/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x y)
(RULES
f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
plus(0,y) -> y
plus(s(x),y) -> plus(x,s(y))
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 F(x,y) -> PLUS(y,z) | plus(x,y) -> plus(z,z)
 PLUS(s(x),y) -> PLUS(x,s(y))
-> QPairs:
 Empty
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))

Conditional Termination Problem 2:
-> Pairs:
 F(x,y) -> PLUS(x,y)
-> QPairs:
 F(x,y) -> PLUS(y,z) | plus(x,y) -> plus(z,z)
 PLUS(s(x),y) -> PLUS(x,s(y))
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(x,y) -> PLUS(y,z) | plus(x,y) -> plus(z,z)
 PLUS(s(x),y) -> PLUS(x,s(y))
-> QPairs:
 Empty
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(x),y) -> PLUS(x,s(y))
->->-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))

Problem 1.1: 

Conditional Subterm Processor:
-> Pairs:
 PLUS(s(x),y) -> PLUS(x,s(y))
-> QPairs:
 Empty
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))
->Projection:
 pi(PLUS) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(x,y) -> PLUS(x,y)
-> QPairs:
 F(x,y) -> PLUS(y,z) | plus(x,y) -> plus(z,z)
 PLUS(s(x),y) -> PLUS(x,s(y))
-> Rules:
 f(x,y) -> plus(y,z) | plus(x,y) -> plus(z,z)
 plus(0,y) -> y
 plus(s(x),y) -> plus(x,s(y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.