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TRS Equational pair #487092729
details
property
value
status
complete
benchmark
AC52.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
2.08952 seconds
cpu usage
1.80172
user time
1.19653
system time
0.605192
max virtual memory
564060.0
max residence set size
6552.0
stage attributes
key
value
starexec-result
YES
output
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:
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