/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR I P V V1 V2 X Y Z)
(STRATEGY CONTEXTSENSITIVE
(U11 1)
(U21 1)
(U22 1)
(U31 1)
(U41 1)
(U42 1)
(U51 1)
(U52 1)
(U61 1)
(U71 1)
(U72 1)
(U81 1)
(__ 1 2)
(isList)
(isNeList)
(isNePal)
(isPal)
(isQid)
(a)
(e)
(i)
(nil)
(o)
(tt)
(u)
)
(RULES
U11(tt) -> tt
U21(tt,V2) -> U22(isList(V2))
U22(tt) -> tt
U31(tt) -> tt
U41(tt,V2) -> U42(isNeList(V2))
U42(tt) -> tt
U51(tt,V2) -> U52(isList(V2))
U52(tt) -> tt
U61(tt) -> tt
U71(tt,P) -> U72(isPal(P))
U72(tt) -> tt
U81(tt) -> tt
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(nil,X) -> X
__(X,nil) -> X
isList(__(V1,V2)) -> U21(isList(V1),V2)
isList(nil) -> tt
isList(V) -> U11(isNeList(V))
isNeList(__(V1,V2)) -> U41(isList(V1),V2)
isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
isNeList(V) -> U31(isQid(V))
isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
isNePal(V) -> U61(isQid(V))
isPal(nil) -> tt
isPal(V) -> U81(isNePal(V))
isQid(a) -> tt
isQid(e) -> tt
isQid(i) -> tt
isQid(o) -> tt
isQid(u) -> tt
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 U21#(tt,V2) -> U22#(isList(V2))
 U21#(tt,V2) -> ISLIST(V2)
 U41#(tt,V2) -> U42#(isNeList(V2))
 U41#(tt,V2) -> ISNELIST(V2)
 U51#(tt,V2) -> U52#(isList(V2))
 U51#(tt,V2) -> ISLIST(V2)
 U71#(tt,P) -> U72#(isPal(P))
 U71#(tt,P) -> ISPAL(P)
 __#(__(X,Y),Z) -> __#(X,__(Y,Z))
 __#(__(X,Y),Z) -> __#(Y,Z)
 ISLIST(__(V1,V2)) -> U21#(isList(V1),V2)
 ISLIST(__(V1,V2)) -> ISLIST(V1)
 ISLIST(V) -> U11#(isNeList(V))
 ISLIST(V) -> ISNELIST(V)
 ISNELIST(__(V1,V2)) -> U41#(isList(V1),V2)
 ISNELIST(__(V1,V2)) -> U51#(isNeList(V1),V2)
 ISNELIST(__(V1,V2)) -> ISLIST(V1)
 ISNELIST(__(V1,V2)) -> ISNELIST(V1)
 ISNELIST(V) -> U31#(isQid(V))
 ISNELIST(V) -> ISQID(V)
 ISNEPAL(__(I,__(P,I))) -> U71#(isQid(I),P)
 ISNEPAL(__(I,__(P,I))) -> ISQID(I)
 ISNEPAL(V) -> U61#(isQid(V))
 ISNEPAL(V) -> ISQID(V)
 ISPAL(V) -> U81#(isNePal(V))
 ISPAL(V) -> ISNEPAL(V)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 U21#(tt,V2) -> U22#(isList(V2))
 U21#(tt,V2) -> ISLIST(V2)
 U41#(tt,V2) -> U42#(isNeList(V2))
 U41#(tt,V2) -> ISNELIST(V2)
 U51#(tt,V2) -> U52#(isList(V2))
 U51#(tt,V2) -> ISLIST(V2)
 U71#(tt,P) -> U72#(isPal(P))
 U71#(tt,P) -> ISPAL(P)
 __#(__(X,Y),Z) -> __#(X,__(Y,Z))
 __#(__(X,Y),Z) -> __#(Y,Z)
 ISLIST(__(V1,V2)) -> U21#(isList(V1),V2)
 ISLIST(__(V1,V2)) -> ISLIST(V1)
 ISLIST(V) -> U11#(isNeList(V))
 ISLIST(V) -> ISNELIST(V)
 ISNELIST(__(V1,V2)) -> U41#(isList(V1),V2)
 ISNELIST(__(V1,V2)) -> U51#(isNeList(V1),V2)
 ISNELIST(__(V1,V2)) -> ISLIST(V1)
 ISNELIST(__(V1,V2)) -> ISNELIST(V1)
 ISNELIST(V) -> U31#(isQid(V))
 ISNELIST(V) -> ISQID(V)
 ISNEPAL(__(I,__(P,I))) -> U71#(isQid(I),P)
 ISNEPAL(__(I,__(P,I))) -> ISQID(I)
 ISNEPAL(V) -> U61#(isQid(V))
 ISNEPAL(V) -> ISQID(V)
 ISPAL(V) -> U81#(isNePal(V))
 ISPAL(V) -> ISNEPAL(V)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 __#(__(X,Y),Z) -> __#(X,__(Y,Z))
 __#(__(X,Y),Z) -> __#(Y,Z)
->->-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 U71#(tt,P) -> ISPAL(P)
 ISNEPAL(__(I,__(P,I))) -> U71#(isQid(I),P)
 ISPAL(V) -> ISNEPAL(V)
->->-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 U21#(tt,V2) -> ISLIST(V2)
 U41#(tt,V2) -> ISNELIST(V2)
 U51#(tt,V2) -> ISLIST(V2)
 ISLIST(__(V1,V2)) -> U21#(isList(V1),V2)
 ISLIST(__(V1,V2)) -> ISLIST(V1)
 ISLIST(V) -> ISNELIST(V)
 ISNELIST(__(V1,V2)) -> U41#(isList(V1),V2)
 ISNELIST(__(V1,V2)) -> U51#(isNeList(V1),V2)
 ISNELIST(__(V1,V2)) -> ISLIST(V1)
 ISNELIST(__(V1,V2)) -> ISNELIST(V1)
->->-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
->->-> Unhiding rules:
 Empty


