + 5, x2 + 3) from w: x1 + 1 #a__sel1 w: max(x1 + 2, x2 + 3) nil w: 5 dbl1 w: x1 + 2 #a__dbl w: 0 #a__sel w: max(x1 + 1, x2 + 2) mark w: x1 a__sel w: max(x1 + 5, x2 + 3) a__dbls w: x1 + 1 quote w: x1 + 2 cons w: max(x1 + 1, x2) sel1 w: max(x1 + 6, x2 + 4) s1 w: x1 USABLE RULES: { 1..39 } Removed DPs: #2 #3 #5 #6 #8..14 #16..21 #23..25 #27 #29..31 #33 #35 Number of SCCs: 5, DPs: 5 SCC { #15 } POLO(Sum)... succeeded. #a__quote w: 2 a__dbl1 w: x1 01 w: 5 s w: x1 + 2 #a__from w: 0 dbls w: x1 + 3 a__indx w: 2 a__from w: 2 #a__indx w: 0 dbl w: x1 + 3 indx w: x1 + 3 #a__dbl1 w: 1 a__dbl w: 2 a__sel1 w: 5 #a__dbls w: 0 #mark w: x1 + 1 0 w: 3 a__quote w: x1 + 1 sel w: x1 + x2 + 3 from w: x1 + 3 #a__sel1 w: 0 nil w: 3 dbl1 w: 1 #a__dbl w: 0 #a__sel w: 0 mark w: 1 a__sel w: 2 a__dbls w: 2 quote w: 2 cons w: x2 + 2 sel1 w: 6 s1 w: x1 + 2 USABLE RULES: { } Removed DPs: #15 Number of SCCs: 4, DPs: 4 SCC { #32 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #a__quote s: [1] p: 0 w: x1 + 1 a__dbl1 s: [1] p: 7 w: x1 + 3 01 s: [] p: 3 w: 4 s s: [1] p: 5 w: x1 #a__from s: [] p: 0 w: 1 dbls s: [1] p: 3 w: x1 a__indx s: [2,1] p: 5 w: x1 + x2 + 5 a__from s: [] p: 2 w: x1 + 4 #a__indx s: [] p: 0 w: x1 dbl s: [1] p: 6 w: x1 indx s: [2,1] p: 5 w: x1 + x2 + 5 #a__dbl1 s: [] p: 0 w: 0 a__dbl s: [1] p: 6 w: x1 a__sel1 s: [1,2] p: 0 w: x1 + x2 + 4 #a__dbls s: [] p: 0 w: 1 #mark s: [] p: 0 w: 0 0 s: [] p: 5 w: 1 a__quote s: [1] p: 2 w: x1 + 4 sel s: [] p: 1 w: x1 + x2 + 1 from s: [] p: 2 w: x1 + 4 #a__sel1 s: [] p: 0 w: 0 nil s: [] p: 3 w: 1 dbl1 s: [1] p: 7 w: x1 + 3 #a__dbl s: [] p: 0 w: 1 #a__sel s: [] p: 0 w: x1 mark s: 1 a__sel s: [] p: 1 w: x1 + x2 + 1 a__dbls s: [1] p: 3 w: x1 quote s: [1] p: 2 w: x1 + 4 cons s: [] p: 2 w: max(x1 + 3, x2) sel1 s: [1,2] p: 0 w: x1 + x2 + 4 s1 s: [] p: 7 w: 1 USABLE RULES: { 1..39 } Removed DPs: #32 Number of SCCs: 3, DPs: 3 SCC { #7 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #a__quote s: [1] p: 0 w: x1 + 1 a__dbl1 s: [1] p: 7 w: x1 + 3 01 s: [] p: 3 w: 4 s s: [1] p: 5 w: x1 #a__from s: [] p: 0 w: 1 dbls s: [1] p: 3 w: x1 a__indx s: [2,1] p: 5 w: x1 + x2 + 5 a__from s: [] p: 2 w: x1 + 4 #a__indx s: [] p: 0 w: x1 dbl s: [1] p: 6 w: x1 indx s: [2,1] p: 5 w: x1 + x2 + 5 #a__dbl1 s: [1] p: 0 w: x1 a__dbl s: [1] p: 6 w: x1 a__sel1 s: [1,2] p: 0 w: x1 + x2 + 4 #a__dbls s: [] p: 0 w: 1 #mark s: [] p: 0 w: 0 0 s: [] p: 5 w: 1 a__quote s: [1] p: 2 w: x1 + 4 sel s: [] p: 1 w: x1 + x2 + 1 from s: [] p: 2 w: x1 + 4 #a__sel1 s: [] p: 0 w: 0 nil s: [] p: 3 w: 1 dbl1 s: [1] p: 7 w: x1 + 3 #a__dbl s: [] p: 0 w: 1 #a__sel s: [] p: 0 w: x1 mark s: 1 a__sel s: [] p: 1 w: x1 + x2 + 1 a__dbls s: [1] p: 3 w: x1 quote s: [1] p: 2 w: x1 + 4 cons s: [] p: 2 w: max(x1 + 3, x2) sel1 s: [1,2] p: 0 w: x1 + x2 + 4 s1 s: [] p: 7 w: 1 USABLE RULES: { 1..39 } Removed DPs: #7 Number of SCCs: 2, DPs: 2 SCC { #4 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #a__quote s: [1] p: 0 w: x1 + 1 a__dbl1 s: [1] p: 7 w: x1 + 3 01 s: [] p: 3 w: 4 s s: [1] p: 5 w: x1 #a__from s: [] p: 0 w: 1 dbls s: [1] p: 3 w: x1 a__indx s: [2,1] p: 5 w: x1 + x2 + 5 a__from s: [] p: 2 w: x1 + 4 #a__indx s: [] p: 0 w: x1 dbl s: [1] p: 6 w: x1 indx s: [2,1] p: 5 w: x1 + x2 + 5 #a__dbl1 s: [1] p: 0 w: x1 a__dbl s: [1] p: 6 w: x1 a__sel1 s: [1,2] p: 0 w: x1 + x2 + 4 #a__dbls s: [] p: 0 w: 1 #mark s: [] p: 0 w: 0 0 s: [] p: 5 w: 1 a__quote s: [1] p: 2 w: x1 + 4 sel s: [] p: 1 w: x1 + x2 + 1 from s: [] p: 2 w: x1 + 4 #a__sel1 s: [1] p: 6 w: x1 nil s: [] p: 3 w: 1 dbl1 s: [1] p: 7 w: x1 + 3 #a__dbl s: [] p: 0 w: 1 #a__sel s: [] p: 0 w: x1 mark s: 1 a__sel s: [] p: 1 w: x1 + x2 + 1 a__dbls s: [1] p: 3 w: x1 quote s: [1] p: 2 w: x1 + 4 cons s: [] p: 2 w: max(x1 + 3, x2) sel1 s: [1,2] p: 0 w: x1 + x2 + 4 s1 s: [] p: 7 w: 1 USABLE RULES: { 1..39 } Removed DPs: #4 Number of SCCs: 1, DPs: 1 SCC { #1 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #a__quote s: [1] p: 0 w: x1 + 1 a__dbl1 s: [1] p: 7 w: x1 + 3 01 s: [] p: 3 w: 4 s s: [1] p: 5 w: x1 #a__from s: [] p: 0 w: 1 dbls s: [1] p: 3 w: x1 a__indx s: [2,1] p: 5 w: x1 + x2 + 5 a__from s: [] p: 2 w: x1 + 4 #a__indx s: [] p: 0 w: x1 dbl s: [1] p: 6 w: x1 indx s: [2,1] p: 5 w: x1 + x2 + 5 #a__dbl1 s: [1] p: 0 w: x1 a__dbl s: [1] p: 6 w: x1 a__sel1 s: [1,2] p: 0 w: x1 + x2 + 4 #a__dbls s: [] p: 0 w: 1 #mark s: [] p: 0 w: 0 0 s: [] p: 5 w: 1 a__quote s: [1] p: 2 w: x1 + 4 sel s: [] p: 1 w: x1 + x2 + 1 from s: [] p: 2 w: x1 + 4 #a__sel1 s: [1] p: 6 w: x1 nil s: [] p: 3 w: 1 dbl1 s: [1] p: 7 w: x1 + 3 #a__dbl s: [] p: 0 w: 1 #a__sel s: [1] p: 1 w: x1 mark s: 1 a__sel s: [] p: 1 w: x1 + x2 + 1 a__dbls s: [1] p: 3 w: x1 quote s: [1] p: 2 w: x1 + 4 cons s: [] p: 2 w: max(x1 + 3, x2) sel1 s: [1,2] p: 0 w: x1 + x2 + 4 s1 s: [] p: 7 w: 1 USABLE RULES: { 1..39 } Removed DPs: #1 Number of SCCs: 0, DPs: 0