/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(),N) -> activate(N) 2: U21(tt(),M,N) -> s(plus(activate(N),activate(M))) 3: U31(tt()) -> 0() 4: U41(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) 5: and(tt(),X) -> activate(X) 6: isNat(n__0()) -> tt() 7: isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2))) 8: isNat(n__s(V1)) -> isNat(activate(V1)) 9: isNat(n__x(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2))) 10: plus(N,0()) -> U11(isNat(N),N) 11: plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N) 12: x(N,0()) -> U31(isNat(N)) 13: x(N,s(M)) -> U41(and(isNat(M),n__isNat(N)),M,N) 14: 0() -> n__0() 15: plus(X1,X2) -> n__plus(X1,X2) 16: isNat(X) -> n__isNat(X) 17: s(X) -> n__s(X) 18: x(X1,X2) -> n__x(X1,X2) 19: activate(n__0()) -> 0() 20: activate(n__plus(X1,X2)) -> plus(X1,X2) 21: activate(n__isNat(X)) -> isNat(X) 22: activate(n__s(X)) -> s(X) 23: activate(n__x(X1,X2)) -> x(X1,X2) 24: activate(X) -> X Number of strict rules: 24 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U21(tt(),M,N) -> #s(plus(activate(N),activate(M))) #2: #U21(tt(),M,N) -> #plus(activate(N),activate(M)) #3: #U21(tt(),M,N) -> #activate(N) #4: #U21(tt(),M,N) -> #activate(M) #5: #x(N,s(M)) -> #U41(and(isNat(M),n__isNat(N)),M,N) #6: #x(N,s(M)) -> #and(isNat(M),n__isNat(N)) #7: #x(N,s(M)) -> #isNat(M) #8: #isNat(n__x(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2))) #9: #isNat(n__x(V1,V2)) -> #isNat(activate(V1)) #10: #isNat(n__x(V1,V2)) -> #activate(V1) #11: #isNat(n__x(V1,V2)) -> #activate(V2) #12: #plus(N,s(M)) -> #U21(and(isNat(M),n__isNat(N)),M,N) #13: #plus(N,s(M)) -> #and(isNat(M),n__isNat(N)) #14: #plus(N,s(M)) -> #isNat(M) #15: #activate(n__x(X1,X2)) -> #x(X1,X2) #16: #x(N,0()) -> #U31(isNat(N)) #17: #x(N,0()) -> #isNat(N) #18: #activate(n__plus(X1,X2)) -> #plus(X1,X2) #19: #isNat(n__plus(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2))) #20: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1)) #21: #isNat(n__plus(V1,V2)) -> #activate(V1) #22: #isNat(n__plus(V1,V2)) -> #activate(V2) #23: #plus(N,0()) -> #U11(isNat(N),N) #24: #plus(N,0()) -> #isNat(N) #25: #and(tt(),X) -> #activate(X) #26: #activate(n__s(X)) -> #s(X) #27: #activate(n__0()) -> #0() #28: #activate(n__isNat(X)) -> #isNat(X) #29: #U31(tt()) -> #0() #30: #U11(tt(),N) -> #activate(N) #31: #isNat(n__s(V1)) -> #isNat(activate(V1)) #32: #isNat(n__s(V1)) -> #activate(V1) #33: #U41(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N)) #34: #U41(tt(),M,N) -> #x(activate(N),activate(M)) #35: #U41(tt(),M,N) -> #activate(N) #36: #U41(tt(),M,N) -> #activate(M) #37: #U41(tt(),M,N) -> #activate(N) Number of SCCs: 1, DPs: 