/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,g(y,z)) -> g(++(x,y),z)
++(x,nil) -> x
f(x,g(y,z)) -> g(f(x,y),z)
f(x,nil) -> g(nil,x)
max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
max(g(g(nil,x),y)) -> max'(x,y)
mem(g(x,y),z) -> or(=(y,z),mem(x,z))
mem(nil,y) -> false
mem(x,max(x)) -> not(null(x))
null(g(x,y)) -> false
null(nil) -> true
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(x,g(y,z)) -> ++#(x,y)
 F(x,g(y,z)) -> F(x,y)
 MAX(g(g(g(x,y),z),u)) -> MAX(g(g(x,y),z))
 MEM(g(x,y),z) -> MEM(x,z)
 MEM(x,max(x)) -> NULL(x)
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(x,g(y,z)) -> ++#(x,y)
 F(x,g(y,z)) -> F(x,y)
 MAX(g(g(g(x,y),z),u)) -> MAX(g(g(x,y),z))
 MEM(g(x,y),z) -> MEM(x,z)
 MEM(x,max(x)) -> NULL(x)
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MEM(g(x,y),z) -> MEM(x,z)
->->-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->->Cycle:
->->-> Pairs:
 MAX(g(g(g(x,y),z),u)) -> MAX(g(g(x,y),z))
->->-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->->Cycle:
->->-> Pairs:
 F(x,g(y,z)) -> F(x,y)
->->-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->->Cycle:
->->-> Pairs:
 ++#(x,g(y,z)) -> ++#(x,y)
->->-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true


The problem is decomposed in 4 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MEM(g(x,y),z) -> MEM(x,z)
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Projection:
 pi(MEM) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MAX(g(g(g(x,y),z),u)) -> MAX(g(g(x,y),z))
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Projection:
 pi(MAX) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 F(x,g(y,z)) -> F(x,y)
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Projection:
 pi(F) = 2

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 ++#(x,g(y,z)) -> ++#(x,y)
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Projection:
 pi(++#) = 2

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(x,g(y,z)) -> g(++(x,y),z)
 ++(x,nil) -> x
 f(x,g(y,z)) -> g(f(x,y),z)
 f(x,nil) -> g(nil,x)
 max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 max(g(g(nil,x),y)) -> max'(x,y)
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(nil,y) -> false
 mem(x,max(x)) -> not(null(x))
 null(g(x,y)) -> false
 null(nil) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.