/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(U11(tt(),N)) -> mark(N) 2: active(U21(tt(),M,N)) -> mark(s(plus(N,M))) 3: active(and(tt(),X)) -> mark(X) 4: active(isNat(0())) -> mark(tt()) 5: active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) 6: active(isNat(s(V1))) -> mark(isNat(V1)) 7: active(plus(N,0())) -> mark(U11(isNat(N),N)) 8: active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) 9: active(U11(X1,X2)) -> U11(active(X1),X2) 10: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) 11: active(s(X)) -> s(active(X)) 12: active(plus(X1,X2)) -> plus(active(X1),X2) 13: active(plus(X1,X2)) -> plus(X1,active(X2)) 14: active(and(X1,X2)) -> and(active(X1),X2) 15: U11(mark(X1),X2) -> mark(U11(X1,X2)) 16: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) 17: s(mark(X)) -> mark(s(X)) 18: plus(mark(X1),X2) -> mark(plus(X1,X2)) 19: plus(X1,mark(X2)) -> mark(plus(X1,X2)) 20: and(mark(X1),X2) -> mark(and(X1,X2)) 21: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) 22: proper(tt()) -> ok(tt()) 23: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) 24: proper(s(X)) -> s(proper(X)) 25: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 26: proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 27: proper(isNat(X)) -> isNat(proper(X)) 28: proper(0()) -> ok(0()) 29: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) 30: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) 31: s(ok(X)) -> ok(s(X)) 32: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 33: and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 34: isNat(ok(X)) -> ok(isNat(X)) 35: top(mark(X)) -> top(proper(X)) 36: top(ok(X)) -> top(active(X)) Number of strict rules: 36 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(U21(tt(),M,N)) -> #s(plus(N,M)) #2: #active(U21(tt(),M,N)) -> #plus(N,M) #3: #U11(ok(X1),ok(X2)) -> #U11(X1,X2) #4: #top(mark(X)) -> #top(proper(X)) #5: #top(mark(X)) -> #proper(X) #6: #active(isNat(s(V1))) -> #isNat(V1) #7: #active(plus(X1,X2)) -> #plus(X1,active(X2)) #8: #active(plus(X1,X2)) -> #active(X2) #9: #active(U11(X1,X2)) -> #U11(active(X1),X2) #10: #active(U11(X1,X2)) -> #active(X1) #11: #active(s(X)) -> #s(active(X)) #12: #active(s(X)) -> #active(X) #13: #proper(s(X)) -> #s(proper(X)) #14: #proper(s(X)) -> #proper(X) #15: #proper(U21(X1,X2,X3)) -> #U21(proper(X1),proper(X2),proper(X3)) #16: #proper(U21(X1,X2,X3)) -> #proper(X1) #17: #proper(U21(X1,X2,X3)) -> #proper(X2) #18: #proper(U21(X1,X2,X3)) -> #proper(X3) #19: #active(plus(X1,X2)) -> #plus(active(X1),X2) #20: #active(plus(X1,X2)) -> #active(X1) #21: #s(ok(X)) -> #s(X) #22: #active(and(X1,X2)) -> #and(active(X1),X2) #23: #active(and(X1,X2)) -> #active(X1) #24: #U21(ok(X1),ok(X2),ok(X3)) -> #U21(X1,X2,X3) #25: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2)) #26: #proper(plus(X1,X2)) -> #proper(X1) #27: #proper(plus(X1,X2)) -> #proper(X2) #28: #and(mark(X1),X2) -> #and(X1,X2) #29: #active(plus(N,0())) -> #U11(isNat(N),N) #30: #active(plus(N,0())) -> #isNat(N) #31: #active(U21(X1,X2,X3)) -> #U21(active(X1),X2,X3) #32: #active(U21(X1,X2,X3)) -> #active(X1) #33: #and(ok(X1),ok(X2)) -> #and(X1,X2) #34: #active(isNat(plus(V1,V2))) -> #and(isNat(V1),isNat(V2)) #35: #active(isNat(plus(V1,V2))) -> #isNat(V1) #36: #active(isNat(plus(V1,V2))) -> #isNat(V2) #37: #isNat(ok(X)) -> #isNat(X) #38: #proper(isNat(X)) -> #isNat(proper(X)) #39: #proper(isNat(X)) -> #proper(X) #40: #s(mark(X)) -> #s(X) #41: #plus(ok(X1),ok(X2)) -> #plus(X1,X2) #42: #plus(X1,mark(X2)) -> #plus(X1,X2) #43: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2)) #44: #proper(and(X1,X2)) -> #proper(X1) #45: #proper(and(X1,X2)) -> #proper(X2) #46: #top(ok(X)) -> #top(active(X)) #47: #top(ok(X)) -> #active(X) #48: #proper(U11(X1,X2)) -> #U11(proper(X1),proper(X2)) #49: #proper(U11(X1,X2)) -> #proper(X1) #50: #proper(U11(X1,X2)) -> #proper(X2) #51: #U21(mark(X1),X2,X3) -> #U21(X1,X2,X3) #52: #active(plus(N,s(M))) -> #U21(and(isNat(M),isNat(N)),M,N) #53: #active(plus(N,s(M))) -> #and(isNat(M),isNat(N)) #54: #active(plus(N,s(M))) -> #isNat(M) #55: #active(plus(N,s(M))) -> #isNat(N) #56: #U11(mark(X1),X2) -> #U11(X1,X2) #57: #plus(mark(X1),X2) -> #plus(X1,X2) Number of SCCs: 9, DPs: 31 SCC { #37 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: x1 top w: 0 and w: 0 #plus w: 0 #top w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 mark w: 0 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 #active w: 0 #U21 w: 0 tt w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #37 Number of SCCs: 8, DPs: 30 