/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 z)
(RULES
*(x,+(y,z)) -> +(*(x,y),*(x,z))
*(x,minus(y)) -> minus(*(x,y))
*(x,0) -> 0
*(x,1) -> x
+(minus(x),x) -> 0
+(x,0) -> x
minus(+(x,y)) -> +(minus(y),minus(x))
minus(minus(x)) -> x
minus(0) -> 0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(x,+(y,z)) -> *#(x,y)
 *#(x,+(y,z)) -> *#(x,z)
 *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
 *#(x,minus(y)) -> *#(x,y)
 *#(x,minus(y)) -> MINUS(*(x,y))
 MINUS(+(x,y)) -> +#(minus(y),minus(x))
 MINUS(+(x,y)) -> MINUS(x)
 MINUS(+(x,y)) -> MINUS(y)
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0

Problem 1: 

SCC Processor:
-> Pairs:
 *#(x,+(y,z)) -> *#(x,y)
 *#(x,+(y,z)) -> *#(x,z)
 *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
 *#(x,minus(y)) -> *#(x,y)
 *#(x,minus(y)) -> MINUS(*(x,y))
 MINUS(+(x,y)) -> +#(minus(y),minus(x))
 MINUS(+(x,y)) -> MINUS(x)
 MINUS(+(x,y)) -> MINUS(y)
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MINUS(+(x,y)) -> MINUS(x)
 MINUS(+(x,y)) -> MINUS(y)
->->-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->->Cycle:
->->-> Pairs:
 *#(x,+(y,z)) -> *#(x,y)
 *#(x,+(y,z)) -> *#(x,z)
 *#(x,minus(y)) -> *#(x,y)
->->-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MINUS(+(x,y)) -> MINUS(x)
 MINUS(+(x,y)) -> MINUS(y)
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->Projection:
 pi(MINUS) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 *#(x,+(y,z)) -> *#(x,y)
 *#(x,+(y,z)) -> *#(x,z)
 *#(x,minus(y)) -> *#(x,y)
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->Projection:
 pi(*#) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))
 *(x,0) -> 0
 *(x,1) -> x
 +(minus(x),x) -> 0
 +(x,0) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 minus(minus(x)) -> x
 minus(0) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.