/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)
(RULES
and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
and(x:S,F) -> F
and(x:S,T) -> x:S
and(x:S,x:S) -> x:S
equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
neg(x:S) -> xor(x:S,T)
or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
xor(x:S,neg(x:S)) -> F
xor(x:S,F) -> x:S
xor(x:S,x:S) -> F
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
 AND(xor(x:S,y:S),z:S) -> XOR(and(x:S,z:S),and(y:S,z:S))
 EQUIV(x:S,y:S) -> XOR(x:S,xor(y:S,T))
 EQUIV(x:S,y:S) -> XOR(y:S,T)
 IMPL(x:S,y:S) -> AND(x:S,y:S)
 IMPL(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,T))
 IMPL(x:S,y:S) -> XOR(x:S,T)
 NEG(x:S) -> XOR(x:S,T)
 OR(x:S,y:S) -> AND(x:S,y:S)
 OR(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,y:S))
 OR(x:S,y:S) -> XOR(x:S,y:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,F) -> F
 and(x:S,T) -> x:S
 and(x:S,x:S) -> x:S
 equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
 impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
 neg(x:S) -> xor(x:S,T)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,neg(x:S)) -> F
 xor(x:S,F) -> x:S
 xor(x:S,x:S) -> F

Problem 1: 

SCC Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
 AND(xor(x:S,y:S),z:S) -> XOR(and(x:S,z:S),and(y:S,z:S))
 EQUIV(x:S,y:S) -> XOR(x:S,xor(y:S,T))
 EQUIV(x:S,y:S) -> XOR(y:S,T)
 IMPL(x:S,y:S) -> AND(x:S,y:S)
 IMPL(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,T))
 IMPL(x:S,y:S) -> XOR(x:S,T)
 NEG(x:S) -> XOR(x:S,T)
 OR(x:S,y:S) -> AND(x:S,y:S)
 OR(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,y:S))
 OR(x:S,y:S) -> XOR(x:S,y:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,F) -> F
 and(x:S,T) -> x:S
 and(x:S,x:S) -> x:S
 equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
 impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
 neg(x:S) -> xor(x:S,T)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,neg(x:S)) -> F
 xor(x:S,F) -> x:S
 xor(x:S,x:S) -> F
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
->->-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,F) -> F
 and(x:S,T) -> x:S
 and(x:S,x:S) -> x:S
 equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
 impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
 neg(x:S) -> xor(x:S,T)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,neg(x:S)) -> F
 xor(x:S,F) -> x:S
 xor(x:S,x:S) -> F

Problem 1: 

Subterm Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,F) -> F
 and(x:S,T) -> x:S
 and(x:S,x:S) -> x:S
 equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
 impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
 neg(x:S) -> xor(x:S,T)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,neg(x:S)) -> F
 xor(x:S,F) -> x:S
 xor(x:S,x:S) -> F
->Projection:
 pi(AND) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,F) -> F
 and(x:S,T) -> x:S
 and(x:S,x:S) -> x:S
 equiv(x:S,y:S) -> xor(x:S,xor(y:S,T))
 impl(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,T))
 neg(x:S) -> xor(x:S,T)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,neg(x:S)) -> F
 xor(x:S,F) -> x:S
 xor(x:S,x:S) -> F
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.