/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: zeros() -> cons(0(),n__zeros()) 2: U11(tt(),L) -> s(length(activate(L))) 3: U21(tt()) -> nil() 4: U31(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) 5: and(tt(),X) -> activate(X) 6: isNat(n__0()) -> tt() 7: isNat(n__length(V1)) -> isNatList(activate(V1)) 8: isNat(n__s(V1)) -> isNat(activate(V1)) 9: isNatIList(V) -> isNatList(activate(V)) 10: isNatIList(n__zeros()) -> tt() 11: isNatIList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2))) 12: isNatList(n__nil()) -> tt() 13: isNatList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatList(activate(V2))) 14: isNatList(n__take(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2))) 15: length(nil()) -> 0() 16: length(cons(N,L)) -> U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) 17: take(0(),IL) -> U21(isNatIList(IL)) 18: take(s(M),cons(N,IL)) -> U31(and(isNatIList(activate(IL)),n__and(n__isNat(M),n__isNat(N))),activate(IL),M,N) 19: zeros() -> n__zeros() 20: take(X1,X2) -> n__take(X1,X2) 21: 0() -> n__0() 22: length(X) -> n__length(X) 23: s(X) -> n__s(X) 24: cons(X1,X2) -> n__cons(X1,X2) 25: isNatIList(X) -> n__isNatIList(X) 26: nil() -> n__nil() 27: isNatList(X) -> n__isNatList(X) 28: isNat(X) -> n__isNat(X) 29: and(X1,X2) -> n__and(X1,X2) 30: activate(n__zeros()) -> zeros() 31: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) 32: activate(n__0()) -> 0() 33: activate(n__length(X)) -> length(activate(X)) 34: activate(n__s(X)) -> s(activate(X)) 35: activate(n__cons(X1,X2)) -> cons(activate(X1),X2) 36: activate(n__isNatIList(X)) -> isNatIList(X) 37: activate(n__nil()) -> nil() 38: activate(n__isNatList(X)) -> isNatList(X) 39: activate(n__isNat(X)) -> isNat(X) 40: activate(n__and(X1,X2)) -> and(activate(X1),X2) 41: activate(X) -> X Number of strict rules: 41 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U11(tt(),L) -> #s(length(activate(L))) #2: #U11(tt(),L) -> #length(activate(L)) #3: #U11(tt(),L) -> #activate(L) #4: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2) #5: #activate(n__cons(X1,X2)) -> #activate(X1) #6: #activate(n__nil()) -> #nil() #7: #activate(n__isNatList(X)) -> #isNatList(X) #8: #activate(n__and(X1,X2)) -> #and(activate(X1),X2) #9: #activate(n__and(X1,X2)) -> #activate(X1) #10: #isNatList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatList(activate(V2))) #11: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1)) #12: #isNatList(n__cons(V1,V2)) -> #activate(V1) #13: #isNatList(n__cons(V1,V2)) -> #activate(V2) #14: #isNatIList(V) -> #isNatList(activate(V)) #15: #isNatIList(V) -> #activate(V) #16: #isNatIList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2))) #17: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1)) #18: #isNatIList(n__cons(V1,V2)) -> #activate(V1) #19: #isNatIList(n__cons(V1,V2)) -> #activate(V2) #20: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2)) #21: #activate(n__take(X1,X2)) -> #activate(X1) #22: #activate(n__take(X1,X2)) -> #activate(X2) #23: #isNatList(n__take(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2))) #24: #isNatList(n__take(V1,V2)) -> #isNat(activate(V1)) #25: #isNatList(n__take(V1,V2)) -> #activate(V1) #26: #isNatList(n__take(V1,V2)) -> #activate(V2) #27: #activate(n__zeros()) -> #zeros() #28: #isNat(n__length(V1)) -> #isNatList(activate(V1)) #29: #isNat(n__length(V1)) -> #activate(V1) #30: #activate(n__isNat(X)) -> #isNat(X) #31: #activate(n__length(X)) -> #length(activate(X)) #32: #activate(n__length(X)) -> #activate(X) #33: #and(tt(),X) -> #activate(X) #34: #activate(n__s(X)) -> #s(activate(X)) #35: #activate(n__s(X)) -> #activate(X) #36: #take(0(),IL) -> #U21(isNatIList(IL)) #37: #take(0(),IL) -> #isNatIList(IL) #38: #activate(n__0()) -> #0() #39: #activate(n__isNatIList(X)) -> #isNatIList(X) #40: #length(cons(N,L)) -> #U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) #41: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNat(N)) #42: #length(cons(N,L)) -> #isNatList(activate(L)) #43: #length(cons(N,L)) -> #activate(L) #44: #length(cons(N,L)) -> #activate(L) #45: #U21(tt()) -> #nil() #46: #zeros() -> #cons(0(),n__zeros()) #47: #zeros() -> #0() #48: #isNat(n__s(V1)) -> #isNat(activate(V1)) #49: #isNat(n__s(V1)) -> #activate(V1) #50: #length(nil()) -> #0() #51: #U31(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL))) #52: #U31(tt(),IL,M,N) -> #activate(N) #53: #U31(tt(),IL,M,N) -> #activate(M) #54: #U31(tt(),IL,M,N) -> #activate(IL) #55: #take(s(M),cons(N,IL)) -> #U31(and(isNatIList(activate(IL)),n__and(n__isNat(M),n__isNat(N))),activate(IL),M,N) #56: #take(s(M),cons(N,IL)) -> #and(isNatIList(activate(IL)),n__and(n__isNat(M),n__isNat(N))) #57: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL)) #58: #take(s(M),cons(N,IL)) -> #activate(IL) #59: #take(s(M),cons(N,IL)) -> #activate(IL) Number of SCCs: 1, DPs: 47 SCC { #2 #3 #5 #7..26 #28..33 #35 #37 #39..44 #48 #49 #52..59 } POLO(Sum)... succeeded. #0 w: 0 U21 w: 1 isNatList w: x1 + 1 U11 w: x2 + 3 #cons w: 0 s w: x1 #isNat w: x1 + 1 #take w: x1 + x2 + 4 activate w: x1 take w: x1 + x2 + 4 and w: x1 + x2 n__zeros w: 1 isNatIList w: x1 + 2 #activate w: x1 + 1 zeros w: 1 n__nil w: 1 n__s w: x1 0 w: 0 #zeros w: 0 n__take w: x1 + x2 + 4 n__isNatList w: x1 + 1 #isNatList w: x1 + 2 #s w: 0 n__cons w: x1 + x2 nil w: 1 n__isNat w: x1 #nil w: 0 n__0 w: 0 n__length w: x1 + 3 isNat w: x1 #U11 w: x2 + 3 U31 w: x2 + x3 + x4 + 4 cons w: x1 + x2 n__isNatIList w: x1 + 2 #isNatIList w: x1 + 3 #U21 w: 0 tt w: 0 n__and w: x1 + x2 length w: x1 + 3 #length w: x1 + 3 #U31 w: x2 + x3 + x4 + 2 #and w: x2 + 1 USABLE RULES: { 1..41 } Removed DPs: #3 #11..15 #17..26 #28 #29 #31 #32 #37 #41..44 #52..59 Number of SCCs: 2, DPs: 14 SCC { #2 #40 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.