/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 v_NonEmpty:S x:S y:S z:S z':S)
(RULES
f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S)
plus(0,y:S) -> y:S
plus(s(x:S),y:S) -> plus(x:S,s(y:S))
)

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

The problem is finite.