SCC { #21 #40 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: 0 top w: 0 and w: 0 #plus w: 0 #top w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: x1 mark w: x1 + 1 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 #active w: 0 #U21 w: 0 tt w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #21 #40 Number of SCCs: 7, DPs: 28 SCC { #4 #46 } POLO(Sum)... POLO(max)... QLPOS... succeeded. U21 s: [3,2,1] p: 6 U11 s: [2,1] p: 5 s s: [1] p: 5 #isNat s: [] p: 0 top s: [] p: 0 and s: [2,1] p: 4 #plus s: [2,1] p: 0 #top s: [1] p: 0 proper s: 1 ok s: 1 0 s: [] p: 0 #s s: [] p: 0 mark s: [1] p: 3 #proper s: [] p: 0 isNat s: [1] p: 3 plus s: [1,2] p: 6 #U11 s: [] p: 0 active s: 1 #active s: [] p: 0 #U21 s: [3,1] p: 0 tt s: [] p: 0 #and s: [2] p: 0 USABLE RULES: { 1..34 } Removed DPs: #4 Number of SCCs: 7, DPs: 27 SCC { #46 } POLO(Sum)... succeeded. U21 w: x3 + 3 U11 w: x2 + 3 s w: x1 + 1 #isNat w: 0 top w: 0 and w: x2 + 3 #plus w: 0 #top w: x1 proper w: x1 + 2 ok w: x1 + 2 0 w: 1 #s w: 0 mark w: 3 #proper w: 0 isNat w: x1 + 1 plus w: x1 + 3 #U11 w: 0 active w: x1 + 1 #active w: 0 #U21 w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1..34 } Removed DPs: #46 Number of SCCs: 6, DPs: 26 SCC { #3 #56 } POLO(Sum)... succeeded. U21 w: x3 + 3 U11 w: x2 + 3 s w: x1 + 1 #isNat w: 0 top w: 0 and w: x2 + 3 #plus w: 0 #top w: x1 proper w: x1 + 2 ok w: x1 + 2 0 w: 1 #s w: 0 mark w: 3 #proper w: 0 isNat w: x1 + 1 plus w: x1 + 3 #U11 w: x2 active w: x1 + 1 #active w: 0 #U21 w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1..34 } Removed DPs: #3 Number of SCCs: 6, DPs: 25 SCC { #56 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: 1 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 + 2 ok w: x1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: x1 active w: x1 + 2 #active w: 0 #U21 w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1 4 5 8 16 20 22 28 30 33 34 } Removed DPs: #56 Number of SCCs: 5, DPs: 24 SCC { #28 #33 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: 1 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 + 2 ok w: x1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: 0 tt w: 1 #and w: x1 USABLE RULES: { 1 4 5 8 16 20 22 28 30 33 34 } Removed DPs: #28 Number of SCCs: 5, DPs: 23 SCC { #33 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 + 2 ok w: x1 + 1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: 0 tt w: 3 #and w: x2 USABLE RULES: { 1 4 16 20 22 28 30 33 } Removed DPs: #33 Number of SCCs: 4, DPs: 22 SCC { #24 #51 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 + 2 ok w: x1 + 1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: x3 tt w: 3 #and w: 0 USABLE RULES: { 1 4 16 20 22 28 30 33 } Removed DPs: #24 Number of SCCs: 4, DPs: 21 SCC { #51 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 + 2 ok w: x1 + 1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: x1 tt w: 3 #and w: 0 USABLE RULES: { 1 4 16 20 22 28 30 33 } Removed DPs: #51 Number of SCCs: 3, DPs: 20 SCC { #41 #42 #57 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: x1 #top w: 0 proper w: x1 + 2 ok w: x1 + 1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: 0 tt w: 3 #and w: 0 USABLE RULES: { 1 4 16 20 22 28 30 33 } Removed DPs: #41 #57 Number of SCCs: 3, DPs: 18 SCC { #42 } POLO(Sum)... succeeded. U21 w: x1 + 3 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: x2 #top w: 0 proper w: x1 + 2 ok w: x1 + 1 0 w: 1 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 2 plus w: x1 + 5 #U11 w: 0 active w: x1 + 2 #active w: 0 #U21 w: 0 tt w: 3 #and w: 0 USABLE RULES: { 1 4 16 20 22 28 30 33 } Removed DPs: #42 Number of SCCs: 2, DPs: 17 SCC { #8 #10 #12 #20 #23 #32 } POLO(Sum)... succeeded. U21 w: x1 + 1 U11 w: x1 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 proper w: x1 ok w: x1 + 1 0 w: 2 #s w: 0 mark w: 4 #proper w: 0 isNat w: 3 plus w: x1 + x2 + 1 #U11 w: 0 active w: x1 + 1 #active w: x1 #U21 w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1 4 16 18..20 30 33 } Removed DPs: #8 #10 #12 #20 #23 #32 Number of SCCs: 1, DPs: 11 SCC { #14 #16..18 #26 #27 #39 #44 #45 #49 #50 } POLO(Sum)... succeeded. U21 w: x1 + x2 + x3 + 1 U11 w: x1 + x2 + 3 s w: x1 + 2 #isNat w: 0 top w: 0 and w: x1 + x2 + 1 #plus w: 0 #top w: 0 proper w: x1 ok w: x1 + 1 0 w: 2 #s w: 0 mark w: 4 #proper w: x1 isNat w: x1 + 2 plus w: x1 + x2 + 1 #U11 w: 0 active w: x1 + 1 #active w: 0 #U21 w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1 4 16 18..20 30 33 } Removed DPs: #14 #16..18 #26 #27 #39 #44 #45 #49 #50 Number of SCCs: 0, DPs: 0