/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) 2: active(sqr(0())) -> mark(0()) 3: active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) 4: active(dbl(0())) -> mark(0()) 5: active(dbl(s(X))) -> mark(s(s(dbl(X)))) 6: active(add(0(),X)) -> mark(X) 7: active(add(s(X),Y)) -> mark(s(add(X,Y))) 8: active(first(0(),X)) -> mark(nil()) 9: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) 10: active(terms(X)) -> terms(active(X)) 11: active(cons(X1,X2)) -> cons(active(X1),X2) 12: active(recip(X)) -> recip(active(X)) 13: active(sqr(X)) -> sqr(active(X)) 14: active(s(X)) -> s(active(X)) 15: active(add(X1,X2)) -> add(active(X1),X2) 16: active(add(X1,X2)) -> add(X1,active(X2)) 17: active(dbl(X)) -> dbl(active(X)) 18: active(first(X1,X2)) -> first(active(X1),X2) 19: active(first(X1,X2)) -> first(X1,active(X2)) 20: terms(mark(X)) -> mark(terms(X)) 21: cons(mark(X1),X2) -> mark(cons(X1,X2)) 22: recip(mark(X)) -> mark(recip(X)) 23: sqr(mark(X)) -> mark(sqr(X)) 24: s(mark(X)) -> mark(s(X)) 25: add(mark(X1),X2) -> mark(add(X1,X2)) 26: add(X1,mark(X2)) -> mark(add(X1,X2)) 27: dbl(mark(X)) -> mark(dbl(X)) 28: first(mark(X1),X2) -> mark(first(X1,X2)) 29: first(X1,mark(X2)) -> mark(first(X1,X2)) 30: proper(terms(X)) -> terms(proper(X)) 31: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 32: proper(recip(X)) -> recip(proper(X)) 33: proper(sqr(X)) -> sqr(proper(X)) 34: proper(s(X)) -> s(proper(X)) 35: proper(0()) -> ok(0()) 36: proper(add(X1,X2)) -> add(proper(X1),proper(X2)) 37: proper(dbl(X)) -> dbl(proper(X)) 38: proper(first(X1,X2)) -> first(proper(X1),proper(X2)) 39: proper(nil()) -> ok(nil()) 40: terms(ok(X)) -> ok(terms(X)) 41: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 42: recip(ok(X)) -> ok(recip(X)) 43: sqr(ok(X)) -> ok(sqr(X)) 44: s(ok(X)) -> ok(s(X)) 45: add(ok(X1),ok(X2)) -> ok(add(X1,X2)) 46: dbl(ok(X)) -> ok(dbl(X)) 47: first(ok(X1),ok(X2)) -> ok(first(X1,X2)) 48: top(mark(X)) -> top(proper(X)) 49: top(ok(X)) -> top(active(X)) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #sqr(ok(X)) -> #sqr(X) #2: #first(X1,mark(X2)) -> #first(X1,X2) #3: #dbl(ok(X)) -> #dbl(X) #4: #recip(ok(X)) -> #recip(X) #5: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #6: #proper(dbl(X)) -> #dbl(proper(X)) #7: #proper(dbl(X)) -> #proper(X) #8: #first(ok(X1),ok(X2)) -> #first(X1,X2) #9: #top(mark(X)) -> #top(proper(X)) #10: #top(mark(X)) -> #proper(X) #11: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2)) #12: #proper(first(X1,X2)) -> #proper(X1) #13: #proper(first(X1,X2)) -> #proper(X2) #14: #terms(ok(X)) -> #terms(X) #15: #active(sqr(X)) -> #sqr(active(X)) #16: #active(sqr(X)) -> #active(X) #17: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z)) #18: #active(first(s(X),cons(Y,Z))) -> #first(X,Z) #19: #active(cons(X1,X2)) -> #cons(active(X1),X2) #20: #active(cons(X1,X2)) -> #active(X1) #21: #s(mark(X)) -> #s(X) #22: #sqr(mark(X)) -> #sqr(X) #23: #add(ok(X1),ok(X2)) -> #add(X1,X2) #24: #active(recip(X)) -> #recip(active(X)) #25: #active(recip(X)) -> #active(X) #26: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #27: #proper(cons(X1,X2)) -> #proper(X1) #28: #proper(cons(X1,X2)) -> #proper(X2) #29: #active(s(X)) -> #s(active(X)) #30: #active(s(X)) -> #active(X) #31: #proper(terms(X)) -> #terms(proper(X)) #32: #proper(terms(X)) -> #proper(X) #33: #top(ok(X)) -> #top(active(X)) #34: #top(ok(X)) -> #active(X) #35: #add(mark(X1),X2) -> #add(X1,X2) #36: #terms(mark(X)) -> #terms(X) #37: #active(add(s(X),Y)) -> #s(add(X,Y)) #38: #active(add(s(X),Y)) -> #add(X,Y) #39: #active(terms(X)) -> #terms(active(X)) #40: #active(terms(X)) -> #active(X) #41: #proper(sqr(X)) -> #sqr(proper(X)) #42: #proper(sqr(X)) -> #proper(X) #43: #active(dbl(s(X))) -> #s(s(dbl(X))) #44: #active(dbl(s(X))) -> #s(dbl(X)) #45: #active(dbl(s(X))) -> #dbl(X) #46: #s(ok(X)) -> #s(X) #47: #first(mark(X1),X2) -> #first(X1,X2) #48: #recip(mark(X)) -> #recip(X) #49: #proper(s(X)) -> #s(proper(X)) #50: #proper(s(X)) -> #proper(X) #51: #dbl(mark(X)) -> #dbl(X) #52: #active(dbl(X)) -> #dbl(active(X)) #53: #active(dbl(X)) -> #active(X) #54: #proper(recip(X)) -> #recip(proper(X)) #55: #proper(recip(X)) -> #proper(X) #56: #active(first(X1,X2)) -> #first(X1,active(X2)) #57: #active(first(X1,X2)) -> #active(X2) #58: #add(X1,mark(X2)) -> #add(X1,X2) #59: #proper(add(X1,X2)) -> #add(proper(X1),proper(X2)) #60: #proper(add(X1,X2)) -> #proper(X1) #61: #proper(add(X1,X2)) -> #proper(X2) #62: #cons(mark(X1),X2) -> #cons(X1,X2) #63: #active(add(X1,X2)) -> #add(X1,active(X2)) #64: #active(add(X1,X2)) -> #active(X2) #65: #active(sqr(s(X))) -> #s(add(sqr(X),dbl(X))) #66: #active(sqr(s(X))) -> #add(sqr(X),dbl(X)) #67: #active(sqr(s(X))) -> #sqr(X) #68: #active(sqr(s(X))) -> #dbl(X) #69: #active(terms(N)) -> #cons(recip(sqr(N)),terms(s(N))) #70: #active(terms(N)) -> #recip(sqr(N)) #71: #active(terms(N)) -> #sqr(N) #72: #active(terms(N)) -> #terms(s(N)) #73: #active(terms(N)) -> #s(N) #74: #active(add(X1,X2)) -> #add(active(X1),X2) #75: #active(add(X1,X2)) -> #active(X1) #76: #active(first(X1,X2)) -> #first(active(X1),X2) #77: #active(first(X1,X2)) -> #active(X1) Number of SCCs: 11, DPs: 41 SCC { #3 #51 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: 0 #recip w: 0 dbl w: 0 top w: 0 #dbl w: x1 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 mark w: x1 + 1 first w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #3 #51 Number of SCCs: 10, DPs: 39 SCC { #4 #48 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: 0 #recip w: x1 dbl w: 0 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 mark w: x1 + 1 first w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #4 #48 Number of SCCs: 9, DPs: 37 SCC { #1 #22 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: 0 #recip w: 0 dbl w: 0 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: x1 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 mark w: x1 + 1 first w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #1 #22 Number of SCCs: 8, DPs: 35 SCC { #14 #36 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: 0 #recip w: 0 dbl w: 0 top w: 0 #dbl w: 0 #terms w: x1 #top w: 0 #sqr w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 mark w: x1 + 1 first w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #14 #36 Number of SCCs: 7, DPs: 33 SCC { #21 #46 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: 0 #recip w: 0 dbl w: 0 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: x1 #first w: 0 nil w: 0 mark w: x1 + 1 first w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 #add w: 0 add w: 0 sqr w: 0 terms w: 0 USABLE RULES: { } Removed DPs: #21 #46 Number of SCCs: 6, DPs: 31 SCC { #9 #33 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #cons s: [2] p: 0 s s: [1] p: 2 recip s: [1] p: 7 #recip s: [] p: 0 dbl s: [1] p: 5 top s: [] p: 0 #dbl s: [] p: 0 #terms s: [] p: 0 #top s: [1] p: 0 #sqr s: [] p: 0 proper s: 1 ok s: 1 0 s: [] p: 2 #s s: [] p: 0 #first s: [2] p: 0 nil