/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 Z)
(STRATEGY CONTEXTSENSITIVE
(f 1)
(g 1)
(sel 1 2)
(0)
(cons 1)
(s 1)
)
(RULES
f(X) -> cons(X,f(g(X)))
g(0) -> s(0)
g(s(X)) -> s(s(g(X)))
sel(0,cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,Z)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 G(s(X)) -> G(X)
 SEL(s(X),cons(Y,Z)) -> SEL(X,Z)
 SEL(s(X),cons(Y,Z)) -> Z
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding Rules:
 f(g(X)) -> F(g(X))
 f(g(X)) -> G(X)

Problem 1: 

SCC Processor:
-> Pairs:
 G(s(X)) -> G(X)
 SEL(s(X),cons(Y,Z)) -> SEL(X,Z)
 SEL(s(X),cons(Y,Z)) -> Z
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding rules:
 f(g(X)) -> F(g(X))
 f(g(X)) -> G(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(s(X)) -> G(X)
->->-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 SEL(s(X),cons(Y,Z)) -> SEL(X,Z)
->->-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
->->-> Unhiding rules:
 Empty


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SubNColl Processor:
-> Pairs:
 G(s(X)) -> G(X)
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding rules:
 Empty
->Projection:
 pi(G) = 1

Problem 1.1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.

Problem 1.2: 

SubNColl Processor:
-> Pairs:
 SEL(s(X),cons(Y,Z)) -> SEL(X,Z)
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding rules:
 Empty
->Projection:
 pi(SEL) = 1

Problem 1.2: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 f(X) -> cons(X,f(g(X)))
 g(0) -> s(0)
 g(s(X)) -> s(s(g(X)))
 sel(0,cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,Z)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.