/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
and(xor(x,y),z) -> xor(and(x,z),and(y,z))
and(x,false) -> false
and(x,true) -> x
and(x,x) -> x
implies(x,y) -> xor(and(x,y),xor(x,true))
not(x) -> xor(x,true)
or(x,y) -> xor(and(x,y),xor(x,y))
xor(x,false) -> x
xor(x,x) -> false
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(xor(x,y),z) -> AND(x,z)
 AND(xor(x,y),z) -> AND(y,z)
 AND(xor(x,y),z) -> XOR(and(x,z),and(y,z))
 IMPLIES(x,y) -> AND(x,y)
 IMPLIES(x,y) -> XOR(and(x,y),xor(x,true))
 IMPLIES(x,y) -> XOR(x,true)
 NOT(x) -> XOR(x,true)
 OR(x,y) -> AND(x,y)
 OR(x,y) -> XOR(and(x,y),xor(x,y))
 OR(x,y) -> XOR(x,y)
-> Rules:
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 and(x,false) -> false
 and(x,true) -> x
 and(x,x) -> x
 implies(x,y) -> xor(and(x,y),xor(x,true))
 not(x) -> xor(x,true)
 or(x,y) -> xor(and(x,y),xor(x,y))
 xor(x,false) -> x
 xor(x,x) -> false

Problem 1: 

SCC Processor:
-> Pairs:
 AND(xor(x,y),z) -> AND(x,z)
 AND(xor(x,y),z) -> AND(y,z)
 AND(xor(x,y),z) -> XOR(and(x,z),and(y,z))
 IMPLIES(x,y) -> AND(x,y)
 IMPLIES(x,y) -> XOR(and(x,y),xor(x,true))
 IMPLIES(x,y) -> XOR(x,true)
 NOT(x) -> XOR(x,true)
 OR(x,y) -> AND(x,y)
 OR(x,y) -> XOR(and(x,y),xor(x,y))
 OR(x,y) -> XOR(x,y)
-> Rules:
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 and(x,false) -> false
 and(x,true) -> x
 and(x,x) -> x
 implies(x,y) -> xor(and(x,y),xor(x,true))
 not(x) -> xor(x,true)
 or(x,y) -> xor(and(x,y),xor(x,y))
 xor(x,false) -> x
 xor(x,x) -> false
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(xor(x,y),z) -> AND(x,z)
 AND(xor(x,y),z) -> AND(y,z)
->->-> Rules:
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 and(x,false) -> false
 and(x,true) -> x
 and(x,x) -> x
 implies(x,y) -> xor(and(x,y),xor(x,true))
 not(x) -> xor(x,true)
 or(x,y) -> xor(and(x,y),xor(x,y))
 xor(x,false) -> x
 xor(x,x) -> false

Problem 1: 

Subterm Processor:
-> Pairs:
 AND(xor(x,y),z) -> AND(x,z)
 AND(xor(x,y),z) -> AND(y,z)
-> Rules:
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 and(x,false) -> false
 and(x,true) -> x
 and(x,x) -> x
 implies(x,y) -> xor(and(x,y),xor(x,true))
 not(x) -> xor(x,true)
 or(x,y) -> xor(and(x,y),xor(x,y))
 xor(x,false) -> x
 xor(x,x) -> false
->Projection:
 pi(AND) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 and(x,false) -> false
 and(x,true) -> x
 and(x,x) -> x
 implies(x,y) -> xor(and(x,y),xor(x,true))
 not(x) -> xor(x,true)
 or(x,y) -> xor(and(x,y),xor(x,y))
 xor(x,false) -> x
 xor(x,x) -> false
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.