/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(half(0())) -> mark(0()) 11: active(half(s(0()))) -> mark(0()) 12: active(half(s(s(X)))) -> mark(s(half(X))) 13: active(half(dbl(X))) -> mark(X) 14: active(terms(X)) -> terms(active(X)) 15: active(cons(X1,X2)) -> cons(active(X1),X2) 16: active(recip(X)) -> recip(active(X)) 17: active(sqr(X)) -> sqr(active(X)) 18: active(s(X)) -> s(active(X)) 19: active(add(X1,X2)) -> add(active(X1),X2) 20: active(add(X1,X2)) -> add(X1,active(X2)) 21: active(dbl(X)) -> dbl(active(X)) 22: active(first(X1,X2)) -> first(active(X1),X2) 23: active(first(X1,X2)) -> first(X1,active(X2)) 24: active(half(X)) -> half(active(X)) 25: terms(mark(X)) -> mark(terms(X)) 26: cons(mark(X1),X2) -> mark(cons(X1,X2)) 27: recip(mark(X)) -> mark(recip(X)) 28: sqr(mark(X)) -> mark(sqr(X)) 29: s(mark(X)) -> mark(s(X)) 30: add(mark(X1),X2) -> mark(add(X1,X2)) 31: add(X1,mark(X2)) -> mark(add(X1,X2)) 32: dbl(mark(X)) -> mark(dbl(X)) 33: first(mark(X1),X2) -> mark(first(X1,X2)) 34: first(X1,mark(X2)) -> mark(first(X1,X2)) 35: half(mark(X)) -> mark(half(X)) 36: proper(terms(X)) -> terms(proper(X)) 37: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 38: proper(recip(X)) -> recip(proper(X)) 39: proper(sqr(X)) -> sqr(proper(X)) 40: proper(s(X)) -> s(proper(X)) 41: proper(0()) -> ok(0()) 42: proper(add(X1,X2)) -> add(proper(X1),proper(X2)) 43: proper(dbl(X)) -> dbl(proper(X)) 44: proper(first(X1,X2)) -> first(proper(X1),proper(X2)) 45: proper(nil()) -> ok(nil()) 46: proper(half(X)) -> half(proper(X)) 47: terms(ok(X)) -> ok(terms(X)) 48: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 49: recip(ok(X)) -> ok(recip(X)) 50: sqr(ok(X)) -> ok(sqr(X)) 51: s(ok(X)) -> ok(s(X)) 52: add(ok(X1),ok(X2)) -> ok(add(X1,X2)) 53: dbl(ok(X)) -> ok(dbl(X)) 54: first(ok(X1),ok(X2)) -> ok(first(X1,X2)) 55: half(ok(X)) -> ok(half(X)) 56: top(mark(X)) -> top(proper(X)) 57: top(ok(X)) -> top(active(X)) Number of strict rules: 57 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #proper(dbl(X)) -> #dbl(proper(X)) #2: #proper(dbl(X)) -> #proper(X) #3: #s(mark(X)) -> #s(X) #4: #half(mark(X)) -> #half(X) #5: #proper(half(X)) -> #half(proper(X)) #6: #proper(half(X)) -> #proper(X) #7: #proper(add(X1,X2)) -> #add(proper(X1),proper(X2)) #8: #proper(add(X1,X2)) -> #proper(X1) #9: #proper(add(X1,X2)) -> #proper(X2) #10: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #11: #proper(cons(X1,X2)) -> #proper(X1) #12: #proper(cons(X1,X2)) -> #proper(X2) #13: #terms(ok(X)) -> #terms(X) #14: #dbl(ok(X)) -> #dbl(X) #15: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #16: #proper(recip(X)) -> #recip(proper(X)) #17: #proper(recip(X)) -> #proper(X) #18: #half(ok(X)) -> #half(X) #19: #proper(s(X)) -> #s(proper(X)) #20: #proper(s(X)) -> #proper(X) #21: #s(ok(X)) -> #s(X) #22: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z)) #23: #active(first(s(X),cons(Y,Z))) -> #first(X,Z) #24: #top(ok(X)) -> #top(active(X)) #25: #top(ok(X)) -> #active(X) #26: #active(half(X)) -> #half(active(X)) #27: #active(half(X)) -> #active(X) #28: #active(first(X1,X2)) -> #first(X1,active(X2)) #29: #active(first(X1,X2)) -> #active(X2) #30: #active(half(s(s(X)))) -> #s(half(X)) #31: #active(half(s(s(X)))) -> #half(X) #32: #add(X1,mark(X2)) -> #add(X1,X2) #33: #top(mark(X)) -> #top(proper(X)) #34: #top(mark(X)) -> #proper(X) #35: #active(terms(X)) -> #terms(active(X)) #36: #active(terms(X)) -> #active(X) #37: #add(mark(X1),X2) -> #add(X1,X2) #38: #add(ok(X1),ok(X2)) -> #add(X1,X2) #39: #recip(ok(X)) -> #recip(X) #40: #terms(mark(X)) -> #terms(X) #41: #active(add(X1,X2)) -> #add(X1,active(X2)) #42: #active(add(X1,X2)) -> #active(X2) #43: #active(add(s(X),Y)) -> #s(add(X,Y)) #44: #active(add(s(X),Y)) -> #add(X,Y) #45: #proper(sqr(X)) -> #sqr(proper(X)) #46: #proper(sqr(X)) -> #proper(X) #47: #first(mark(X1),X2) -> #first(X1,X2) #48: #active(dbl(s(X))) -> #s(s(dbl(X))) #49: #active(dbl(s(X))) -> #s(dbl(X)) #50: #active(dbl(s(X))) -> #dbl(X) #51: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2)) #52: #proper(first(X1,X2)) -> #proper(X1) #53: #proper(first(X1,X2)) -> #proper(X2) #54: #sqr(mark(X)) -> #sqr(X) #55: #active(first(X1,X2)) -> #first(active(X1),X2) #56: #active(first(X1,X2)) -> #active(X1) #57: #first(X1,mark(X2)) -> #first(X1,X2) #58: #recip(mark(X)) -> #recip(X) #59: #active(sqr(X)) -> #sqr(active(X)) #60: #active(sqr(X)) -> #active(X) #61: #dbl(mark(X)) -> #dbl(X) #62: #active(add(X1,X2)) -> #add(active(X1),X2) #63: #active(add(X1,X2)) -> #active(X1) #64: #cons(mark(X1),X2) -> #cons(X1,X2) #65: #proper(terms(X)) -> #terms(proper(X)) #66: #proper(terms(X)) -> #proper(X) #67: #active(dbl(X)) -> #dbl(active(X)) #68: #active(dbl(X)) -> #active(X) #69: #active(recip(X)) -> #recip(active(X)) #70: #active(recip(X)) -> #active(X) #71: #active(sqr(s(X))) -> #s(add(sqr(X),dbl(X))) #72: #active(sqr(s(X))) -> #add(sqr(X),dbl(X)) #73: #active(sqr(s(X))) -> #sqr(X) #74: #active(sqr(s(X))) -> #dbl(X) #75: #active(terms(N)) -> #cons(recip(sqr(N)),terms(s(N))) #76: #active(terms(N)) -> #recip(sqr(N)) #77: #active(terms(N)) -> #sqr(N) #78: #active(terms(N)) -> #terms(s(N)) #79: #active(terms(N)) -> #s(N) #80: #first(ok(X1),ok(X2)) -> #first(X1,X2) #81: #active(cons(X1,X2)) -> #cons(active(X1),X2) #82: #active(cons(X1,X2)) -> #active(X1) #83: #sqr(ok(X)) -> #sqr(X) #84: #active(s(X)) -> #s(active(X)) #85: #active(s(X)) -> #active(X) Number of SCCs: 12, DPs: 45 SCC { #14 #61 } 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 #half w: 0 half 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 #61 Number of SCCs: 11, DPs: 43 SCC { #4 #18 } 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 #half w: x1 half 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 #18 Number of SCCs: 10, DPs: 41 SCC { #39 #58 } 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 #half w: 0 half 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: #39 #58 Number of SCCs: 9, DPs: 39 SCC { #3 #21 } 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 #half w: 0 half 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: #3 #21 Number of SCCs: 8, DPs: 37 SCC { #54 #83 } 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 #half w: 0 half 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: #54 #83 Number of SCCs: 7, DPs: 35 SCC { #13 #40 } 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 #half w: 0 half 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: #13 #40 Number of SCCs: 6, DPs: 33 SCC { #24 #33 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #cons s: [2] p: 0 s s: [1] p: 3 recip s: 1 #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 #half s: [] p: 0 half s: [1] p: 6 #sqr s: [] p: 0 proper s: 1 ok s: 1 0 s: [] p: 3 #s s: [] p: 0 #first s: [] p: 0 nil s: [] p: 4 mark s: [1] p: 3 first s: [1,2] p: 7 #proper s: [] p: 0 active s: 1 cons s: [1] p: 3 #active s: [] p: 0 #add s: [] p: 0 add s: [2,1] p: 4 sqr s: [1] p: 5 terms s: [1] p: 6 USABLE RULES: { 1..55 } Removed DPs: #33 Number of SCCs: 6, DPs: 32 SCC { #24 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: x1 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 2 ok w: x1 + 2 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 