/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: active(zeros()) -> mark(cons(0(),zeros())) 2: active(U11(tt(),L)) -> mark(s(length(L))) 3: active(and(tt(),X)) -> mark(X) 4: active(isNat(0())) -> mark(tt()) 5: active(isNat(length(V1))) -> mark(isNatList(V1)) 6: active(isNat(s(V1))) -> mark(isNat(V1)) 7: active(isNatIList(V)) -> mark(isNatList(V)) 8: active(isNatIList(zeros())) -> mark(tt()) 9: active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2))) 10: active(isNatList(nil())) -> mark(tt()) 11: active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2))) 12: active(length(nil())) -> mark(0()) 13: active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L)) 14: active(cons(X1,X2)) -> cons(active(X1),X2) 15: active(U11(X1,X2)) -> U11(active(X1),X2) 16: active(s(X)) -> s(active(X)) 17: active(length(X)) -> length(active(X)) 18: active(and(X1,X2)) -> and(active(X1),X2) 19: cons(mark(X1),X2) -> mark(cons(X1,X2)) 20: U11(mark(X1),X2) -> mark(U11(X1,X2)) 21: s(mark(X)) -> mark(s(X)) 22: length(mark(X)) -> mark(length(X)) 23: and(mark(X1),X2) -> mark(and(X1,X2)) 24: proper(zeros()) -> ok(zeros()) 25: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 26: proper(0()) -> ok(0()) 27: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) 28: proper(tt()) -> ok(tt()) 29: proper(s(X)) -> s(proper(X)) 30: proper(length(X)) -> length(proper(X)) 31: proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 32: proper(isNat(X)) -> isNat(proper(X)) 33: proper(isNatList(X)) -> isNatList(proper(X)) 34: proper(isNatIList(X)) -> isNatIList(proper(X)) 35: proper(nil()) -> ok(nil()) 36: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 37: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) 38: s(ok(X)) -> ok(s(X)) 39: length(ok(X)) -> ok(length(X)) 40: and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 41: isNat(ok(X)) -> ok(isNat(X)) 42: isNatList(ok(X)) -> ok(isNatList(X)) 43: isNatIList(ok(X)) -> ok(isNatIList(X)) 44: top(mark(X)) -> top(proper(X)) 45: top(ok(X)) -> top(active(X)) Number of strict rules: 45 Direct POLO(bPol) ... removes: 8 5 10 7 12 isNatList w: x1 U11 w: x1 + x2 + 1 s w: x1 top w: x1 and w: x1 + x2 isNatIList w: x1 + 1 zeros w: 0 proper w: x1 ok w: x1 0 w: 0 nil w: 1 mark w: x1 isNat w: x1 active w: x1 cons w: 2 * x1 + 2 * x2 tt w: 0 length w: x1 + 1 Number of strict rules: 40 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(U11(tt(),L)) -> #s(length(L)) #2: #active(U11(tt(),L)) -> #length(L) #3: #isNatIList(ok(X)) -> #isNatIList(X) #4: #proper(s(X)) -> #s(proper(X)) #5: #proper(s(X)) -> #proper(X) #6: #isNatList(ok(X)) -> #isNatList(X) #7: #isNat(ok(X)) -> #isNat(X) #8: #U11(ok(X1),ok(X2)) -> #U11(X1,X2) #9: #s(ok(X)) -> #s(X) #10: #active(isNat(s(V1))) -> #isNat(V1) #11: #and(ok(X1),ok(X2)) -> #and(X1,X2) #12: #active(length(cons(N,L))) -> #U11(and(isNatList(L),isNat(N)),L) #13: #active(length(cons(N,L))) -> #and(isNatList(L),isNat(N)) #14: #active(length(cons(N,L))) -> #isNatList(L) #15: #active(length(cons(N,L))) -> #isNat(N) #16: #active(isNatIList(cons(V1,V2))) -> #and(isNat(V1),isNatIList(V2)) #17: #active(isNatIList(cons(V1,V2))) -> #isNat(V1) #18: #active(isNatIList(cons(V1,V2))) -> #isNatIList(V2) #19: #active(isNatList(cons(V1,V2))) -> #and(isNat(V1),isNatList(V2)) #20: #active(isNatList(cons(V1,V2))) -> #isNat(V1) #21: #active(isNatList(cons(V1,V2))) -> #isNatList(V2) #22: #and(mark(X1),X2) -> #and(X1,X2) #23: #top(ok(X)) -> #top(active(X)) #24: #top(ok(X)) -> #active(X) #25: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2)) #26: #proper(and(X1,X2)) -> #proper(X1) #27: #proper(and(X1,X2)) -> #proper(X2) #28: #active(cons(X1,X2)) -> #cons(active(X1),X2) #29: #active(cons(X1,X2)) -> #active(X1) #30: #proper(length(X)) -> #length(proper(X)) #31: #proper(length(X)) -> #proper(X) #32: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #33: #proper(cons(X1,X2)) -> #proper(X1) #34: #proper(cons(X1,X2)) -> #proper(X2) #35: #U11(mark(X1),X2) -> #U11(X1,X2) #36: #length(ok(X)) -> #length(X) #37: #proper(isNatList(X)) -> #isNatList(proper(X)) #38: #proper(isNatList(X)) -> #proper(X) #39: #top(mark(X)) -> #top(proper(X)) #40: #top(mark(X)) -> #proper(X) #41: #length(mark(X)) -> #length(X) #42: #proper(isNatIList(X)) -> #isNatIList(proper(X)) #43: #proper(isNatIList(X)) -> #proper(X) #44: #proper(U11(X1,X2)) -> #U11(proper(X1),proper(X2)) #45: #proper(U11(X1,X2)) -> #proper(X1) #46: #proper(U11(X1,X2)) -> #proper(X2) #47: #active(length(X)) -> #length(active(X)) #48: #active(length(X)) -> #active(X) #49: #proper(isNat(X)) -> #isNat(proper(X)) #50: #proper(isNat(X)) -> #proper(X) #51: #cons(mark(X1),X2) -> #cons(X1,X2) #52: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #53: #s(mark(X)) -> #s(X) #54: #active(s(X)) -> #s(active(X)) #55: #active(s(X)) -> #active(X) #56: #active(zeros()) -> #cons(0(),zeros()) #57: #active(U11(X1,X2)) -> #U11(active(X1),X2) #58: #active(U11(X1,X2)) -> #active(X1) #59: #active(and(X1,X2)) -> #and(active(X1),X2) #60: #active(and(X1,X2)) -> #active(X1) Number of SCCs: 11, DPs: 31 SCC { #6 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 top w: 0 and w: 0 isNatIList w: 0 #top w: 0 zeros w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #isNatList w: x1 #s w: 0 nil w: 0 mark w: 0 #proper w: 0 isNat w: 0 #U11 w: 0 active w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #6 Number of SCCs: 10, DPs: 30 SCC { #3 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 top w: 0 and w: 0 isNatIList w: 0 #top w: 0 zeros w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: 0 #proper w: 0 isNat w: 0 #U11 w: 0 active w: 0 cons w: 0 #active w: 0 #isNatIList w: x1 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 9, DPs: 29 SCC { #7 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: x1 top w: 0 and w: 0 isNatIList w: 0 #top w: 0 zeros w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: 0 #proper w: 0 isNat w: 0 #U11 w: 0 active w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #7 Number of SCCs: 8, DPs: 28 SCC { #9 #53 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 top w: 0 and w: 0 isNatIList w: 0 #top w: 0 zeros w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: x1 nil w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 0 #U11 w: 0 active w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #9 #53 Number of SCCs: 7, DPs: 26 SCC { #36 #41 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 top w: 0 and w: 0 isNatIList w: 0 #top w: 0 zeros w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 0 #U11 w: 0 active w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: x1 #and w: 0 USABLE RULES: { } Removed DPs: #36 #41 Number of SCCs: 6, DPs: 24 SCC { #23 #39 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.