The problem is decomposed in 3 subproblems.

Problem 1.1: 

SubNColl Processor:
-> Pairs:
 __#(__(X,Y),Z) -> __#(X,__(Y,Z))
 __#(__(X,Y),Z) -> __#(Y,Z)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Projection:
 pi(__#) = 1

Problem 1.1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.

Problem 1.2: 

SubNColl Processor:
-> Pairs:
 U71#(tt,P) -> ISPAL(P)
 ISNEPAL(__(I,__(P,I))) -> U71#(isQid(I),P)
 ISPAL(V) -> ISNEPAL(V)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Projection:
 pi(U71#) = 2
 pi(ISNEPAL) = 1
 pi(ISPAL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 U71#(tt,P) -> ISPAL(P)
 ISPAL(V) -> ISNEPAL(V)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

SubNColl Processor:
-> Pairs:
 U21#(tt,V2) -> ISLIST(V2)
 U41#(tt,V2) -> ISNELIST(V2)
 U51#(tt,V2) -> ISLIST(V2)
 ISLIST(__(V1,V2)) -> U21#(isList(V1),V2)
 ISLIST(__(V1,V2)) -> ISLIST(V1)
 ISLIST(V) -> ISNELIST(V)
 ISNELIST(__(V1,V2)) -> U41#(isList(V1),V2)
 ISNELIST(__(V1,V2)) -> U51#(isNeList(V1),V2)
 ISNELIST(__(V1,V2)) -> ISLIST(V1)
 ISNELIST(__(V1,V2)) -> ISNELIST(V1)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Projection:
 pi(U21#) = 2
 pi(U41#) = 2
 pi(U51#) = 2
 pi(ISLIST) = 1
 pi(ISNELIST) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 U21#(tt,V2) -> ISLIST(V2)
 U41#(tt,V2) -> ISNELIST(V2)
 U51#(tt,V2) -> ISLIST(V2)
 ISLIST(V) -> ISNELIST(V)
-> Rules:
 U11(tt) -> tt
 U21(tt,V2) -> U22(isList(V2))
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt,V2) -> U42(isNeList(V2))
 U42(tt) -> tt
 U51(tt,V2) -> U52(isList(V2))
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt,P) -> U72(isPal(P))
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(nil,X) -> X
 __(X,nil) -> X
 isList(__(V1,V2)) -> U21(isList(V1),V2)
 isList(nil) -> tt
 isList(V) -> U11(isNeList(V))
 isNeList(__(V1,V2)) -> U41(isList(V1),V2)
 isNeList(__(V1,V2)) -> U51(isNeList(V1),V2)
 isNeList(V) -> U31(isQid(V))
 isNePal(__(I,__(P,I))) -> U71(isQid(I),P)
 isNePal(V) -> U61(isQid(V))
 isPal(nil) -> tt
 isPal(V) -> U81(isNePal(V))
 isQid(a) -> tt
 isQid(e) -> tt
 isQid(i) -> tt
 isQid(o) -> tt
 isQid(u) -> tt
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.