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


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YES

Problem 1: 

(VAR L X X1 X2 Y)
(RULES
a__eq(0,0) -> true
a__eq(s(X),s(Y)) -> a__eq(X,Y)
a__eq(X,Y) -> false
a__eq(X1,X2) -> eq(X1,X2)
a__inf(X) -> cons(X,inf(s(X)))
a__inf(X) -> inf(X)
a__length(cons(X,L)) -> s(length(L))
a__length(nil) -> 0
a__length(X) -> length(X)
a__take(0,X) -> nil
a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
a__take(X1,X2) -> take(X1,X2)
mark(0) -> 0
mark(cons(X1,X2)) -> cons(X1,X2)
mark(eq(X1,X2)) -> a__eq(X1,X2)
mark(false) -> false
mark(inf(X)) -> a__inf(mark(X))
mark(length(X)) -> a__length(mark(X))
mark(nil) -> nil
mark(s(X)) -> s(X)
mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
mark(true) -> true
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__EQ(s(X),s(Y)) -> A__EQ(X,Y)
 MARK(eq(X1,X2)) -> A__EQ(X1,X2)
 MARK(inf(X)) -> A__INF(mark(X))
 MARK(inf(X)) -> MARK(X)
 MARK(length(X)) -> A__LENGTH(mark(X))
 MARK(length(X)) -> MARK(X)
 MARK(take(X1,X2)) -> A__TAKE(mark(X1),mark(X2))
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true

Problem 1: 

SCC Processor:
-> Pairs:
 A__EQ(s(X),s(Y)) -> A__EQ(X,Y)
 MARK(eq(X1,X2)) -> A__EQ(X1,X2)
 MARK(inf(X)) -> A__INF(mark(X))
 MARK(inf(X)) -> MARK(X)
 MARK(length(X)) -> A__LENGTH(mark(X))
 MARK(length(X)) -> MARK(X)
 MARK(take(X1,X2)) -> A__TAKE(mark(X1),mark(X2))
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__EQ(s(X),s(Y)) -> A__EQ(X,Y)
->->-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->->Cycle:
->->-> Pairs:
 MARK(inf(X)) -> MARK(X)
 MARK(length(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
->->-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A__EQ(s(X),s(Y)) -> A__EQ(X,Y)
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->Projection:
 pi(A__EQ) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MARK(inf(X)) -> MARK(X)
 MARK(length(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->Projection:
 pi(MARK) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__eq(0,0) -> true
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> cons(X,inf(s(X)))
 a__inf(X) -> inf(X)
 a__length(cons(X,L)) -> s(length(L))
 a__length(nil) -> 0
 a__length(X) -> length(X)
 a__take(0,X) -> nil
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__take(X1,X2) -> take(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(false) -> false
 mark(inf(X)) -> a__inf(mark(X))
 mark(length(X)) -> a__length(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(X)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(true) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.