/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR a b c n t x)
(RULES
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
f'(triple(a,b,c),C) -> triple(a,b,s(c))
f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
fold(t,x,0) -> t
fold(t,x,s(n)) -> f(fold(t,x,n),x)
foldB(t,0) -> t
foldB(t,s(n)) -> f(foldB(t,n),B)
foldC(t,0) -> t
foldC(t,s(n)) -> f(foldC(t,n),C)
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''(foldB(triple(s(a),0,c),b))
 F'(triple(a,b,c),A) -> FOLDB(triple(s(a),0,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDC(triple(a,b,0),c)
 FOLD(t,x,s(n)) -> F(fold(t,x,n),x)
 FOLD(t,x,s(n)) -> FOLD(t,x,n)
 FOLDB(t,s(n)) -> F(foldB(t,n),B)
 FOLDB(t,s(n)) -> FOLDB(t,n)
 FOLDC(t,s(n)) -> F(foldC(t,n),C)
 FOLDC(t,s(n)) -> FOLDC(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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''(foldB(triple(s(a),0,c),b))
 F'(triple(a,b,c),A) -> FOLDB(triple(s(a),0,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDC(triple(a,b,0),c)
 FOLD(t,x,s(n)) -> F(fold(t,x,n),x)
 FOLD(t,x,s(n)) -> FOLD(t,x,n)
 FOLDB(t,s(n)) -> F(foldB(t,n),B)
 FOLDB(t,s(n)) -> FOLDB(t,n)
 FOLDC(t,s(n)) -> F(foldC(t,n),C)
 FOLDC(t,s(n)) -> FOLDC(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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''(foldB(triple(s(a),0,c),b))
 F'(triple(a,b,c),A) -> FOLDB(triple(s(a),0,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDC(triple(a,b,0),c)
 FOLDB(t,s(n)) -> F(foldB(t,n),B)
 FOLDB(t,s(n)) -> FOLDB(t,n)
 FOLDC(t,s(n)) -> F(foldC(t,n),C)
 FOLDC(t,s(n)) -> FOLDC(t,n)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->->Cycle:
->->-> Pairs:
 FOLD(t,x,s(n)) -> FOLD(t,x,n)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 F(t,x) -> F'(t,g(x))
 F'(triple(a,b,c),A) -> F''(foldB(triple(s(a),0,c),b))
 F'(triple(a,b,c),A) -> FOLDB(triple(s(a),0,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDC(triple(a,b,0),c)
 FOLDB(t,s(n)) -> F(foldB(t,n),B)
 FOLDB(t,s(n)) -> FOLDB(t,n)
 FOLDC(t,s(n)) -> F(foldC(t,n),C)
 FOLDC(t,s(n)) -> FOLDC(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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 + X2
[f'](X1,X2) = X1 + X2
[f''](X) = X
[foldB](X1,X2) = X1 + X2
[foldC](X1,X2) = X1 + X2
[g](X) = X
[0] = 0
[A] = 1
[B] = 2
[C] = 2
[s](X) = X + 2
[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
[FOLDB](X1,X2) = 2.X1 + 2.X2 + 2
[FOLDC](X1,X2) = 2.X1 + 2.X2 + 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 F'(triple(a,b,c),A) -> F''(foldB(triple(s(a),0,c),b))
 F'(triple(a,b,c),A) -> FOLDB(triple(s(a),0,c),b)
 F'(triple(a,b,c),B) -> F(triple(a,b,c),A)
 F''(triple(a,b,c)) -> FOLDC(triple(a,b,0),c)
 FOLDB(t,s(n)) -> F(foldB(t,n),B)
 FOLDB(t,s(n)) -> FOLDB(t,n)
 FOLDC(t,s(n)) -> F(foldC(t,n),C)
 FOLDC(t,s(n)) -> FOLDC(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FOLDC(t,s(n)) -> FOLDC(t,n)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->->Cycle:
->->-> Pairs:
 FOLDB(t,s(n)) -> FOLDB(t,n)
->->-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C


The problem is decomposed in 2 subproblems.

Problem 1.1.1: 

Subterm Processor:
-> Pairs:
 FOLDC(t,s(n)) -> FOLDC(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Projection:
 pi(FOLDC) = 2

Problem 1.1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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.

Problem 1.1.2: 

Subterm Processor:
-> Pairs:
 FOLDB(t,s(n)) -> FOLDB(t,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Projection:
 pi(FOLDB) = 2

Problem 1.1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 FOLD(t,x,s(n)) -> FOLD(t,x,n)
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 g(A) -> A
 g(B) -> A
 g(B) -> B
 g(C) -> A
 g(C) -> B
 g(C) -> C
->Projection:
 pi(FOLD) = 3

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
 f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
 f'(triple(a,b,c),C) -> triple(a,b,s(c))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
 fold(t,x,0) -> t
 fold(t,x,s(n)) -> f(fold(t,x,n),x)
 foldB(t,0) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B)
 foldC(t,0) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C)
 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.