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