/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 a b c t x y z)
(RULES
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
foldf(x,cons(y,z)) -> f(foldf(x,z),y)
foldf(x,nil) -> x
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(t,x) -> F'(t,g(x))
 F(t,x) -> G(x)
 F'(triple(a,b,c),A) -> F''(foldf(triple(cons(A,a),nil,c),b))
 F'(triple(a,b,c),A) -> FOLDF(triple(cons(A,a),nil,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDF(triple(a,b,nil),c)
 FOLDF(x,cons(y,z)) -> F(foldf(x,z),y)
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C

Problem 1: 

SCC Processor:
-> Pairs:
 F(t,x) -> F'(t,g(x))
 F(t,x) -> G(x)
 F'(triple(a,b,c),A) -> F''(foldf(triple(cons(A,a),nil,c),b))
 F'(triple(a,b,c),A) -> FOLDF(triple(cons(A,a),nil,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDF(triple(a,b,nil),c)
 FOLDF(x,cons(y,z)) -> F(foldf(x,z),y)
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(t,x) -> F'(t,g(x))
 F'(triple(a,b,c),A) -> F''(foldf(triple(cons(A,a),nil,c),b))
 F'(triple(a,b,c),A) -> FOLDF(triple(cons(A,a),nil,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDF(triple(a,b,nil),c)
 FOLDF(x,cons(y,z)) -> F(foldf(x,z),y)
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(t,x) -> F'(t,g(x))
 F'(triple(a,b,c),A) -> F''(foldf(triple(cons(A,a),nil,c),b))
 F'(triple(a,b,c),A) -> FOLDF(triple(cons(A,a),nil,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDF(triple(a,b,nil),c)
 FOLDF(x,cons(y,z)) -> F(foldf(x,z),y)
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
-> Usable rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = X1 + 2.X2
[f'](X1,X2) = X1 + 2.X2
[f''](X) = X + 2
[foldf](X1,X2) = X1 + X2
[g](X) = X
[A] = 1
[B] = 2
[C] = 2
[cons](X1,X2) = 2.X1 + X2
[nil] = 0
[triple](X1,X2,X3) = 2.X2 + X3 + 2
[F](X1,X2) = 2.X1 + 2.X2 + 2
[F'](X1,X2) = 2.X1 + 2.X2 + 1
[F''](X) = 2.X + 2
[FOLDF](X1,X2) = 2.X1 + 2.X2 + 2

Problem 1: 

SCC Processor:
-> Pairs:
 F'(triple(a,b,c),A) -> F''(foldf(triple(cons(A,a),nil,c),b))
 F'(triple(a,b,c),A) -> FOLDF(triple(cons(A,a),nil,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDF(triple(a,b,nil),c)
 FOLDF(x,cons(y,z)) -> F(foldf(x,z),y)
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C

Problem 1: 

Subterm Processor:
-> Pairs:
 FOLDF(x,cons(y,z)) -> FOLDF(x,z)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Projection:
 pi(FOLDF) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldf(triple(cons(A,a),nil,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,cons(C,c))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil),c)
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 foldf(x,nil) -> x
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.