/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__fib(N) -> a__sel(mark(N),a__fib1(s(0()),s(0()))) 2: a__fib1(X,Y) -> cons(mark(X),fib1(Y,add(X,Y))) 3: a__add(0(),X) -> mark(X) 4: a__add(s(X),Y) -> s(a__add(mark(X),mark(Y))) 5: a__sel(0(),cons(X,XS)) -> mark(X) 6: a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS)) 7: mark(fib(X)) -> a__fib(mark(X)) 8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) 9: mark(fib1(X1,X2)) -> a__fib1(mark(X1),mark(X2)) 10: mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) 11: mark(s(X)) -> s(mark(X)) 12: mark(0()) -> 0() 13: mark(cons(X1,X2)) -> cons(mark(X1),X2) 14: a__fib(X) -> fib(X) 15: a__sel(X1,X2) -> sel(X1,X2) 16: a__fib1(X1,X2) -> fib1(X1,X2) 17: a__add(X1,X2) -> add(X1,X2) Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__fib1(X,Y) -> #mark(X) #2: #a__sel(s(N),cons(X,XS)) -> #a__sel(mark(N),mark(XS)) #3: #a__sel(s(N),cons(X,XS)) -> #mark(N) #4: #a__sel(s(N),cons(X,XS)) -> #mark(XS) #5: #mark(cons(X1,X2)) -> #mark(X1) #6: #mark(fib1(X1,X2)) -> #a__fib1(mark(X1),mark(X2)) #7: #mark(fib1(X1,X2)) -> #mark(X1) #8: #mark(fib1(X1,X2)) -> #mark(X2) #9: #mark(s(X)) -> #mark(X) #10: #mark(fib(X)) -> #a__fib(mark(X)) #11: #mark(fib(X)) -> #mark(X) #12: #mark(add(X1,X2)) -> #a__add(mark(X1),mark(X2)) #13: #mark(add(X1,X2)) -> #mark(X1) #14: #mark(add(X1,X2)) -> #mark(X2) #15: #a__sel(0(),cons(X,XS)) -> #mark(X) #16: #a__add(0(),X) -> #mark(X) #17: #a__fib(N) -> #a__sel(mark(N),a__fib1(s(0()),s(0()))) #18: #a__fib(N) -> #mark(N) #19: #a__fib(N) -> #a__fib1(s(0()),s(0())) #20: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2)) #21: #mark(sel(X1,X2)) -> #mark(X1) #22: #mark(sel(X1,X2)) -> #mark(X2) #23: #a__add(s(X),Y) -> #a__add(mark(X),mark(Y)) #24: #a__add(s(X),Y) -> #mark(X) #25: #a__add(s(X),Y) -> #mark(Y) Number of SCCs: 1, DPs: 25 SCC { #1..25 } POLO(Sum)... POLO(max)... succeeded. s w: x1 #a__add w: max(x1 + 1, x2 + 1) a__add w: max(x1, x2) #a__fib1 w: max(x1 + 2) fib1 w: max(x1 + 2, x2 + 2) fib w: x1 + 7 #mark w: x1 + 1 0 w: 1 sel w: max(x1 + 5, x2 + 3) #a__sel w: max(x1 + 2, x2 + 3) mark w: x1 a__sel w: max(x1 + 5, x2 + 3) #a__fib w: x1 + 7 cons w: max(x1 + 1, x2) a__fib w: x1 + 7 add w: max(x1, x2) a__fib1 w: max(x1 + 2, x2 + 2) USABLE RULES: { 1..17 } Removed DPs: #1 #3..8 #10 #11 #15 #17..22 Number of SCCs: 2, DPs: 9 SCC { #2 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. s s: [1] p: 0 w: x1 #a__add s: [2] p: 0 w: max(x2) a__add s: [1,2] p: 1 w: max(x1, x2) #a__fib1 s: [2] p: 0 w: x2 fib1 s: [] p: 1 w: max(x1 + 2, x2 + 2) fib s: [] p: 1 w: 5 #mark s: [] p: 0 w: 1 0 s: [] p: 0 w: 0 sel s: [] p: 1 w: x2 + 2 #a__sel s: [1] p: 0 w: x1 mark s: 1 a__sel s: [] p: 1 w: x2 + 2 #a__fib s: [] p: 0 w: 0 cons s: [] p: 1 w: max(x1 + 1, x2) a__fib s: [] p: 1 w: 5 add s: [1,2] p: 1 w: max(x1, x2) a__fib1 s: [] p: 1 w: max(x1 + 2, x2 + 2) USABLE RULES: { 1..17 } Removed DPs: #2 Number of SCCs: 1, DPs: 8 SCC { #9 #12..14 #16 #23..25 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. s s: [1] p: 0 w: x1 #a__add s: [1,2] p: 3 w: max(x1, x2) a__add s: [1,2] p: 3 w: max(x1, x2) #a__fib1 s: [2] p: 0 w: x2 fib1 s: [1] p: 4 w: max(x1, x2) fib s: [] p: 2 w: x1 + 5 #mark s: 1 0 s: [] p: 1 w: 1 sel s: [1,2] p: 3 w: x1 + x2 + 2 #a__sel s: [1] p: 0 w: x1 mark s: 1 a__sel s: [1,2] p: 3 w: x1 + x2 + 2 #a__fib s: [] p: 0 w: 0 cons s: [1] p: 4 w: max(x1, x2) a__fib s: [] p: 2 w: x1 + 5 add s: [1,2] p: 3 w: max(x1, x2) a__fib1 s: [1] p: 4 w: max(x1, x2) USABLE RULES: { 1..17 } Removed DPs: #9 #13 #14 #16 #23..25 Number of SCCs: 0, DPs: 0