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TRS Equational pair #487092732
details
property
value
status
complete
benchmark
AC15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0429611 seconds
cpu usage
0.048033
user time
0.018922
system time
0.029111
max virtual memory
113188.0
max residence set size
4084.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x) (THEORY (AC f)) (RULES f(f(x,x),g(x)) -> f(x,h(x)) f(g(g(x)),x) -> f(g(x),g(x)) ) Problem 1: Reduction Order Processor: -> Rules: f(f(x,x),g(x)) -> f(x,h(x)) f(g(g(x)),x) -> f(g(x),g(x)) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = X1 + X2 + 2 [g](X) = 2.X + 2 [h](X) = 2.X + 2 Problem 1: Reduction Order Processor: -> Rules: f(g(g(x)),x) -> f(g(x),g(x)) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = X1 + X2 + 1 [g](X) = 2.X + 2 [h](X) = 2.X Problem 1: Dependency Pairs Processor: -> FAxioms: F(f(x1,x2),x3) = F(x1,f(x2,x3)) F(x1,x2) = F(x2,x1) -> Pairs: Empty -> EAxioms: f(f(x1,x2),x3) = f(x1,f(x2,x3)) f(x1,x2) = f(x2,x1) -> Rules: Empty -> SRules: F(f(x1,x2),x3) -> F(x1,x2) F(x1,f(x2,x3)) -> F(x2,x3) Problem 1: SCC Processor: -> FAxioms: F(f(x1,x2),x3) = F(x1,f(x2,x3)) F(x1,x2) = F(x2,x1) -> Pairs: Empty -> EAxioms: f(f(x1,x2),x3) = f(x1,f(x2,x3)) f(x1,x2) = f(x2,x1) -> Rules: Empty -> SRules: F(f(x1,x2),x3) -> F(x1,x2) F(x1,f(x2,x3)) -> F(x2,x3) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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