TRS Equational pair #516978225

details

property	value
status	complete
benchmark	AC07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.838920116425 seconds
cpu usage	0.701440218
max memory	4550656.0

stage attributes

key	value
output-size	21044
starexec-result	YES

output

/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 x xs y)
(THEORY 
(AC plus))
(RULES
S(cons(x,xs)) -> plus(x,S(xs))
S(nil) -> 0
int(0,0) -> cons(0,nil)
int(0,s(y)) -> cons(0,int(s(0),s(y)))
int(s(x),0) -> nil
int(s(x),s(y)) -> intlist(int(x,y))
intlist(cons(x,y)) -> cons(s(x),intlist(y))
intlist(nil) -> nil
plus(x,0) -> x
plus(x,s(y)) -> s(plus(x,y))
sum(x,y) -> S(int(x,y))
)

Problem 1: 

Reduction Order Processor:
-> Rules:
 S(cons(x,xs)) -> plus(x,S(xs))
 S(nil) -> 0
 int(0,0) -> cons(0,nil)
 int(0,s(y)) -> cons(0,int(s(0),s(y)))
 int(s(x),0) -> nil
 int(s(x),s(y)) -> intlist(int(x,y))
 intlist(cons(x,y)) -> cons(s(x),intlist(y))
 intlist(nil) -> nil
 plus(x,0) -> x
 plus(x,s(y)) -> s(plus(x,y))
 sum(x,y) -> S(int(x,y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[S](X) = X
[int](X1,X2) = 2.X1 + 2.X2 + 2
[intlist](X) = X
[plus](X1,X2) = X1 + X2
[sum](X1,X2) = 2.X1 + 2.X2 + 2
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[nil] = 2
[s](X) = X

Problem 1: 

Reduction Order Processor:
-> Rules:
 S(cons(x,xs)) -> plus(x,S(xs))
 int(0,0) -> cons(0,nil)
 int(0,s(y)) -> cons(0,int(s(0),s(y)))
 int(s(x),0) -> nil
 int(s(x),s(y)) -> intlist(int(x,y))
 intlist(cons(x,y)) -> cons(s(x),intlist(y))
 intlist(nil) -> nil
 plus(x,0) -> x
 plus(x,s(y)) -> s(plus(x,y))
 sum(x,y) -> S(int(x,y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[S](X) = X + 1
[int](X1,X2) = 2.X1 + 2.X2 + 1
[intlist](X) = X
[plus](X1,X2) = X1 + X2
[sum](X1,X2) = 2.X1 + 2.X2 + 2
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[nil] = 0
[s](X) = X

Problem 1: 

Reduction Order Processor:
-> Rules:

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