/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(),V1,V2) -> U32(isNat(activate(V1)),activate(V2)) 7: U32(tt(),V2) -> U33(isNat(activate(V2))) 8: U33(tt()) -> tt() 9: U41(tt(),N) -> activate(N) 10: U51(tt(),M,N) -> s(plus(activate(N),activate(M))) 11: U61(tt()) -> 0() 12: U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) 13: and(tt(),X) -> activate(X) 14: isNat(n__0()) -> tt() 15: isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) 16: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 17: isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) 18: isNatKind(n__0()) -> tt() 19: isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) 20: isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 21: isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) 22: plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N) 23: plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) 24: x(N,0()) -> U61(and(isNat(N),n__isNatKind(N))) 25: x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) 26: 0() -> n__0() 27: plus(X1,X2) -> n__plus(X1,X2) 28: isNatKind(X) -> n__isNatKind(X) 29: s(X) -> n__s(X) 30: x(X1,X2) -> n__x(X1,X2) 31: and(X1,X2) -> n__and(X1,X2) 32: isNat(X) -> n__isNat(X) 33: activate(n__0()) -> 0() 34: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) 35: activate(n__isNatKind(X)) -> isNatKind(X) 36: activate(n__s(X)) -> s(activate(X)) 37: activate(n__x(X1,X2)) -> x(activate(X1),activate(X2)) 38: activate(n__and(X1,X2)) -> and(activate(X1),X2) 39: activate(n__isNat(X)) -> isNat(X) 40: activate(X) -> X Number of strict rules: 40 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: #activate(n__isNatKind(X)) -> #isNatKind(X) #5: #activate(n__x(X1,X2)) -> #x(activate(X1),activate(X2)) #6: #activate(n__x(X1,X2)) -> #activate(X1) #7: #activate(n__x(X1,X2)) -> #activate(X2) #8: #activate(n__and(X1,X2)) -> #and(activate(X1),X2) #9: #activate(n__and(X1,X2)) -> #activate(X1) #10: #U31(tt(),V1,V2) -> #U32(isNat(activate(V1)),activate(V2)) #11: #U31(tt(),V1,V2) -> #isNat(activate(V1)) #12: #U31(tt(),V1,V2) -> #activate(V1) #13: #U31(tt(),V1,V2) -> #activate(V2) #14: #and(tt(),X) -> #activate(X) #15: #U41(tt(),N) -> #activate(N) #16: #U61(tt()) -> #0() #17: #x(N,0()) -> #U61(and(isNat(N),n__isNatKind(N))) #18: #x(N,0()) -> #and(isNat(N),n__isNatKind(N)) #19: #x(N,0()) -> #isNat(N) #20: #plus(N,s(M)) -> #U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) #21: #plus(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))) #22: #plus(N,s(M)) -> #and(isNat(M),n__isNatKind(M)) #23: #plus(N,s(M)) -> #isNat(M) #24: #U71(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N)) #25: #U71(tt(),M,N) -> #x(activate(N),activate(M)) #26: #U71(tt(),M,N) -> #activate(N) #27: #U71(tt(),M,N) -> #activate(M) #28: #U71(tt(),M,N) -> #activate(N) #29: #x(N,s(M)) -> #U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) #30: #x(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))) #31: #x(N,s(M)) -> #and(isNat(M),n__isNatKind(M)) #32: #x(N,s(M)) -> #isNat(M) #33: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #34: #isNatKind(n__s(V1)) -> #activate(V1) #35: #U32(tt(),V2) -> #U33(isNat(activate(V2))) #36: #U32(tt(),V2) -> #isNat(activate(V2)) #37: #U32(tt(),V2) -> #activate(V2) #38: #activate(n__isNat(X)) -> #isNat(X) #39: #U51(tt(),M,N) -> #s(plus(activate(N),activate(M))) #40: #U51(tt(),M,N) -> #plus(activate(N),activate(M)) #41: #U51(tt(),M,N) -> #activate(N) #42: #U51(tt(),M,N) -> #activate(M) #43: #activate(n__0()) -> #0() #44: #plus(N,0()) -> #U41(and(isNat(N),n__isNatKind(N)),N) #45: #plus(N,0()) -> #and(isNat(N),n__isNatKind(N)) #46: #plus(N,0()) -> #isNat(N) #47: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2)) #48: #activate(n__plus(X1,X2)) -> #activate(X1) #49: #activate(n__plus(X1,X2)) -> #activate(X2) #50: #isNat(n__x(V1,V2)) -> #U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) #51: #isNat(n__x(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #52: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1)) #53: #isNat(n__x(V1,V2)) -> #activate(V1) #54: #isNat(n__x(V1,V2)) -> #activate(V2) #55: #isNat(n__x(V1,V2)) -> #activate(V1) #56: #isNat(n__x(V1,V2)) -> #activate(V2) #57: #isNatKind(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #58: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #59: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #60: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #61: #activate(n__s(X)) -> #s(activate(X)) #62: #activate(n__s(X)) -> #activate(X) #63: #isNatKind(n__x(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #64: #isNatKind(n__x(V1,V2)) -> #isNatKind(activate(V1)) #65: #isNatKind(n__x(V1,V2)) -> #activate(V1) #66: #isNatKind(n__x(V1,V2)) -> #activate(V2) #67: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #68: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #69: #isNat(n__s(V1)) -> #activate(V1) #70: #isNat(n__s(V1)) -> #activate(V1) #71: #U11(tt(),V1,V2) -> #U12(isNat(activate(V1)),activate(V2)) #72: #U11(tt(),V1,V2) -> #isNat(activate(V1)) #73: #U11(tt(),V1,V2) -> #activate(V1) #74: #U11(tt(),V1,V2) -> #activate(V2) #75: #isNat(n__plus(V1,V2)) -> #U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) #76: #isNat(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) #77: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #78: #isNat(n__plus(V1,V2)) -> #activate(V1) #79: #isNat(n__plus(V1,V2)) -> #activate(V2) #80: #isNat(n__plus(V1,V2)) -> #activate(V1) #81: #isNat(n__plus(V1,V2)) -> #activate(V2) #82: #U21(tt(),V1) -> #U22(isNat(activate(V1))) #83: #U21(tt(),V1) -> #isNat(activate(V1)) #84: #U21(tt(),V1) -> #activate(V1) Number of SCCs: 1, DPs: 76 SCC { #2..15 #18..34 #36..38 #40..42 #44..60 #62..81 #83 #84 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 #U32 w: max(x2 + 2) isNatKind w: x1 U21 w: 0 U11 w: 0 s w: x1 #isNat w: x1 + 1 activate w: x1 U71 w: max(x1 + 2, x2 + 3, x3 + 4) n__isNatKind w: x1 and w: max(x1, x2) #plus w: max(x1 + 1, x2 + 5) #activate w: x1 + 1 #U13 w: 0 U12 w: 0 #U33 w: 0 x w: max(x1 + 4, x2 + 3) n__s w: x1 #U12 w: max(x1 + 1, x2 + 1) 0 w: 2 #x w: max(x1 + 5, x2 + 4) #s w: 0 n__isNat w: x1 n__plus w: max(x1, x2 + 4) U32 w: 0 U33 w: 0 n__0 w: 2 isNat w: x1 n__x w: max(x1 + 4, x2 + 3) plus w: max(x1, x2 + 4) U61 w: 5 #U51 w: max(x2 + 5, x3 + 1) #U11 w: max(x1 + 1, x2 + 1, x3 + 5) U31 w: max(x3 + 1) #U41 w: max(x2 + 1) #U21 w: max(x2 + 1) #U22 w: 0 tt w: 0 n__and w: max(x1, x2) #U71 w: max(x2 + 4, x3 + 5) U13 w: 0 U22 w: 0 U51 w: max(x2 + 4, x3) #isNatKind w: x1 + 1 U41 w: max(x2) #U31 w: max(x1 + 3, x2 + 3, x3 + 3) #and w: max(x2 + 1) #U61 w: 0 USABLE RULES: { 1..40 } Removed DPs: #6 #7 #10..13 #18 #19 #22 #23 #26..28 #30..32 #36 #37 #42 #49..57 #60 #63..66 #74 #76 #79 #81 Number of SCCs: 1, DPs: 39 SCC { #2..5 #8 #9 #14 #15 #20 #21 #24 #25 #29 #33 #34 #38 #40 #41 #44..48 #58 #59 #62 #67..73 #75 #77 #78 #80 #83 #84 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 #U32 w: max(x2 + 2) isNatKind w: x1 U21 w: 0 U11 w: 0 s w: x1 #isNat w: x1 + 6 activate w: x1 U71 w: max(x1 + 1, x2 + 2, x3 + 4) n__isNatKind w: x1 and w: max(x1, x2) #plus w: max(x1 + 6, x2 + 9) #activate w: x1 + 6 #U13 w: 0 U12 w: 0 #U33 w: 0 x w: max(x1 + 4, x2 + 2) n__s w: x1 #U12 w: max(x2 + 7) 0 w: 3 #x w: max(x1 + 10, x2 + 8) #s w: 0 n__isNat w: x1 n__plus w: max(x1, x2 + 3) U32 w: 0 U33 w: 0 n__0 w: 3 isNat w: x1 n__x w: max(x1 + 4, x2 + 2) plus w: max(x1, x2 + 3) U61 w: 5 #U51 w: max(x1 + 5, x2 + 9, x3 + 6) #U11 w: max(x1 + 5, x2 + 6, x3 + 9) U31 w: max(x3 + 1) #U41 w: max(x2 + 6) #U21 w: max(x2 + 6) #U22 w: 0 tt w: 0 n__and w: max(x1, x2) #U71 w: max(x1 + 2, x2 + 8, x3 + 10) U13 w: 0 U22 w: 0 U51 w: max(x2 + 3, x3) #isNatKind w: x1 + 6 U41 w: max(x2) #U31 w: max(x1 + 3, x2 + 3, x3 + 3) #and w: max(x2 + 6) #U61 w: 0 USABLE RULES: { 1..40 } Removed DPs: #2 #3 #71 Number of SCCs: 1, DPs: 36 SCC { #4 #5 #8 #9 #14 #15 #20 #21 #24 #25 #29 #33 #34 #38 #40 #41 #44..48 #58 #59 #62 #67..70 #72 #73 #75 #77 #78 #80 #83 #84 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U32 s: [1] p: 0 isNatKind s: [1] p: 0 U21 s: [2] p: 0 U11 s: [] p: 3 s s: [1] p: 7 #isNat s: [1] p: 4 activate s: 1 U71 s: [2,3,1] p: 10 n__isNatKind s: [1] p: 0 and s: [2,1] p: 4 #plus s: [2,1] p: 8 #activate s: [1] p: 5 #U13 s: [] p: 0 U12 s: [] p: 2 #U33 s: [] p: 0 x s: [2,1] p: 10 n__s s: [1] p: 7 #U12 s: [1] p: 0 0 s: [] p: 2 #x s: [2,1] p: 10 #s s: [] p: 0 n__isNat s: 1 n__plus s: [1,2] p: 9 U32 s: [1,2] p: 7 U33 s: [] p: 2 n__0 s: [] p: 2 isNat s: 1 n__x s: [2,1] p: 10 plus s: [1,2] p: 9 U61 s: [1] p: 2 #U51 s: [2,3] p: 8 #U11 s: [2] p: 5 U31 s: [2,3] p: 7 #U41 s: [1,2] p: 6 #U21 s: [1,2] p: 6 #U22 s: [] p: 0 tt s: [] p: 1 n__and s: [2,1] p: 4 #U71 s: [2,3,1] p: 10 U13 s: [] p: 2 U22 s: 1 U51 s: [3,2,1] p: 9 #isNatKind s: [1] p: 5 U41 s: 2 #U31 s: [3,1] p: 0 #and s: [2] p: 5 #U61 s: [] p: 0 USABLE RULES: { 1..40 } Removed DPs: #4 #5 #9 #15 #21 #24 #25 #29 #33 #34 #38 #41 #44..48 #58 #59 #62 #67..70 #72 #75 #77 #78 #80 #83 #84 Number of SCCs: 2, DPs: 4 SCC { #8 #14 } POLO(Sum)... succeeded. #0 w: 0 #U32 w: 2 isNatKind w: 2 U21 w: x1 U11 w: x1 + x2 + x3 + 8 s w: x1 + 2 #isNat w: 1 activate w: x1 + 2 U71 w: x1 + x2 + x3 + 1 n__isNatKind w: 2 and w: x2 + 1 #plus w: 1 #activate w: x1 + 1 #U13 w: 0 U12 w: x2 + 12 #U33 w: 0 x w: x1 + 2 n__s w: 1 #U12 w: 1 0 w: 6 #x w: 1 #s w: 0 n__isNat w: x1 + 1 n__plus w: 1 U32 w: 6 U33 w: 7 n__0 w: 7 isNat w: 4 n__x w: 1 plus w: x1 + x2 U61 w: x1 #U51 w: 1 #U11 w: 1 U31 w: 5 #U41 w: 1 #U21 w: 1 #U22 w: 0 tt w: 5 n__and w: x1 + x2 + 2 #U71 w: 0 U13 w: x1 U22 w: 0 U51 w: x1 + x2 + x3 + 1 #isNatKind w: 1 U41 w: x2 + 6 #U31 w: 2 #and w: x2 + 2 #U61 w: 0 USABLE RULES: { } Removed DPs: #8 #14 Number of SCCs: 1, DPs: 2 SCC { #20 #40 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U32 s: [1] p: 0 isNatKind s: [1] p: 0 U21 s: [2] p: 0 U11 s: [] p: 3 s s: [1] p: 7 #isNat s: [1] p: 4 activate s: 1 U71 s: [2,3,1] p: 10 n__isNatKind s: [1] p: 0 and s: 2 #plus s: [2,1] p: 7 #activate s: [1] p: 5 #U13 s: [] p: 0 U12 s: [] p: 2 #U33 s: [] p: 0 x s: [2,1] p: 10 n__s s: [1] p: 7 #U12 s: [1] p: 0 0 s: [] p: 2 #x s: [2,1] p: 10 #s s: [] p: 0 n__isNat s: 1 n__plus s: [1,2] p: 9 U32 s: [1,2] p: 7 U33 s: [] p: 2 n__0 s: [] p: 2 isNat s: 1 n__x s: [2,1] p: 10 plus s: [1,2] p: 9 U61 s: [1] p: 2 #U51 s: [2,3,1] p: 7 #U11 s: [2] p: 5 U31 s: [2,3] p: 7 #U41 s: [1,2] p: 6 #U21 s: [1,2] p: 6 #U22 s: [] p: 0 tt s: [] p: 1 n__and s: 2 #U71 s: [2,3,1] p: 10 U13 s: [] p: 2 U22 s: 1 U51 s: [3,2,1] p: 9 #isNatKind s: [1] p: 5 U41 s: 2 #U31 s: [3,1] p: 0 #and s: [2] p: 5 #U61 s: [] p: 0 USABLE RULES: { 1..40 } Removed DPs: #20 #40 Number of SCCs: 0, DPs: 0