s: [] p: 3 mark s: [1] p: 0 first s: [1,2] p: 4 #proper s: [] p: 0 active s: 1 cons s: [1] p: 7 #active s: [] p: 0 #add s: [2] p: 0 add s: [1,2] p: 4 sqr s: [1] p: 5 terms s: [1] p: 8 USABLE RULES: { 1..47 } Removed DPs: #9 Number of SCCs: 6, DPs: 30 SCC { #33 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: x1 #sqr w: 0 proper w: 3 ok w: x1 + 2 0 w: 1 #s w: 0 #first w: 0 nil w: 1 mark w: 0 first w: x1 #proper w: 0 active w: x1 + 1 cons w: x2 #active w: 0 #add w: 0 add w: x2 sqr w: x1 terms w: x1 USABLE RULES: { 1..47 } Removed DPs: #33 Number of SCCs: 5, DPs: 29 SCC { #5 #62 } POLO(Sum)... succeeded. #cons w: x2 s w: x1 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: x1 #sqr w: 0 proper w: 3 ok w: x1 + 2 0 w: 1 #s w: 0 #first w: 0 nil w: 1 mark w: 0 first w: x1 #proper w: 0 active w: x1 + 1 cons w: x2 #active w: 0 #add w: 0 add w: x2 sqr w: x1 terms w: x1 USABLE RULES: { 1..47 } Removed DPs: #5 Number of SCCs: 5, DPs: 28 SCC { #62 } POLO(Sum)... succeeded. #cons w: x1 s w: 0 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 2 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 + 1 first w: x1 + x2 #proper w: 0 active w: x1 cons w: x2 #active w: 0 #add w: 0 add w: x1 + x2 sqr w: x1 terms w: x1 USABLE RULES: { 20 22 23 25..29 35 39 40 42 43 45..47 } Removed DPs: #62 Number of SCCs: 4, DPs: 27 SCC { #23 #35 #58 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 2 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 + 1 first w: x1 + x2 #proper w: 0 active w: x1 cons w: x2 #active w: 0 #add w: x2 add w: x1 + x2 sqr w: x1 terms w: x1 USABLE RULES: { 20 22 23 25..29 35 39 40 42 43 45..47 } Removed DPs: #23 #58 Number of SCCs: 4, DPs: 25 SCC { #35 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 2 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 + 1 first w: x1 + x2 #proper w: 0 active w: x1 cons w: x2 #active w: 0 #add w: x1 add w: x1 + x2 sqr w: x1 terms w: x1 USABLE RULES: { 20 22 23 25..29 35 39 40 42 43 45..47 } Removed DPs: #35 Number of SCCs: 3, DPs: 24 SCC { #2 #8 #47 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 recip w: x1 #recip w: 0 dbl w: x1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: 2 ok w: x1 + 1 0 w: 0 #s w: 0 #first w: x1 + x2 nil w: 1 mark w: x1 + 1 first w: x1 + x2 #proper w: 0 active w: x1 cons w: x2 #active w: 0 #add w: 0 add w: x1 + x2 sqr w: x1 terms w: x1 USABLE RULES: { 20 22 23 25..29 35 39 40 42 43 45..47 } Removed DPs: #2 #8 #47 Number of SCCs: 2, DPs: 21 SCC { #16 #20 #25 #30 #40 #53 #57 #64 #75 #77 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 + 1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: x1 + 1 ok w: 1 0 w: 0 #s w: 0 #first w: 0 nil w: 0 mark w: 2 first w: x1 + x2 + 1 #proper w: 0 active w: 1 cons w: x1 + 1 #active w: x1 #add w: 0 add w: x1 + x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 20..23 25..29 35 39..43 45 47 } Removed DPs: #16 #20 #25 #30 #40 #53 #57 #64 #75 #77 Number of SCCs: 1, DPs: 11 SCC { #7 #12 #13 #27 #28 #32 #42 #50 #55 #60 #61 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 + 1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #sqr w: 0 proper w: x1 ok w: 1 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: 2 first w: x1 + x2 + 1 #proper w: x1 active w: 1 cons w: x1 + x2 + 1 #active w: 0 #add w: 0 add w: x1 + x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 20..23 25..27 29 39..43 45 47 } Removed DPs: #7 #12 #13 #27 #28 #32 #42 #50 #55 #60 #61 Number of SCCs: 0, DPs: 0