first w: x2 + 1 #proper w: 0 active w: x1 + 1 cons w: x1 #active w: 0 #add w: 0 add w: x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 1..55 } Removed DPs: #24 Number of SCCs: 5, DPs: 31 SCC { #15 #64 } POLO(Sum)... succeeded. #cons w: x2 s w: x1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: x1 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 2 ok w: x1 + 2 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 first w: x2 + 1 #proper w: 0 active w: x1 + 1 cons w: x1 #active w: 0 #add w: 0 add w: x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 1..55 } Removed DPs: #15 Number of SCCs: 5, DPs: 30 SCC { #64 } POLO(Sum)... succeeded. #cons w: x1 s w: x1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 2 ok w: x1 + 3 0 w: 0 #s w: 0 #first w: 0 nil w: 3 mark w: x1 + 1 first w: x2 + 1 #proper w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #add w: 0 add w: x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 35 55 } Removed DPs: #64 Number of SCCs: 4, DPs: 29 SCC { #32 #37 #38 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 2 ok w: x1 + 3 0 w: 0 #s w: 0 #first w: 0 nil w: 3 mark w: x1 + 1 first w: x2 + 1 #proper w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #add w: x1 add w: x2 + 1 sqr w: 1 terms w: x1 + 1 USABLE RULES: { 35 55 } Removed DPs: #37 #38 Number of SCCs: 4, DPs: 27 SCC { #32 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 recip w: x1 + 1 #recip w: 0 dbl w: x1 + 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 2 ok w: x1 + 3 0 w: 0 #s w: 0 #first w: 0 nil w: 3 mark w: x1 + 1 first w: x2 + 1 #proper w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #add w: x2 add w: x2 + 1 sqr w: 1 terms w: x1 + 1 USABLE RULES: { 35 55 } Removed DPs: #32 Number of SCCs: 3, DPs: 26 SCC { #47 #57 #80 } POLO(Sum)... succeeded. #cons w: 0 s w: 2 recip w: x1 + 1 #recip w: 0 dbl w: 2 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: x1 + 1 ok w: x1 + 2 0 w: 1 #s w: 0 #first w: x2 nil w: 1 mark w: x1 + 4 first w: 2 #proper w: 0 active w: 1 cons w: x1 + x2 + 1 #active w: 0 #add w: 0 add w: x1 + 2 sqr w: x1 + 1 terms w: 2 USABLE RULES: { } Removed DPs: #57 #80 Number of SCCs: 3, DPs: 24 SCC { #47 } POLO(Sum)... succeeded. #cons w: 0 s w: 2 recip w: 0 #recip w: 0 dbl w: 1 top w: 0 #dbl w: 0 #terms w: 0 #top w: 0 #half w: 0 half w: 2 #sqr w: 0 proper w: 1 ok w: x1 + 1 0 w: 1 #s w: 0 #first w: x1 nil w: 1 mark w: x1 + 6 first w: 0 #proper w: 0 active w: x1 + 1 cons w: 3 #active w: 0 #add w: 0 add w: 2 sqr w: x1 + 1 terms w: x1 USABLE RULES: { } Removed DPs: #47 Number of SCCs: 2, DPs: 23 SCC { #27 #29 #36 #42 #56 #60 #63 #68 #70 #82 #85 } 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 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: 1 ok w: 2 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 + 5 first w: x1 + x2 + 1 #proper w: 0 active w: x1 cons w: x1 + x2 + 3 #active w: x1 #add w: 0 add w: x1 + x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 25 29 32 35 47 51 53 55 } Removed DPs: #27 #29 #36 #42 #56 #60 #63 #68 #70 #82 #85 Number of SCCs: 1, DPs: 12 SCC { #2 #6 #8 #9 #11 #12 #17 #20 #46 #52 #53 #66 } 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 #half w: 0 half w: x1 + 1 #sqr w: 0 proper w: 1 ok w: 2 0 w: 0 #s w: 0 #first w: 0 nil w: 1 mark w: x1 + 5 first w: x1 + x2 + 1 #proper w: x1 active w: x1 cons w: x1 + x2 + 3 #active w: 0 #add w: 0 add w: x1 + x2 + 1 sqr w: x1 + 1 terms w: x1 + 1 USABLE RULES: { 25 29 32 35 47 51 53 55 } Removed DPs: #2 #6 #8 #9 #11 #12 #17 #20 #46 #52 #53 #66 Number of SCCs: 0, DPs: 0