/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)
(RULES
bin(0,s(y)) -> 0
bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
bin(x,0) -> s(0)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 BIN(s(x),s(y)) -> BIN(x,s(y))
 BIN(s(x),s(y)) -> BIN(x,y)
-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)

Problem 1: 

SCC Processor:
-> Pairs:
 BIN(s(x),s(y)) -> BIN(x,s(y))
 BIN(s(x),s(y)) -> BIN(x,y)
-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 BIN(s(x),s(y)) -> BIN(x,s(y))
 BIN(s(x),s(y)) -> BIN(x,y)
->->-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)

Problem 1: 

Subterm Processor:
-> Pairs:
 BIN(s(x),s(y)) -> BIN(x,s(y))
 BIN(s(x),s(y)) -> BIN(x,y)
-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)
->Projection:
 pi(BIN) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 bin(0,s(y)) -> 0
 bin(s(x),s(y)) -> +(bin(x,s(y)),bin(x,y))
 bin(x,0) -> s(0)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.