/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
+(+(x,y),z) -> +(x,+(y,z))
+(a,+(b,z)) -> +(b,+(a,z))
+(a,b) -> +(b,a)
f(+(x,y),z) -> +(f(x,z),f(y,z))
f(a,y) -> a
f(b,y) -> b
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(a,+(b,z)) -> +#(a,z)
 +#(a,+(b,z)) -> +#(b,+(a,z))
 F(+(x,y),z) -> +#(f(x,z),f(y,z))
 F(+(x,y),z) -> F(x,z)
 F(+(x,y),z) -> F(y,z)
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b

Problem 1: 

SCC Processor:
-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(a,+(b,z)) -> +#(a,z)
 +#(a,+(b,z)) -> +#(b,+(a,z))
 F(+(x,y),z) -> +#(f(x,z),f(y,z))
 F(+(x,y),z) -> F(x,z)
 F(+(x,y),z) -> F(y,z)
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(a,+(b,z)) -> +#(a,z)
->->-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->->Cycle:
->->-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
->->-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->->Cycle:
->->-> Pairs:
 F(+(x,y),z) -> F(x,z)
 F(+(x,y),z) -> F(y,z)
->->-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 +#(a,+(b,z)) -> +#(a,z)
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Projection:
 pi(+#) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Projection:
 pi(+#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 F(+(x,y),z) -> F(x,z)
 F(+(x,y),z) -> F(y,z)
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Projection:
 pi(F) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(+(x,y),z) -> +(x,+(y,z))
 +(a,+(b,z)) -> +(b,+(a,z))
 +(a,b) -> +(b,a)
 f(+(x,y),z) -> +(f(x,z),f(y,z))
 f(a,y) -> a
 f(b,y) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.