/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 X Y)
(STRATEGY CONTEXTSENSITIVE
(from 1)
(length)
(length1)
(0)
(cons 1)
(nil)
(s 1)
)
(RULES
from(X) -> cons(X,from(s(X)))
length(cons(X,Y)) -> s(length1(Y))
length(nil) -> 0
length1(X) -> length(X)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 LENGTH(cons(X,Y)) -> LENGTH1(Y)
 LENGTH1(X) -> LENGTH(X)
-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 LENGTH(cons(X,Y)) -> LENGTH1(Y)
 LENGTH1(X) -> LENGTH(X)
-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 LENGTH(cons(X,Y)) -> LENGTH1(Y)
 LENGTH1(X) -> LENGTH(X)
->->-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
->->-> Unhiding rules:
 Empty

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 LENGTH(cons(X,Y)) -> LENGTH1(Y)
 LENGTH1(X) -> LENGTH(X)
-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[cons](X1,X2) = 2.X2 + 2
[LENGTH](X) = 2.X + 2
[LENGTH1](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 LENGTH1(X) -> LENGTH(X)
-> Rules:
 from(X) -> cons(X,from(s(X)))
 length(cons(X,Y)) -> s(length1(Y))
 length(nil) -> 0
 length1(X) -> length(X)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.