/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__U11(tt(),M,N) -> a__U12(tt(),M,N) 2: a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) 3: a__U21(tt(),M,N) -> a__U22(tt(),M,N) 4: a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) 5: a__plus(N,0()) -> mark(N) 6: a__plus(N,s(M)) -> a__U11(tt(),M,N) 7: a__x(N,0()) -> 0() 8: a__x(N,s(M)) -> a__U21(tt(),M,N) 9: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) 10: mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) 11: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) 12: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) 13: mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) 14: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) 15: mark(tt()) -> tt() 16: mark(s(X)) -> s(mark(X)) 17: mark(0()) -> 0() 18: a__U11(X1,X2,X3) -> U11(X1,X2,X3) 19: a__U12(X1,X2,X3) -> U12(X1,X2,X3) 20: a__plus(X1,X2) -> plus(X1,X2) 21: a__U21(X1,X2,X3) -> U21(X1,X2,X3) 22: a__U22(X1,X2,X3) -> U22(X1,X2,X3) 23: a__x(X1,X2) -> x(X1,X2) Number of strict rules: 23 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__U12(tt(),M,N) -> #a__plus(mark(N),mark(M)) #2: #a__U12(tt(),M,N) -> #mark(N) #3: #a__U12(tt(),M,N) -> #mark(M) #4: #a__plus(N,s(M)) -> #a__U11(tt(),M,N) #5: #mark(U22(X1,X2,X3)) -> #a__U22(mark(X1),X2,X3) #6: #mark(U22(X1,X2,X3)) -> #mark(X1) #7: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3) #8: #mark(U11(X1,X2,X3)) -> #mark(X1) #9: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2)) #10: #mark(plus(X1,X2)) -> #mark(X1) #11: #mark(plus(X1,X2)) -> #mark(X2) #12: #mark(U21(X1,X2,X3)) -> #a__U21(mark(X1),X2,X3) #13: #mark(U21(X1,X2,X3)) -> #mark(X1) #14: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2)) #15: #mark(x(X1,X2)) -> #mark(X1) #16: #mark(x(X1,X2)) -> #mark(X2) #17: #mark(U12(X1,X2,X3)) -> #a__U12(mark(X1),X2,X3) #18: #mark(U12(X1,X2,X3)) -> #mark(X1) #19: #a__plus(N,0()) -> #mark(N) #20: #mark(s(X)) -> #mark(X) #21: #a__U21(tt(),M,N) -> #a__U22(tt(),M,N) #22: #a__U11(tt(),M,N) -> #a__U12(tt(),M,N) #23: #a__x(N,s(M)) -> #a__U21(tt(),M,N) #24: #a__U22(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N)) #25: #a__U22(tt(),M,N) -> #a__x(mark(N),mark(M)) #26: #a__U22(tt(),M,N) -> #mark(N) #27: #a__U22(tt(),M,N) -> #mark(M) #28: #a__U22(tt(),M,N) -> #mark(N) Number of SCCs: 1, DPs: 28 SCC { #1..28 } POLO(Sum)... POLO(max)... succeeded. a__plus w: max(x1, x2) U21 w: max(x1 + 2, x2 + 1, x3 + 3) U11 w: max(x1, x2, x3) s w: x1 #a__x w: max(x1 + 3, x2 + 1) a__U22 w: max(x1 + 3, x2 + 1, x3 + 3) #a__U11 w: max(x2, x3) a__x w: max(x1 + 3, x2 + 1) U12 w: max(x1, x2, x3) x w: max(x1 + 3, x2 + 1) #a__U12 w: max(x1, x2, x3) #a__U21 w: max(x2 + 1, x3 + 3) #a__plus w: max(x1, x2) #mark w: x1 0 w: 4 a__U21 w: max(x1 + 2, x2 + 1, x3 + 3) mark w: x1 a__U11 w: max(x1, x2, x3) a__U12 w: max(x1, x2, x3) plus w: max(x1, x2) #a__U22 w: max(x1 + 3, x2 + 1, x3 + 3) tt w: 0 U22 w: max(x1 + 3, x2 + 1, x3 + 3) USABLE RULES: { 1..23 } Removed DPs: #6 #13 #15 #16 #26..28 Number of SCCs: 1, DPs: 21 SCC { #1..5 #7..12 #14 #17..25 } POLO(Sum)... POLO(max)... succeeded. a__plus w: max(x1, x2 + 5) U21 w: max(x1 + 5, x2 + 11, x3 + 6) U11 w: max(x1 + 2, x2 + 5, x3) s w: x1 #a__x w: max(x1 + 8, x2 + 13) a__U22 w: max(x1 + 7, x2 + 11, x3 + 6) #a__U11 w: max(x1 + 1, x2 + 7, x3 + 2) a__x w: max(x1 + 6, x2 + 11) U12 w: max(x1 + 2, x2 + 5, x3) x w: max(x1 + 6, x2 + 11) #a__U12 w: max(x2 + 7, x3 + 2) #a__U21 w: max(x1 + 6, x2 + 13, x3 + 8) #a__plus w: max(x1 + 2, x2 + 7) #mark w: x1 + 2 0 w: 7 a__U21 w: max(x1 + 5, x2 + 11, x3 + 6) mark w: x1 a__U11 w: max(x1 + 2, x2 + 5, x3) a__U12 w: max(x1 + 2, x2 + 5, x3) plus w: max(x1, x2 + 5) #a__U22 w: max(x2 + 13, x3 + 8) tt w: 3 U22 w: max(x1 + 7, x2 + 11, x3 + 6) USABLE RULES: { 1..23 } Removed DPs: #3 #8 #11 #18 Number of SCCs: 1, DPs: 17 SCC { #1 #2 #4 #5 #7 #9 #10 #12 #14 #17 #19..25 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 6 U21 s: [3,2,1] p: 7 U11 s: [2,3,1] p: 6 s s: [1] p: 5 #a__x s: [1,2] p: 7 a__U22 s: [3,2,1] p: 7 #a__U11 s: [2,3] p: 3 a__x s: [1,2] p: 7 U12 s: [2,3,1] p: 6 x s: [1,2] p: 7 #a__U12 s: [2,3] p: 3 #a__U21 s: [3,2,1] p: 7 #a__plus s: [2,1] p: 3 #mark s: [1] p: 2 0 s: [] p: 1 a__U21 s: [3,2,1] p: 7 mark s: 1 a__U11 s: [2,3,1] p: 6 a__U12 s: [2,3,1] p: 6 plus s: [2,1] p: 6 #a__U22 s: [3,2,1] p: 7 tt s: [] p: 4 U22 s: [3,2,1] p: 7 USABLE RULES: { 1..23 } Removed DPs: #2 #5 #7 #9 #10 #12 #14 #17 #19 #20 #23..25 Number of SCCs: 1, DPs: 3 SCC { #1 #4 #22 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 6 U21 s: [3,2,1] p: 7 U11 s: [2,3,1] p: 6 s s: [1] p: 5 #a__x s: [1,2] p: 7 a__U22 s: [3,2,1] p: 7 #a__U11 s: [2,3] p: 3 a__x s: [1,2] p: 7 U12 s: [2,3,1] p: 6 x s: [1,2] p: 7 #a__U12 s: [2,3] p: 3 #a__U21 s: [3,2,1] p: 7 #a__plus s: [2,1] p: 3 #mark s: [1] p: 2 0 s: [] p: 1 a__U21 s: [3,2,1] p: 7 mark s: 1 a__U11 s: [2,3,1] p: 6 a__U12 s: [2,3,1] p: 6 plus s: [2,1] p: 6 #a__U22 s: [3,2,1] p: 7 tt s: [] p: 4 U22 s: [3,2,1] p: 7 USABLE RULES: { 1..23 } Removed DPs: #4 Number of SCCs: 0, DPs: 0