/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(isNatKind(activate(V1)),activate(V1),activate(V2)) 2: U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) 3: U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) 4: U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2)) 5: U15(tt(),V2) -> U16(isNat(activate(V2))) 6: U16(tt()) -> tt() 7: U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) 8: U22(tt(),V1) -> U23(isNat(activate(V1))) 9: U23(tt()) -> tt() 10: U31(tt(),V2) -> U32(isNatKind(activate(V2))) 11: U32(tt()) -> tt() 12: U41(tt()) -> tt() 13: U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N)) 14: U52(tt(),N) -> activate(N) 15: U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) 16: U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) 17: U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) 18: U64(tt(),M,N) -> s(plus(activate(N),activate(M))) 19: isNat(n__0()) -> tt() 20: isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) 21: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 22: isNatKind(n__0()) -> tt() 23: isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) 24: isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) 25: plus(N,0()) -> U51(isNat(N),N) 26: plus(N,s(M)) -> U61(isNat(M),M,N) 27: 0() -> n__0() 28: plus(X1,X2) -> n__plus(X1,X2) 29: s(X) -> n__s(X) 30: activate(n__0()) -> 0() 31: activate(n__plus(X1,X2)) -> plus(X1,X2) 32: activate(n__s(X)) -> s(X) 33: activate(X) -> X Number of strict rules: 33 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U12(tt(),V1,V2) -> #U13(isNatKind(activate(V2)),activate(V1),activate(V2)) #2: #U12(tt(),V1,V2) -> #isNatKind(activate(V2)) #3: #U12(tt(),V1,V2) -> #activate(V2) #4: #U12(tt(),V1,V2) -> #activate(V1) #5: #U12(tt(),V1,V2) -> #activate(V2) #6: #U51(tt(),N) -> #U52(isNatKind(activate(N)),activate(N)) #7: #U51(tt(),N) -> #isNatKind(activate(N)) #8: #U51(tt(),N) -> #activate(N) #9: #U51(tt(),N) -> #activate(N) #10: #isNatKind(n__s(V1)) -> #U41(isNatKind(activate(V1))) #11: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #12: #isNatKind(n__s(V1)) -> #activate(V1) #13: #isNatKind(n__plus(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V2)) #14: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #15: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #16: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #17: #activate(n__plus(X1,X2)) -> #plus(X1,X2) #18: #U52(tt(),N) -> #activate(N) #19: #activate(n__0()) -> #0() #20: #plus(N,0()) -> #U51(isNat(N),N) #21: #plus(N,0()) -> #isNat(N) #22: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2)) #23: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #24: #isNat(n__plus(V1,V2)) -> #activate(V1) #25: #isNat(n__plus(V1,V2)) -> #activate(V1) #26: #isNat(n__plus(V1,V2)) -> #activate(V2) #27: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1)) #28: #U21(tt(),V1) -> #isNatKind(activate(V1)) #29: #U21(tt(),V1) -> #activate(V1) #30: #U21(tt(),V1) -> #activate(V1) #31: #U31(tt(),V2) -> #U32(isNatKind(activate(V2))) #32: #U31(tt(),V2) -> #isNatKind(activate(V2)) #33: #U31(tt(),V2) -> #activate(V2) #34: #U15(tt(),V2) -> #U16(isNat(activate(V2))) #35: #U15(tt(),V2) -> #isNat(activate(V2)) #36: #U15(tt(),V2) -> #activate(V2) #37: #U63(tt(),M,N) -> #U64(isNatKind(activate(N)),activate(M),activate(N)) #38: #U63(tt(),M,N) -> #isNatKind(activate(N)) #39: #U63(tt(),M,N) -> #activate(N) #40: #U63(tt(),M,N) -> #activate(M) #41: #U63(tt(),M,N) -> #activate(N) #42: #activate(n__s(X)) -> #s(X) #43: #plus(N,s(M)) -> #U61(isNat(M),M,N) #44: #plus(N,s(M)) -> #isNat(M) #45: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #46: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #47: #isNat(n__s(V1)) -> #activate(V1) #48: #isNat(n__s(V1)) -> #activate(V1) #49: #U62(tt(),M,N) -> #U63(isNat(activate(N)),activate(M),activate(N)) #50: #U62(tt(),M,N) -> #isNat(activate(N)) #51: #U62(tt(),M,N) -> #activate(N) #52: #U62(tt(),M,N) -> #activate(M) #53: #U62(tt(),M,N) -> #activate(N) #54: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2)) #55: #U13(tt(),V1,V2) -> #isNatKind(activate(V2)) #56: #U13(tt(),V1,V2) -> #activate(V2) #57: #U13(tt(),V1,V2) -> #activate(V1) #58: #U13(tt(),V1,V2) -> #activate(V2) #59: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2)) #60: #U11(tt(),V1,V2) -> #isNatKind(activate(V1)) #61: #U11(tt(),V1,V2) -> #activate(V1) #62: #U11(tt(),V1,V2) -> #activate(V1) #63: #U11(tt(),V1,V2) -> #activate(V2) #64: #U22(tt(),V1) -> #U23(isNat(activate(V1))) #65: #U22(tt(),V1) -> #isNat(activate(V1)) #66: #U22(tt(),V1) -> #activate(V1) #67: #U61(tt(),M,N) -> #U62(isNatKind(activate(M)),activate(M),activate(N)) #68: #U61(tt(),M,N) -> #isNatKind(activate(M)) #69: #U61(tt(),M,N) -> #activate(M) #70: #U61(tt(),M,N) -> #activate(M) #71: #U61(tt(),M,N) -> #activate(N) #72: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2)) #73: #U14(tt(),V1,V2) -> #isNat(activate(V1)) #74: #U14(tt(),V1,V2) -> #activate(V1) #75: #U14(tt(),V1,V2) -> #activate(V2) #76: #U64(tt(),M,N) -> #s(plus(activate(N),activate(M))) #77: #U64(tt(),M,N) -> #plus(activate(N),activate(M)) #78: #U64(tt(),M,N) -> #activate(N) #79: #U64(tt(),M,N) -> #activate(M) Number of SCCs: 1, DPs: 72 SCC { #1..9 #11..18 #20..30 #32 #33 #35..41 #43..63 #65..75 #77..79 } POLO(Sum)... succeeded. #0 w: 0 #U32 w: 0 isNatKind w: 1 U16 w: 4 U21 w: x1 U11 w: 2 U64 w: x2 + x3 + 7 s w: x1 + 3 #isNat w: x1 activate w: x1 #plus w: x1 + x2 + 2 #activate w: x1 + 3 #U23 w: 0 U23 w: 2 U63 w: x2 + x3 + 7 #U13 w: x2 + x3 + 3 #U52 w: x2 + 3 U12 w: x1 + x3 + 2 #U16 w: 0 n__s w: x1 + 3 #U12 w: x2 + x3 + 3 #U62 w: x2 + x3 + 4 0 w: 1 #U14 w: x2 + x3 + 3 #s w: 0 U62 w: x2 + x3 + 7 n__plus w: x1 + x2 + 4 #U63 w: x2 + x3 + 4 #U15 w: x2 + 3 U32 w: 0 n__0 w: 1 U14 w: 4 isNat w: 2 U52 w: x2 U15 w: 4 U61 w: x2 + x3 + 7 plus w: x1 + x2 + 4 #U51 w: x2 + 3 #U11 w: x2 + x3 + 4 #U64 w: x2 + x3 + 4 U31 w: 0 #U41 w: 0 #U21 w: x2 + 3 #U22 w: x2 + 3 tt w: 2 U13 w: x2 + x3 + 4 U22 w: 2 U51 w: x2 + 2 #isNatKind w: x1 + 2 U41 w: 0 #U31 w: x2 + 4 #U61 w: x2 + x3 + 5 USABLE RULES: { 3..9 13..18 25..33 } Removed DPs: #2 #7 #11..17 #21 #23..26 #28 #32 #33 #35 #38..41 #44 #46 #50..53 #55 #59..63 #65 #67..71 #73 #77..79 Number of SCCs: 0, DPs: 0