/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) 2: U12(tt(),V2) -> U13(isNat(activate(V2))) 3: U13(tt()) -> tt() 4: U21(tt(),V1) -> U22(isNat(activate(V1))) 5: U22(tt()) -> tt() 6: U31(tt(),N) -> activate(N) 7: U41(tt(),M,N) -> s(plus(activate(N),activate(M))) 8: and(tt(),X) -> activate(X) 9: isNat(n__0()) -> tt() 10: isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) 11: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 12: isNatKind(n__0()) -> tt() 13: isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) 14: isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 15: plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N) 16: plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) 17: 0() -> n__0() 18: plus(X1,X2) -> n__plus(X1,X2) 19: isNatKind(X) -> n__isNatKind(X) 20: s(X) -> n__s(X) 21: and(X1,X2) -> n__and(X1,X2) 22: isNat(X) -> n__isNat(X) 23: activate(n__0()) -> 0() 24: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) 25: activate(n__isNatKind(X)) -> isNatKind(X) 26: activate(n__s(X)) -> s(activate(X)) 27: activate(n__and(X1,X2)) -> and(activate(X1),X2) 28: activate(n__isNat(X)) -> isNat(X) 29: activate(X) -> X Number of strict rules: 29 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U12(tt(),V2) -> #U13(isNat(activate(V2))) #2: #U12(tt(),V2) -> #isNat(activate(V2)) #3: #U12(tt(),V2) -> #activate(V2) #4: #U31(tt(),N) -> #activate(N) #5: #isNatKind(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #6: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #7: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #8: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #9: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #10: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #11: #isNat(n__s(V1)) -> #activate(V1) #12: #isNat(n__s(V1)) -> #activate(V1) #13: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2)) #14: #activate(n__plus(X1,X2)) -> #activate(X1) #15: #activate(n__plus(X1,X2)) -> #activate(X2) #16: #activate(n__0()) -> #0() #17: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #18: #isNatKind(n__s(V1)) -> #activate(V1) #19: #activate(n__isNatKind(X)) -> #isNatKind(X) #20: #U41(tt(),M,N) -> #s(plus(activate(N),activate(M))) #21: #U41(tt(),M,N) -> #plus(activate(N),activate(M)) #22: #U41(tt(),M,N) -> #activate(N) #23: #U41(tt(),M,N) -> #activate(M) #24: #isNat(n__plus(V1,V2)) -> #U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) #25: #isNat(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #26: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #27: #isNat(n__plus(V1,V2)) -> #activate(V1) #28: #isNat(n__plus(V1,V2)) -> #activate(V2) #29: #isNat(n__plus(V1,V2)) -> #activate(V1) #30: #isNat(n__plus(V1,V2)) -> #activate(V2) #31: #activate(n__isNat(X)) -> #isNat(X) #32: #activate(n__and(X1,X2)) -> #and(activate(X1),X2) #33: #activate(n__and(X1,X2)) -> #activate(X1) #34: #activate(n__s(X)) -> #s(activate(X)) #35: #activate(n__s(X)) -> #activate(X) #36: #plus(N,s(M)) -> #U41(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) #37: #plus(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))) #38: #plus(N,s(M)) -> #and(isNat(M),n__isNatKind(M)) #39: #plus(N,s(M)) -> #isNat(M) #40: #U11(tt(),V1,V2) -> #U12(isNat(activate(V1)),activate(V2)) #41: #U11(tt(),V1,V2) -> #isNat(activate(V1)) #42: #U11(tt(),V1,V2) -> #activate(V1) #43: #U11(tt(),V1,V2) -> #activate(V2) #44: #and(tt(),X) -> #activate(X) #45: #plus(N,0()) -> #U31(and(isNat(N),n__isNatKind(N)),N) #46: #plus(N,0()) -> #and(isNat(N),n__isNatKind(N)) #47: #plus(N,0()) -> #isNat(N) #48: #U21(tt(),V1) -> #U22(isNat(activate(V1))) #49: #U21(tt(),V1) -> #isNat(activate(V1)) #50: #U21(tt(),V1) -> #activate(V1) Number of SCCs: 1, DPs: 45 SCC { #2..15 #17..19 #21..33 #35..47 #49 #50 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 isNatKind w: x1 + 2 U21 w: max(x1 + 2, x2 + 1) U11 w: max(x1 + 13, x2 + 15, x3 + 18) s w: x1 #isNat w: x1 + 6 activate w: x1 n__isNatKind w: x1 + 2 and w: max(x1 + 1, x2 + 3) #plus w: max(x1 + 14, x2 + 12) #activate w: x1 + 2 #U13 w: 0 U12 w: max(x1 + 10, x2 + 18) n__s w: x1 #U12 w: max(x1 + 7, x2 + 7) 0 w: 1 #s w: 0 n__isNat w: x1 + 5 n__plus w: max(x1 + 12, x2 + 13) n__0 w: 1 isNat w: x1 + 5 plus w: max(x1 + 12, x2 + 13) #U11 w: max(x1 + 1, x2 + 13, x3 + 9) U31 w: max(x2) #U41 w: max(x2 + 12, x3 + 14) #U21 w: max(x2 + 6) #U22 w: 0 tt w: 0 n__and w: max(x1 + 1, x2 + 3) U13 w: x1 + 6 U22 w: 2 #isNatKind w: x1 + 3 U41 w: max(x1 + 1, x2 + 13, x3 + 12) #U31 w: max(x2 + 3) #and w: max(x2 + 4) USABLE RULES: { 1..29 } Removed DPs: #2..8 #10..12 #14 #15 #18 #19 #22..33 #37..47 #50 Number of SCCs: 4, DPs: 6 SCC { #35 } POLO(Sum)... succeeded. #0 w: 0 isNatKind w: 3 U21 w: x1 + x2 U11 w: x3 + 6 s w: 1 #isNat w: 1 activate w: 2 n__isNatKind w: 4 and w: 1 #plus w: 1 #activate w: x1 + 1 #U13 w: 0 U12 w: 8 n__s w: x1 + 2 #U12 w: 1 0 w: 3 #s w: 0 n__isNat w: 4 n__plus w: x1 + 4 n__0 w: 4 isNat w: x1 + 3 plus w: 3 #U11 w: 0 U31 w: x2 + 4 #U41 w: 0 #U21 w: 1 #U22 w: 0 tt w: 8 n__and w: 2 U13 w: 8 U22 w: x1 + 4 #isNatKind w: 1 U41 w: x1 + x2 + 3 #U31 w: 1 #and w: 1 USABLE RULES: { 3 } Removed DPs: #35 Number of SCCs: 3, DPs: 5 SCC { #17 } POLO(Sum)... succeeded. #0 w: 0 isNatKind w: 1 U21 w: x1 + x2 U11 w: 1 s w: x1 + 1 #isNat w: 1 activate w: x1 n__isNatKind w: 1 and w: x2 #plus w: 1 #activate w: 1 #U13 w: 0 U12 w: 1 n__s w: x1 + 1 #U12 w: 1 0 w: 1 #s w: 0 n__isNat w: x1 + 1 n__plus w: x1 + x2 n__0 w: 1 isNat w: x1 + 1 plus w: x1 + x2 #U11 w: 0 U31 w: x2 #U41 w: 0 #U21 w: 1 #U22 w: 0 tt w: 1 n__and w: x2 U13 w: 1 U22 w: x1 #isNatKind w: x1 + 1 U41 w: x2 + x3 + 1 #U31 w: 1 #and w: 1 USABLE RULES: { 1..29 } Removed DPs: #17 Number of SCCs: 2, DPs: 4 SCC { #9 #49 } POLO(Sum)... succeeded. #0 w: 0 isNatKind w: 1 U21 w: x1 + x2 U11 w: 1 s w: x1 + 2 #isNat w: x1 + 1 activate w: x1 n__isNatKind w: 1 and w: x2 #plus w: 1 #activate w: 1 #U13 w: 0 U12 w: 1 n__s w: x1 + 2 #U12 w: 1 0 w: 1 #s w: 0 n__isNat w: x1 + 1 n__plus w: x1 + x2 n__0 w: 1 isNat w: x1 + 1 plus w: x1 + x2 #U11 w: 0 U31 w: x2 #U41 w: 0 #U21 w: x2 + 2 #U22 w: 0 tt w: 1 n__and w: x2 U13 w: 1 U22 w: x1 #isNatKind w: x1 + 1 U41 w: x2 + x3 + 2 #U31 w: 1 #and w: 1 USABLE RULES: { 1..29 } Removed DPs: #9 #49 Number of SCCs: 1, DPs: 2 SCC { #21 #36 } POLO(Sum)... succeeded. #0 w: 0 isNatKind w: 1 U21 w: x1 + x2 U11 w: x2 + 1 s w: x1 + 2 #isNat w: x1 + 1 activate w: x1 n__isNatKind w: 1 and w: x2 #plus w: x2 + 1 #activate w: 1 #U13 w: 0 U12 w: x1 n__s w: x1 + 2 #U12 w: 1 0 w: 1 #s w: 0 n__isNat w: x1 + 1 n__plus w: x1 + x2 n__0 w: 1 isNat w: x1 + 1 plus w: x1 + x2 #U11 w: 0 U31 w: x2 #U41 w: x2 + 2 #U21 w: x2 + 2 #U22 w: 0 tt w: 1 n__and w: x2 U13 w: 1 U22 w: x1 #isNatKind w: x1 + 1 U41 w: x2 + x3 + 2 #U31 w: 1 #and w: 1 USABLE RULES: { 1..29 } Removed DPs: #21 #36 Number of SCCs: 0, DPs: 0