/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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(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(X1,X2) 32: activate(n__0()) -> 0() 33: activate(n__length(X)) -> length(X) 34: activate(n__s(X)) -> s(X) 35: activate(n__cons(X1,X2)) -> cons(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(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(X1,X2) #5: #activate(n__nil()) -> #nil() #6: #activate(n__isNatList(X)) -> #isNatList(X) #7: #activate(n__and(X1,X2)) -> #and(X1,X2) #8: #isNatList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatList(activate(V2))) #9: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1)) #10: #isNatList(n__cons(V1,V2)) -> #activate(V1) #11: #isNatList(n__cons(V1,V2)) -> #activate(V2) #12: #isNatIList(V) -> #isNatList(activate(V)) #13: #isNatIList(V) -> #activate(V) #14: #isNatIList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2))) #15: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1)) #16: #isNatIList(n__cons(V1,V2)) -> #activate(V1) #17: #isNatIList(n__cons(V1,V2)) -> #activate(V2) #18: #activate(n__take(X1,X2)) -> #take(X1,X2) #19: #isNatList(n__take(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2))) #20: #isNatList(n__take(V1,V2)) -> #isNat(activate(V1)) #21: #isNatList(n__take(V1,V2)) -> #activate(V1) #22: #isNatList(n__take(V1,V2)) -> #activate(V2) #23: #activate(n__zeros()) -> #zeros() #24: #isNat(n__length(V1)) -> #isNatList(activate(V1)) #25: #isNat(n__length(V1)) -> #activate(V1) #26: #activate(n__isNat(X)) -> #isNat(X) #27: #activate(n__length(X)) -> #length(X) #28: #and(tt(),X) -> #activate(X) #29: #activate(n__s(X)) -> #s(X) #30: #take(0(),IL) -> #U21(isNatIList(IL)) #31: #take(0(),IL) -> #isNatIList(IL) #32: #activate(n__0()) -> #0() #33: #activate(n__isNatIList(X)) -> #isNatIList(X) #34: #length(cons(N,L)) -> #U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) #35: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNat(N)) #36: #length(cons(N,L)) -> #isNatList(activate(L)) #37: #length(cons(N,L)) -> #activate(L) #38: #length(cons(N,L)) -> #activate(L) #39: #U21(tt()) -> #nil() #40: #zeros() -> #cons(0(),n__zeros()) #41: #zeros() -> #0() #42: #isNat(n__s(V1)) -> #isNat(activate(V1)) #43: #isNat(n__s(V1)) -> #activate(V1) #44: #length(nil()) -> #0() #45: #U31(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL))) #46: #U31(tt(),IL,M,N) -> #activate(N) #47: #U31(tt(),IL,M,N) -> #activate(M) #48: #U31(tt(),IL,M,N) -> #activate(IL) #49: #take(s(M),cons(N,IL)) -> #U31(and(isNatIList(activate(IL)),n__and(isNat(M),n__isNat(N))),activate(IL),M,N) #50: #take(s(M),cons(N,IL)) -> #and(isNatIList(activate(IL)),n__and(isNat(M),n__isNat(N))) #51: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL)) #52: #take(s(M),cons(N,IL)) -> #activate(IL) #53: #take(s(M),cons(N,IL)) -> #isNat(M) #54: #take(s(M),cons(N,IL)) -> #activate(IL) Number of SCCs: 1, DPs: 42 SCC { #2 #3 #6..22 #24..28 #31 #33..38 #42 #43 #46..54 } POLO(Sum)... succeeded. #0 w: 0 U21 w: x1 + 1 isNatList w: x1 + 2 U11 w: x1 + x2 + 3 #cons w: 0 s w: x1 #isNat w: x1 + 1 #take w: x1 + x2 + 4 activate w: x1 take w: x1 + x2 + 5 and w: x2 n__zeros w: 1 isNatIList w: x1 + 3 #activate w: x1 zeros w: 1 n__nil w: 2 n__s w: x1 0 w: 0 #zeros w: 0 n__take w: x1 + x2 + 5 n__isNatList w: x1 + 2 #isNatList w: x1 + 2 #s w: 0 n__cons w: x1 + x2 nil w: 2 n__isNat w: x1 + 1 #nil w: 0 n__0 w: 0 n__length w: x1 + 4 isNat w: x1 + 1 #U11 w: x2 + 3 U31 w: x2 + x3 + x4 + 5 cons w: x1 + x2 n__isNatIList w: x1 + 3 #isNatIList w: x1 + 3 #U21 w: 0 tt w: 1 n__and w: x2 length w: x1 + 4 #length w: x1 + 3 #U31 w: x2 + x3 + x4 + 1 #and w: x2 USABLE RULES: { 1..41 } Removed DPs: #3 #9..13 #15..22 #24 #25 #27 #31 #35..38 #43 #46..54 Number of SCCs: 3, DPs: 9 SCC { #42 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.