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

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.