YES

Problem 1: 

(VAR x y z)
(THEORY 
(AC times plus))
(RULES
times(plus(x,y),z) -> plus(times(x,z),times(y,z))
times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
)

Problem 1: 

Dependency Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
 PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5))
 PLUS(x3,x4) = PLUS(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
 PLUS(plus(x3,x4),x5) -> PLUS(x3,x4)
 PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5)

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
 PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5))
 PLUS(x3,x4) = PLUS(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
 PLUS(plus(x3,x4),x5) -> PLUS(x3,x4)
 PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 1
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 1
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 0
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 0
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(x,z)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 1
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(plus(x,y),z) -> TIMES(y,z)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 1
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[times](X1,X2) = X1 + X2 + 2
[a] = 1
[f](X) = 2.X + 2
[g](X1,X2) = 0
[plus](X1,X2) = 2
[TIMES](X1,X2) = 2.X1 + 2.X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[times](X1,X2) = X1 + X2 + 2
[a] = 2
[f](X) = 2.X + 2
[g](X1,X2) = 0
[plus](X1,X2) = 0
[TIMES](X1,X2) = X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[times](X1,X2) = X1 + X2 + 1
[a] = 2
[f](X) = 2.X + 1
[g](X1,X2) = 0
[plus](X1,X2) = 0
[TIMES](X1,X2) = 2.X1 + 2.X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> FAxioms:
 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
 times(x3,x4) -> times(x4,x3)
 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
 plus(x3,x4) -> plus(x4,x3)
 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
 TIMES(x3,x4) -> TIMES(x4,x3)
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
->->-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 Empty

Problem 1: 

Reduction Pairs Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Usable Equations:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> Usable Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 Empty
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 1
->Interpretation:
 
[times](X1,X2) = X1.X2 + X1 + X2
[a] = 0
[f](X) = X + 1
[g](X1,X2) = X1
[plus](X1,X2) = X1 + X2 + 1
[TIMES](X1,X2) = X1.X2 + X1 + X2
[PLUS](X1,X2) = 0

Problem 1: 

SCC Processor:
-> FAxioms:
 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
 TIMES(x3,x4) = TIMES(x4,x3)
-> Pairs:
 Empty
-> EAxioms:
 times(times(x3,x4),x5) = times(x3,times(x4,x5))
 times(x3,x4) = times(x4,x3)
 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
 plus(x3,x4) = plus(x4,x3)
-> Rules:
 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
-> SRules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.