/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: U101(tt(),M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N)) 2: U102(tt(),M,N) -> U103(isNat(activate(N)),activate(M),activate(N)) 3: U103(tt(),M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N)) 4: U104(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) 5: U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) 6: U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) 7: U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) 8: U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2)) 9: U15(tt(),V2) -> U16(isNat(activate(V2))) 10: U16(tt()) -> tt() 11: U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) 12: U22(tt(),V1) -> U23(isNat(activate(V1))) 13: U23(tt()) -> tt() 14: U31(tt(),V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2)) 15: U32(tt(),V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2)) 16: U33(tt(),V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2)) 17: U34(tt(),V1,V2) -> U35(isNat(activate(V1)),activate(V2)) 18: U35(tt(),V2) -> U36(isNat(activate(V2))) 19: U36(tt()) -> tt() 20: U41(tt(),V2) -> U42(isNatKind(activate(V2))) 21: U42(tt()) -> tt() 22: U51(tt()) -> tt() 23: U61(tt(),V2) -> U62(isNatKind(activate(V2))) 24: U62(tt()) -> tt() 25: U71(tt(),N) -> U72(isNatKind(activate(N)),activate(N)) 26: U72(tt(),N) -> activate(N) 27: U81(tt(),M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N)) 28: U82(tt(),M,N) -> U83(isNat(activate(N)),activate(M),activate(N)) 29: U83(tt(),M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N)) 30: U84(tt(),M,N) -> s(plus(activate(N),activate(M))) 31: U91(tt(),N) -> U92(isNatKind(activate(N))) 32: U92(tt()) -> 0() 33: isNat(n__0()) -> tt() 34: isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) 35: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 36: isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2)) 37: isNatKind(n__0()) -> tt() 38: isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2)) 39: isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 40: isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) 41: plus(N,0()) -> U71(isNat(N),N) 42: plus(N,s(M)) -> U81(isNat(M),M,N) 43: x(N,0()) -> U91(isNat(N),N) 44: x(N,s(M)) -> U101(isNat(M),M,N) 45: 0() -> n__0() 46: plus(X1,X2) -> n__plus(X1,X2) 47: s(X) -> n__s(X) 48: x(X1,X2) -> n__x(X1,X2) 49: activate(n__0()) -> 0() 50: activate(n__plus(X1,X2)) -> plus(X1,X2) 51: activate(n__s(X)) -> s(X) 52: activate(n__x(X1,X2)) -> x(X1,X2) 53: activate(X) -> X Number of strict rules: 53 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U102(tt(),M,N) -> #U103(isNat(activate(N)),activate(M),activate(N)) #2: #U102(tt(),M,N) -> #isNat(activate(N)) #3: #U102(tt(),M,N) -> #activate(N) #4: #U102(tt(),M,N) -> #activate(M) #5: #U102(tt(),M,N) -> #activate(N) #6: #x(N,0()) -> #U91(isNat(N),N) #7: #x(N,0()) -> #isNat(N) #8: #U83(tt(),M,N) -> #U84(isNatKind(activate(N)),activate(M),activate(N)) #9: #U83(tt(),M,N) -> #isNatKind(activate(N)) #10: #U83(tt(),M,N) -> #activate(N) #11: #U83(tt(),M,N) -> #activate(M) #12: #U83(tt(),M,N) -> #activate(N) #13: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #14: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #15: #isNat(n__s(V1)) -> #activate(V1) #16: #isNat(n__s(V1)) -> #activate(V1) #17: #plus(N,s(M)) -> #U81(isNat(M),M,N) #18: #plus(N,s(M)) -> #isNat(M) #19: #plus(N,0()) -> #U71(isNat(N),N) #20: #plus(N,0()) -> #isNat(N) #21: #isNatKind(n__plus(V1,V2)) -> #U41(isNatKind(activate(V1)),activate(V2)) #22: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #23: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #24: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #25: #U12(tt(),V1,V2) -> #U13(isNatKind(activate(V2)),activate(V1),activate(V2)) #26: #U12(tt(),V1,V2) -> #isNatKind(activate(V2)) #27: #U12(tt(),V1,V2) -> #activate(V2) #28: #U12(tt(),V1,V2) -> #activate(V1) #29: #U12(tt(),V1,V2) -> #activate(V2) #30: #isNatKind(n__x(V1,V2)) -> #U61(isNatKind(activate(V1)),activate(V2)) #31: #isNatKind(n__x(V1,V2)) -> #isNatKind(activate(V1)) #32: #isNatKind(n__x(V1,V2)) -> #activate(V1) #33: #isNatKind(n__x(V1,V2)) -> #activate(V2) #34: #activate(n__s(X)) -> #s(X) #35: #U15(tt(),V2) -> #U16(isNat(activate(V2))) #36: #U15(tt(),V2) -> #isNat(activate(V2)) #37: #U15(tt(),V2) -> #activate(V2) #38: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1)) #39: #U21(tt(),V1) -> #isNatKind(activate(V1)) #40: #U21(tt(),V1) -> #activate(V1) #41: #U21(tt(),V1) -> #activate(V1) #42: #U61(tt(),V2) -> #U62(isNatKind(activate(V2))) #43: #U61(tt(),V2) -> #isNatKind(activate(V2)) #44: #U61(tt(),V2) -> #activate(V2) #45: #U22(tt(),V1) -> #U23(isNat(activate(V1))) #46: #U22(tt(),V1) -> #isNat(activate(V1)) #47: #U22(tt(),V1) -> #activate(V1) #48: #U91(tt(),N) -> #U92(isNatKind(activate(N))) #49: #U91(tt(),N) -> #isNatKind(activate(N)) #50: #U91(tt(),N) -> #activate(N) #51: #U31(tt(),V1,V2) -> #U32(isNatKind(activate(V1)),activate(V1),activate(V2)) #52: #U31(tt(),V1,V2) -> #isNatKind(activate(V1)) #53: #U31(tt(),V1,V2) -> #activate(V1) #54: #U31(tt(),V1,V2) -> #activate(V1) #55: #U31(tt(),V1,V2) -> #activate(V2) #56: #U84(tt(),M,N) -> #s(plus(activate(N),activate(M))) #57: #U84(tt(),M,N) -> #plus(activate(N),activate(M)) #58: #U84(tt(),M,N) -> #activate(N) #59: #U84(tt(),M,N) -> #activate(M) #60: #activate(n__x(X1,X2)) -> #x(X1,X2) #61: #activate(n__0()) -> #0() #62: #U71(tt(),N) -> #U72(isNatKind(activate(N)),activate(N)) #63: #U71(tt(),N) -> #isNatKind(activate(N)) #64: #U71(tt(),N) -> #activate(N) #65: #U71(tt(),N) -> #activate(N) #66: #U41(tt(),V2) -> #U42(isNatKind(activate(V2))) #67: #U41(tt(),V2) -> #isNatKind(activate(V2)) #68: #U41(tt(),V2) -> #activate(V2) #69: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2)) #70: #U13(tt(),V1,V2) -> #isNatKind(activate(V2)) #71: #U13(tt(),V1,V2) -> #activate(V2) #72: #U13(tt(),V1,V2) -> #activate(V1) #73: #U13(tt(),V1,V2) -> #activate(V2) #74: #isNatKind(n__s(V1)) -> #U51(isNatKind(activate(V1))) #75: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #76: #isNatKind(n__s(V1)) -> #activate(V1) #77: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2)) #78: #U11(tt(),V1,V2) -> #isNatKind(activate(V1)) #79: #U11(tt(),V1,V2) -> #activate(V1) #80: #U11(tt(),V1,V2) -> #activate(V1) #81: #U11(tt(),V1,V2) -> #activate(V2) #82: #x(N,s(M)) -> #U101(isNat(M),M,N) #83: #x(N,s(M)) -> #isNat(M) #84: #U82(tt(),M,N) -> #U83(isNat(activate(N)),activate(M),activate(N)) #85: #U82(tt(),M,N) -> #isNat(activate(N)) #86: #U82(tt(),M,N) -> #activate(N) #87: #U82(tt(),M,N) -> #activate(M) #88: #U82(tt(),M,N) -> #activate(N) #89: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2)) #90: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #91: #isNat(n__plus(V1,V2)) -> #activate(V1) #92: #isNat(n__plus(V1,V2)) -> #activate(V1) #93: #isNat(n__plus(V1,V2)) -> #activate(V2) #94: #U81(tt(),M,N) -> #U82(isNatKind(activate(M)),activate(M),activate(N)) #95: #U81(tt(),M,N) -> #isNatKind(activate(M)) #96: #U81(tt(),M,N) -> #activate(M) #97: #U81(tt(),M,N) -> #activate(M) #98: #U81(tt(),M,N) -> #activate(N) #99: #U34(tt(),V1,V2) -> #U35(isNat(activate(V1)),activate(V2)) #100: #U34(tt(),V1,V2) -> #isNat(activate(V1)) #101: #U34(tt(),V1,V2) -> #activate(V1) #102: #U34(tt(),V1,V2) -> #activate(V2) #103: #U92(tt()) -> #0() #104: #U72(tt(),N) -> #activate(N) #105: #isNat(n__x(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V1),activate(V2)) #106: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1)) #107: #isNat(n__x(V1,V2)) -> #activate(V1) #108: #isNat(n__x(V1,V2)) -> #activate(V1) #109: #isNat(n__x(V1,V2)) -> #activate(V2) #110: #U33(tt(),V1,V2) -> #U34(isNatKind(activate(V2)),activate(V1),activate(V2)) #111: #U33(tt(),V1,V2) -> #isNatKind(activate(V2)) #112: #U33(tt(),V1,V2) -> #activate(V2) #113: #U33(tt(),V1,V2) -> #activate(V1) #114: #U33(tt(),V1,V2) -> #activate(V2) #115: #U103(tt(),M,N) -> #U104(isNatKind(activate(N)),activate(M),activate(N)) #116: #U103(tt(),M,N) -> #isNatKind(activate(N)) #117: #U103(tt(),M,N) -> #activate(N) #118: #U103(tt(),M,N) -> #activate(M) #119: #U103(tt(),M,N) -> #activate(N) #120: #U101(tt(),M,N) -> #U102(isNatKind(activate(M)),activate(M),activate(N)) #121: #U101(tt(),M,N) -> #isNatKind(activate(M)) #122: #U101(tt(),M,N) -> #activate(M) #123: #U101(tt(),M,N) -> #activate(M) #124: #U101(tt(),M,N) -> #activate(N) #125: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2)) #126: #U14(tt(),V1,V2) -> #isNat(activate(V1)) #127: #U14(tt(),V1,V2) -> #activate(V1) #128: #U14(tt(),V1,V2) -> #activate(V2) #129: #U32(tt(),V1,V2) -> #U33(isNatKind(activate(V2)),activate(V1),activate(V2)) #130: #U32(tt(),V1,V2) -> #isNatKind(activate(V2)) #131: #U32(tt(),V1,V2) -> #activate(V2) #132: #U32(tt(),V1,V2) -> #activate(V1) #133: #U32(tt(),V1,V2) -> #activate(V2) #134: #U104(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N)) #135: #U104(tt(),M,N) -> #x(activate(N),activate(M)) #136: #U104(tt(),M,N) -> #activate(N) #137: #U104(tt(),M,N) -> #activate(M) #138: #U104(tt(),M,N) -> #activate(N) #139: #activate(n__plus(X1,X2)) -> #plus(X1,X2) #140: #U35(tt(),V2) -> #U36(isNat(activate(V2))) #141: #U35(tt(),V2) -> #isNat(activate(V2)) #142: #U35(tt(),V2) -> #activate(V2) Number of SCCs: 1, DPs: 131 SCC { #1..33 #36..41 #43 #44 #46 #47 #49..55 #57..60 #62..65 #67..73 #75..102 #104..139 #141 #142 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 #U72 w: max(x1, x2 + 2) #U32 w: max(x1 + 11, x2 + 6, x3 + 8) isNatKind w: 1 U16 w: x1 + 3 U21 w: max(x1, x2 + 2) #U83 w: max(x2 + 3, x3 + 2) U11 w: 0 s w: x1 #isNat w: x1 + 2 U42 w: x1 U91 w: 0 #U35 w: max(x2 + 4) #U101 w: max(x2 + 13, x3 + 10) activate w: x1 #U82 w: max(x2 + 3, x3 + 2) #U104 w: max(x1 + 8, x2 + 13, x3 + 10) U71 w: max(x2) #U81 w: max(x2 + 3, x3 + 2) #U92 w: 0 #plus w: max(x1 + 2, x2 + 3) U101 w: max(x2 + 11, x3 + 8) #activate w: x1 + 2 U103 w: max(x2 + 11, x3 + 8) #U23 w: 0 U84 w: max(x1 + 2, x2 + 3, x3) U23 w: 3 U35 w: max(x2 + 1) U72 w: max(x2) #U13 w: max(x2 + 2, x3 + 3) U34 w: max(x3 + 3) #U103 w: max(x2 + 13, x3 + 10) U12 w: max(x2 + 2, x3 + 1) #U33 w: max(x1 + 11, x2 + 5, x3 + 7) x w: max(x1 + 8, x2 + 11) #U16 w: 0 n__s w: x1 U104 w: max(x2 + 11, x3 + 8) #U42 w: 0 #U12 w: max(x2 + 2, x3 + 4) #U62 w: 0 U83 w: max(x2 + 3, x3) 0 w: 0 #U14 w: max(x1 + 2, x2 + 2, x3 + 3) #U36 w: 0 U36 w: x1 + 1 #U102 w: max(x2 + 13, x3 + 10) #x w: max(x1 + 10, x2 + 13) #s w: 0 U62 w: 1 n__plus w: max(x1, x2 + 3) #U15 w: max(x2 + 3) U32 w: max(x1, x2 + 1) U33 w: max(x1 + 1, x2 + 2) n__0 w: 0 #U34 w: max(x2 + 3, x3 + 4) U14 w: max(x1 + 2) isNat w: 0 n__x w: max(x1 + 8, x2 + 11) plus w: max(x1, x2 + 3) U15 w: max(x1 + 1) U61 w: max(x1) #U51 w: 0 #U11 w: max(x1, x2 + 2, x3 + 4) U31 w: 0 U92 w: 0 #U41 w: max(x2 + 3) U102 w: max(x2 + 11, x3 + 8) #U21 w: max(x2 + 2) U81 w: max(x2 + 3, x3) U82 w: max(x2 + 3, x3) #U22 w: max(x2 + 2) tt w: 1 #U84 w: max(x1 + 2, x2 + 3, x3 + 2) #U71 w: max(x2 + 2) U13 w: max(x1 + 1) U22 w: max(x1 + 1) U51 w: 1 #isNatKind w: x1 + 2 U41 w: max(x1) #U31 w: max(x1 + 11, x2 + 9, x3 + 11) #U91 w: max(x2 + 9) #U61 w: max(x2 + 11) USABLE RULES: { 1..4 20..32 37..53 } Removed DPs: #2..7 #11 #18 #21 #24 #26 #27 #29..33 #36 #37 #43 #44 #49 #50 #52..55 #59 #67 #68 #70 #71 #73 #81 #83 #87 #93 #95..97 #100..102 #105..114 #116..119 #121..124 #128 #130..133 #136..138 #141 #142 Number of SCCs: 1, DPs: 56 SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #38..41 #46 #47 #57 #58 #60 #62..65 #69 #72 #75..80 #82 #84..86 #88..92 #94 #98 #104 #115 #120 #126 #127 #134 #135 #139 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U72 s: [2] p: 1 #U32 s: [1,3] p: 0 isNatKind s: [] p: 1 U16 s: 1 U21 s: 1 #U83 s: [3,2] p: 1 U11 s: [] p: 