/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: and(tt(),X) -> activate(X) 4: isNat(n__0()) -> tt() 5: isNat(n__length(V1)) -> isNatList(activate(V1)) 6: isNat(n__s(V1)) -> isNat(activate(V1)) 7: isNatIList(V) -> isNatList(activate(V)) 8: isNatIList(n__zeros()) -> tt() 9: isNatIList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2))) 10: isNatList(n__nil()) -> tt() 11: isNatList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatList(activate(V2))) 12: length(nil()) -> 0() 13: length(cons(N,L)) -> U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) 14: zeros() -> n__zeros() 15: 0() -> n__0() 16: length(X) -> n__length(X) 17: s(X) -> n__s(X) 18: cons(X1,X2) -> n__cons(X1,X2) 19: isNatIList(X) -> n__isNatIList(X) 20: nil() -> n__nil() 21: isNatList(X) -> n__isNatList(X) 22: isNat(X) -> n__isNat(X) 23: activate(n__zeros()) -> zeros() 24: activate(n__0()) -> 0() 25: activate(n__length(X)) -> length(activate(X)) 26: activate(n__s(X)) -> s(activate(X)) 27: activate(n__cons(X1,X2)) -> cons(activate(X1),X2) 28: activate(n__isNatIList(X)) -> isNatIList(X) 29: activate(n__nil()) -> nil() 30: activate(n__isNatList(X)) -> isNatList(X) 31: activate(n__isNat(X)) -> isNat(X) 32: activate(X) -> X Number of strict rules: 32 Direct POLO(bPol) ... removes: 8 5 10 7 12 isNatList w: x1 U11 w: x1 + x2 + 1 s w: x1 activate w: x1 and w: x1 + x2 n__zeros w: 0 isNatIList w: x1 + 1 zeros w: 0 n__nil w: 1 n__s w: x1 0 w: 0 n__isNatList w: x1 n__cons w: 2 * x1 + 2 * x2 nil w: 1 n__isNat w: x1 n__0 w: 0 n__length w: x1 + 1 isNat w: x1 cons w: 2 * x1 + 2 * x2 n__isNatIList w: x1 + 1 tt w: 0 length w: x1 + 1 Number of strict rules: 27 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__nil()) -> #nil() #5: #isNat(n__s(V1)) -> #isNat(activate(V1)) #6: #isNat(n__s(V1)) -> #activate(V1) #7: #length(cons(N,L)) -> #U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) #8: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNat(N)) #9: #length(cons(N,L)) -> #isNatList(activate(L)) #10: #length(cons(N,L)) -> #activate(L) #11: #length(cons(N,L)) -> #activate(L) #12: #isNatIList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatIList(activate(V2))) #13: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1)) #14: #isNatIList(n__cons(V1,V2)) -> #activate(V1) #15: #isNatIList(n__cons(V1,V2)) -> #activate(V2) #16: #isNatList(n__cons(V1,V2)) -> #and(isNat(activate(V1)),n__isNatList(activate(V2))) #17: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1)) #18: #isNatList(n__cons(V1,V2)) -> #activate(V1) #19: #isNatList(n__cons(V1,V2)) -> #activate(V2) #20: #activate(n__0()) -> #0() #21: #activate(n__zeros()) -> #zeros() #22: #activate(n__isNat(X)) -> #isNat(X) #23: #activate(n__isNatList(X)) -> #isNatList(X) #24: #activate(n__length(X)) -> #length(activate(X)) #25: #activate(n__length(X)) -> #activate(X) #26: #activate(n__isNatIList(X)) -> #isNatIList(X) #27: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2) #28: #activate(n__cons(X1,X2)) -> #activate(X1) #29: #activate(n__s(X)) -> #s(activate(X)) #30: #activate(n__s(X)) -> #activate(X) #31: #and(tt(),X) -> #activate(X) #32: #zeros() -> #cons(0(),n__zeros()) #33: #zeros() -> #0() Number of SCCs: 1, DPs: 25 SCC { #2 #3 #5..19 #22..26 #28 #30 #31 } POLO(Sum)... succeeded. #0 w: 0 isNatList w: 2 U11 w: 1 #cons w: 0 s w: 1 #isNat w: 3 activate w: x1 + 1 and w: x2 + 1 n__zeros w: 1 isNatIList w: 2 #activate w: 3 zeros w: 2 n__nil w: 0 n__s w: 0 0 w: 1 #zeros w: 0 n__isNatList w: 1 #isNatList w: 3 #s w: 0 n__cons w: 0 nil w: 1 n__isNat w: 2 #nil w: 0 n__0 w: 1 n__length w: 0 isNat w: 3 #U11 w: 3 cons w: 1 n__isNatIList w: 1 #isNatIList w: 3 tt w: 3 length w: 1 #length w: 3 #and w: x1 USABLE RULES: { 1..4 6 9 11 13..32 } Removed DPs: #8 Number of SCCs: 1, DPs: 24 SCC { #2 #3 #5..7 #9..19 #22..26 #28 #30 #31 } POLO(Sum)... succeeded. #0 w: 0 isNatList w: x1 + 2 U11 w: x2 + 4 #cons w: 0 s w: x1 #isNat w: x1 + 4 activate w: x1 and w: x2 n__zeros w: 0 isNatIList w: x1 + 2 #activate w: x1 + 3 zeros w: 0 n__nil w: 0 n__s w: x1 0 w: 0 #zeros w: 0 n__isNatList w: x1 + 2 #isNatList w: x1 + 5 #s w: 0 n__cons w: x1 + x2 nil w: 0 n__isNat w: x1 + 2 #nil w: 0 n__0 w: 0 n__length w: x1 + 4 isNat w: x1 + 2 #U11 w: x2 + 6 cons w: x1 + x2 n__isNatIList w: x1 + 2 #isNatIList w: x1 + 5 tt w: 2 length w: x1 + 4 #length w: x1 + 6 #and w: x1 + x2 + 1 USABLE RULES: { 1..4 6 9 11 13..32 } Removed DPs: #3 #6 #9..11 #13..15 #17..19 #22 #24 #25 Number of SCCs: 3, DPs: 10 SCC { #5 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #0 w: 0 isNatList w: 1 U11 w: max(x1 + 1, 0) #cons w: max(x2 - 1, 0) s w: max(x1 + 2, 0) #isNat w: max(x1 - 1, 0) activate w: max(x1, 0) and w: max(x1 + x2 - 3, 0) n__zeros w: 6 isNatIList w: 0 #activate w: max(x1 - 1, 0) zeros w: 6 n__nil w: 1 n__s w: max(x1 + 2, 0) 0 w: 1 #zeros w: 0 n__isNatList w: 1 #isNatList w: 0 #s w: 0 n__cons w: 1 nil w: 1 n__isNat w: 3 #nil w: 0 n__0 w: 1 n__length w: 2 isNat w: 3 #U11 w: 0 cons w: 1 n__isNatIList w: 0 #isNatIList w: max(x1 - 1, 0) tt w: 3 length w: 2 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..32 } Removed DPs: #5 Number of SCCs: 2, DPs: 9 SCC { #2 #7 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #0 w: 0 isNatList w: 1 U11 w: max(x1 + 1, 0) #cons w: max(x2 - 1, 0) s w: max(x1 + 2, 0) #isNat w: max(x1 - 1, 0) activate w: max(x1, 0) and w: max(x1 + x2 - 3, 0) n__zeros w: 6 isNatIList w: 0 #activate w: max(x1 - 1, 0) zeros w: 6 n__nil w: 1 n__s w: max(x1 + 2, 0) 0 w: 1 #zeros w: 0 n__isNatList w: 1 #isNatList w: 0 #s w: 0 n__cons w: 1 nil w: 1 n__isNat w: 3 #nil w: 0 n__0 w: 1 n__length w: 2 isNat w: 3 #U11 w: max(x1 - 2, 0) cons w: 1 n__isNatIList w: 0 #isNatIList w: max(x1 - 1, 0) tt w: 3 length w: 2 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..32 } Removed DPs: #2 Number of SCCs: 1, DPs: 7 SCC { #12 #16 #23 #26 #28 #30 #31 } POLO(Sum)... succeeded. #0 w: 0 isNatList w: 2 U11 w: 5 #cons w: 0 s w: 6 #isNat w: 4 activate w: 1 and w: 3 n__zeros w: 3 isNatIList w: x1 + 2 #activate w: x1 + 3 zeros w: 2 n__nil w: 3 n__s w: x1 + 7 0 w: 2 #zeros w: 0 n__isNatList w: 1 #isNatList w: 4 #s w: 0 n__cons w: x1 + 4 nil w: 2 n__isNat w: 1 #nil w: 0 n__0 w: 3 n__length w: 2 isNat w: 2 #U11 w: 7 cons w: 3 n__isNatIList w: 3 #isNatIList w: 6 tt w: 3 length w: x1 + 1 #length w: 6 #and w: x2 + 3 USABLE RULES: { } Removed DPs: #28 #30 Number of SCCs: 1, DPs: 5 SCC { #12 #16 #23 #26 #31 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.