/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(activate(X1),activate(X2)) 32: activate(n__s(X)) -> s(activate(X)) 33: activate(X) -> X Number of strict rules: 33 Direct poly ... failed. Freezing ... 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(activate(X1),activate(X2)) #18: #activate(n__plus(X1,X2)) -> #activate(X1) #19: #activate(n__plus(X1,X2)) -> #activate(X2) #20: #U52(tt(),N) -> #activate(N) #21: #activate(n__0()) -> #0() #22: #plus(N,0()) -> #U51(isNat(N),N) #23: #plus(N,0()) -> #isNat(N) #24: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2)) #25: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #26: #isNat(n__plus(V1,V2)) -> #activate(V1) #27: #isNat(n__plus(V1,V2)) -> #activate(V1) #28: #isNat(n__plus(V1,V2)) -> #activate(V2) #29: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1)) #30: #U21(tt(),V1) -> #isNatKind(activate(V1)) #31: #U21(tt(),V1) -> #activate(V1) #32: #U21(tt(),V1) -> #activate(V1) #33: #U31(tt(),V2) -> #U32(isNatKind(activate(V2))) #34: #U31(tt(),V2) -> #isNatKind(activate(V2)) #35: #U31(tt(),V2) -> #activate(V2) #36: #U15(tt(),V2) -> #U16(isNat(activate(V2))) #37: #U15(tt(),V2) -> #isNat(activate(V2)) #38: #U15(tt(),V2) -> #activate(V2) #39: #U63(tt(),M,N) -> #U64(isNatKind(activate(N)),activate(M),activate(N)) #40: #U63(tt(),M,N) -> #isNatKind(activate(N)) #41: #U63(tt(),M,N) -> #activate(N) #42: #U63(tt(),M,N) -> #activate(M) #43: #U63(tt(),M,N) -> #activate(N) #44: #activate(n__s(X)) -> #s(activate(X)) #45: #activate(n__s(X)) -> #activate(X) #46: #plus(N,s(M)) -> #U61(isNat(M),M,N) #47: #plus(N,s(M)) -> #isNat(M) #48: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #49: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #50: #isNat(n__s(V1)) -> #activate(V1) #51: #isNat(n__s(V1)) -> #activate(V1) #52: #U62(tt(),M,N) -> #U63(isNat(activate(N)),activate(M),activate(N)) #53: #U62(tt(),M,N) -> #isNat(activate(N)) #54: #U62(tt(),M,N) -> #activate(N) #55: #U62(tt(),M,N) -> #activate(M) #56: #U62(tt(),M,N) -> #activate(N) #57: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2)) #58: #U13(tt(),V1,V2) -> #isNatKind(activate(V2)) #59: #U13(tt(),V1,V2) -> #activate(V2) #60: #U13(tt(),V1,V2) -> #activate(V1) #61: #U13(tt(),V1,V2) -> #activate(V2) #62: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2)) #63: #U11(tt(),V1,V2) -> #isNatKind(activate(V1)) #64: #U11(tt(),V1,V2) -> #activate(V1) #65: #U11(tt(),V1,V2) -> #activate(V1) #66: #U11(tt(),V1,V2) -> #activate(V2) #67: #U22(tt(),V1) -> #U23(isNat(activate(V1))) #68: #U22(tt(),V1) -> #isNat(activate(V1)) #69: #U22(tt(),V1) -> #activate(V1) #70: #U61(tt(),M,N) -> #U62(isNatKind(activate(M)),activate(M),activate(N)) #71: #U61(tt(),M,N) -> #isNatKind(activate(M)) #72: #U61(tt(),M,N) -> #activate(M) #73: #U61(tt(),M,N) -> #activate(M) #74: #U61(tt(),M,N) -> #activate(N) #75: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2)) #76: #U14(tt(),V1,V2) -> #isNat(activate(V1)) #77: #U14(tt(),V1,V2) -> #activate(V1) #78: #U14(tt(),V1,V2) -> #activate(V2) #79: #U64(tt(),M,N) -> #s(plus(activate(N),activate(M))) #80: #U64(tt(),M,N) -> #plus(activate(N),activate(M)) #81: #U64(tt(),M,N) -> #activate(N) #82: #U64(tt(),M,N) -> #activate(M) Number of SCCs: 1, DPs: 75 SCC { #1..9 #11..20 #22..32 #34 #35 #37..43 #45..66 #68..78 #80..82 } Sum... succeeded. #0() w: (0) #U32(x1) w: (0) isNatKind(x1) w: (1 + x1) U16(x1) w: (24454) U21(x1,x2) w: (4) U11(x1,x2,x3) w: (19266 + x3 + x2) U64(x1,x2,x3) w: (22125 + x3 + x2) s(x1) w: (5 + x1) #isNat(x1) w: (7 + x1) activate(x1) w: (x1) #plus(x1,x2) w: (6 + x2 + x1) #activate(x1) w: (2 + x1) #U23(x1) w: (0) U23(x1) w: (14136) U63(x1,x2,x3) w: (22125 + x3 + x2) #U13(x1,x2,x3) w: (10 + x3 + x2) #U52(x1,x2) w: (3 + x2) U12(x1,x2,x3) w: (19266 + x3 + x1) #U16(x1) w: (0) n__s(x1) w: (5 + x1) #U12(x1,x2,x3) w: (11 + x3 + x2) #U62(x1,x2,x3) w: (9 + x3 + x2) 0() w: (2) #U14(x1,x2,x3) w: (9 + x3 + x2) #s(x1) w: (0) U62(x1,x2,x3) w: (22125 + x3 + x2) n__plus(x1,x2) w: (22120 + x2 + x1) #U63(x1,x2,x3) w: (8 + x3 + x2) #U15(x1,x2) w: (8 + x2) U32(x1) w: (24454) n__0() w: (2) U14(x1,x2,x3) w: (68176 + x1) isNat(x1) w: (1) U52(x1,x2) w: (302 + x2) U15(x1,x2) w: (24453) U61(x1,x2,x3) w: (22125 + x3 + x2) plus(x1,x2) w: (22120 + x2 + x1) #U51(x1,x2) w: (4 + x2) #U11(x1,x2,x3) w: (12 + x3 + x2) #U64(x1,x2,x3) w: (7 + x3 + x2) U31(x1,x2) w: (24453) #U41(x1) w: (0) #U21(x1,x2) w: (9 + x2) #U22(x1,x2) w: (8 + x2) tt() w: (24455) U13(x1,x2,x3) w: (43721 + x3 + x1) U22(x1,x2) w: (8408 + x1) U51(x1,x2) w: (4806 + x2) #isNatKind(x1) w: (1 + x1) U41(x1) w: (6 + x1) #U31(x1,x2) w: (3 + x2) #U61(x1,x2,x3) w: (10 + x3 + x2) USABLE RULES: { 13..18 25..33 } Removed DPs: #1..9 #11..20 #22..32 #34 #35 #37..43 #45..66 #68..78 #80..82 Number of SCCs: 0, DPs: 0