1 s s: [1] p: 1 #isNat s: [1] p: 1 U42 s: [] p: 1 U91 s: 1 #U35 s: [1] p: 0 #U101 s: [3,2,1] p: 7 activate s: 1 #U82 s: [3,2] p: 1 #U104 s: [3,2,1] p: 7 U71 s: [2] p: 6 #U81 s: [3,2] p: 1 #U92 s: [] p: 0 #plus s: [1,2] p: 1 U101 s: [3,2,1] p: 7 #activate s: [1] p: 1 U103 s: [3,2,1] p: 7 #U23 s: [] p: 0 U84 s: [3,2,1] p: 6 U23 s: [] p: 1 U35 s: 1 U72 s: [1,2] p: 5 #U13 s: [2] p: 3 U34 s: [] p: 1 #U103 s: [3,2,1] p: 7 U12 s: [] p: 1 #U33 s: [2,3,1] p: 0 x s: [1,2] p: 7 #U16 s: [] p: 0 n__s s: [1] p: 1 U104 s: [3,2,1] p: 7 #U42 s: [] p: 0 #U12 s: [2] p: 4 #U62 s: [] p: 0 U83 s: [3,2,1] p: 6 0 s: [] p: 0 #U14 s: [2] p: 2 #U36 s: [] p: 0 U36 s: [] p: 1 #U102 s: [3,2,1] p: 7 #x s: [1,2] p: 7 #s s: [] p: 0 U62 s: 1 n__plus s: [1,2] p: 6 #U15 s: [] p: 0 U32 s: 1 U33 s: 1 n__0 s: [] p: 0 #U34 s: [3,2] p: 0 U14 s: [] p: 1 isNat s: [] p: 1 n__x s: [1,2] p: 7 plus s: [1,2] p: 6 U15 s: [] p: 1 U61 s: [] p: 1 #U51 s: [] p: 0 #U11 s: [2] p: 5 U31 s: 1 U92 s: 1 #U41 s: [2] p: 0 U102 s: [3,2,1] p: 7 #U21 s: [2] p: 1 U81 s: [3,2,1] p: 6 U82 s: [3,2,1] p: 6 #U22 s: [2] p: 1 tt s: [] p: 1 #U84 s: [3,2] p: 1 #U71 s: [2] p: 1 U13 s: [] p: 1 U22 s: 1 U51 s: [] p: 1 #isNatKind s: [1] p: 1 U41 s: 1 #U31 s: [3,1,2] p: 0 #U91 s: [2] p: 0 #U61 s: [1] p: 0 USABLE RULES: { 1..53 } Removed DPs: #9 #10 #12 #17 #19 #20 #22 #23 #25 #28 #58 #60 #69 #72 #75 #77..80 #82 #85 #86 #88..92 #98 #126 #127 #134 #135 #139 Number of SCCs: 1, DPs: 3 SCC { #13 #38 #46 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U72 s: [2] p: 1 #U32 s: [1,3] p: 0 isNatKind s: [] p: 1 U16 s: 1 U21 s: 1 #U83 s: [3,2] p: 1 U11 s: [] p: 1 s s: [1] p: 1 #isNat s: [1] p: 8 U42 s: [] p: 1 U91 s: 1 #U35 s: [1] p: 0 #U101 s: [3,2,1] p: 7 activate s: 1 #U82 s: [3,2] p: 1 #U104 s: [3,2,1] p: 7 U71 s: [2] p: 6 #U81 s: [3,2] p: 1 #U92 s: [] p: 0 #plus s: [1,2] p: 1 U101 s: [3,2,1] p: 7 #activate s: [1] p: 1 U103 s: [3,2,1] p: 7 #U23 s: [] p: 0 U84 s: [3,2,1] p: 6 U23 s: [] p: 1 U35 s: 1 U72 s: [1,2] p: 5 #U13 s: [2] p: 3 U34 s: [] p: 1 #U103 s: [3,2,1] p: 7 U12 s: [] p: 1 #U33 s: [2,3,1] p: 0 x s: [1,2] p: 7 #U16 s: [] p: 0 n__s s: [1] p: 1 U104 s: [3,2,1] p: 7 #U42 s: [] p: 0 #U12 s: [2] p: 4 #U62 s: [] p: 0 U83 s: [3,2,1] p: 6 0 s: [] p: 0 #U14 s: [2] p: 2 #U36 s: [] p: 0 U36 s: [] p: 1 #U102 s: [3,2,1] p: 7 #x s: [1,2] p: 7 #s s: [] p: 0 U62 s: 1 n__plus s: [1,2] p: 6 #U15 s: [] p: 0 U32 s: 1 U33 s: 1 n__0 s: [] p: 0 #U34 s: [3,2] p: 0 U14 s: [] p: 1 isNat s: [] p: 1 n__x s: [1,2] p: 7 plus s: [1,2] p: 6 U15 s: [] p: 1 U61 s: [] p: 1 #U51 s: [] p: 0 #U11 s: [2] p: 5 U31 s: 1 U92 s: 1 #U41 s: [2] p: 0 U102 s: [3,2,1] p: 7 #U21 s: [2] p: 8 U81 s: [3,2,1] p: 6 U82 s: [3,2,1] p: 6 #U22 s: [2] p: 8 tt s: [] p: 1 #U84 s: [3,2] p: 1 #U71 s: [2] p: 1 U13 s: [] p: 1 U22 s: 1 U51 s: [] p: 1 #isNatKind s: [1] p: 1 U41 s: 1 #U31 s: [3,1,2] p: 0 #U91 s: [2] p: 0 #U61 s: [1] p: 0 USABLE RULES: { 1..53 } Removed DPs: #13 Number of SCCs: 0, DPs: 0