32 SCC { #2..15 #17..25 #28 #30..37 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 U21 w: max(x1, x2, x3) U11 w: max(x2) s w: x1 #isNat w: x1 activate w: x1 and w: max(x2) #plus w: max(x1, x2) #activate w: x1 x w: max(x1 + 3, x2) n__s w: x1 0 w: 2 #x w: max(x1 + 3, x2) #s w: 0 n__isNat w: x1 n__plus w: max(x1, x2) n__0 w: 2 isNat w: x1 n__x w: max(x1 + 3, x2) plus w: max(x1, x2) #U11 w: max(x1, x2) U31 w: 3 #U41 w: max(x1 + 2, x2, x3 + 3) #U21 w: max(x1, x2, x3) tt w: 2 U41 w: max(x2, x3 + 3) #U31 w: 0 #and w: max(x2) USABLE RULES: { 1..24 } Removed DPs: #6 #9 #10 #17 #35 #37 Number of SCCs: 1, DPs: 26 SCC { #2..5 #7 #8 #11..15 #18..25 #28 #30..34 #36 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 U21 w: max(x1, x2 + 3, x3) U11 w: max(x2) s w: x1 #isNat w: x1 activate w: x1 and w: max(x2) #plus w: max(x1, x2) #activate w: x1 x w: max(x1 + 4, x2 + 1) n__s w: x1 0 w: 2 #x w: max(x1 + 4, x2 + 1) #s w: 0 n__isNat w: x1 n__plus w: max(x1, x2 + 3) n__0 w: 2 isNat w: x1 n__x w: max(x1 + 4, x2 + 1) plus w: max(x1, x2 + 3) #U11 w: max(x1, x2) U31 w: 4 #U41 w: max(x1 + 3, x2 + 1, x3 + 4) #U21 w: max(x1, x2, x3) tt w: 2 U41 w: max(x1 + 2, x2 + 1, x3 + 4) #U31 w: 0 #and w: max(x2) USABLE RULES: { 1..24 } Removed DPs: #7 #8 #11 #19 #22 #36 Number of SCCs: 1, DPs: 20 SCC { #2..5 #12..15 #18 #20 #21 #23..25 #28 #30..34 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 U21 w: max(x1, x2 + 4, x3) U11 w: max(x2) s w: x1 #isNat w: x1 activate w: x1 and w: max(x2) #plus w: max(x1, x2 + 1) #activate w: x1 x w: max(x1 + 6, x2 + 2) n__s w: x1 0 w: 2 #x w: max(x1 + 6, x2 + 2) #s w: 0 n__isNat w: x1 n__plus w: max(x1, x2 + 4) n__0 w: 2 isNat w: x1 n__x w: max(x1 + 6, x2 + 2) plus w: max(x1, x2 + 4) #U11 w: max(x1, x2) U31 w: 6 #U41 w: max(x1 + 3, x2 + 2, x3 + 6) #U21 w: max(x1, x2 + 1, x3) tt w: 2 U41 w: max(x1 + 4, x2 + 2, x3 + 6) #U31 w: 0 #and w: max(x1 + 1, x2) USABLE RULES: { 1..24 } Removed DPs: #4 #14 Number of SCCs: 1, DPs: 18 SCC { #2 #3 #5 #12 #13 #15 #18 #20 #21 #23..25 #28 #30..34 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 U21 s: [3,2,1] p: 4 U11 s: 2 s s: [1] p: 2 #isNat s: 1 activate s: 1 and s: 2 #plus s: [1,2] p: 4 #activate s: [1] p: 2 x s: [1,2] p: 6 n__s s: [1] p: 2 0 s: [] p: 1 #x s: [1,2] p: 6 #s s: [] p: 0 n__isNat s: [1] p: 0 n__plus s: [1,2] p: 4 n__0 s: [] p: 1 isNat s: [1] p: 0 n__x s: [1,2] p: 6 plus s: [1,2] p: 4 #U11 s: [2] p: 4 U31 s: [1] p: 2 #U41 s: [3,2,1] p: 6 #U21 s: [3,2,1] p: 4 tt s: [] p: 0 U41 s: [3,2,1] p: 6 #U31 s: [] p: 0 #and s: [2,1] p: 3 USABLE RULES: { 1..24 } Removed DPs: #2 #3 #5 #12 #13 #15 #18 #20 #21 #23..25 #28 #30 #31 #33 #34 Number of SCCs: 0, DPs: 0