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TRS Equational pair #487092762
details
property
value
status
complete
benchmark
AC26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
4.92545 seconds
cpu usage
4.45288
user time
2.99332
system time
1.45957
max virtual memory
694660.0
max residence set size
9540.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x y z) (THEORY (AC plus times)) (RULES plus(x,plus(s(y),z)) -> plus(s(plus(x,y)),z) plus(x,0) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,times(0,z)) -> times(0,z) times(x,times(s(y),z)) -> times(plus(times(x,y),x),z) times(x,0) -> 0 times(x,s(y)) -> plus(times(x,y),x) ) Problem 1: Dependency Pairs Processor: -> FAxioms: 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) -> Pairs: PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(plus(s(plus(x,y)),z),x3) PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(s(plus(x,y)),z) PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(x,y) PLUS(plus(x,0),x3) -> PLUS(x,x3) PLUS(plus(x,s(y)),x3) -> PLUS(s(plus(x,y)),x3) PLUS(plus(x,s(y)),x3) -> PLUS(x,y) PLUS(x,plus(s(y),z)) -> PLUS(s(plus(x,y)),z) PLUS(x,plus(s(y),z)) -> PLUS(x,y) PLUS(x,s(y)) -> PLUS(x,y) TIMES(times(x,times(0,z)),x3) -> TIMES(times(0,z),x3) TIMES(times(x,times(s(y),z)),x3) -> PLUS(times(x,y),x) TIMES(times(x,times(s(y),z)),x3) -> TIMES(plus(times(x,y),x),z) TIMES(times(x,times(s(y),z)),x3) -> TIMES(times(plus(times(x,y),x),z),x3) TIMES(times(x,times(s(y),z)),x3) -> TIMES(x,y) TIMES(times(x,0),x3) -> TIMES(0,x3) TIMES(times(x,s(y)),x3) -> PLUS(times(x,y),x) TIMES(times(x,s(y)),x3) -> TIMES(plus(times(x,y),x),x3) TIMES(times(x,s(y)),x3) -> TIMES(x,y) TIMES(x,times(s(y),z)) -> PLUS(times(x,y),x) TIMES(x,times(s(y),z)) -> TIMES(plus(times(x,y),x),z) TIMES(x,times(s(y),z)) -> TIMES(x,y) TIMES(x,s(y)) -> PLUS(times(x,y),x) TIMES(x,s(y)) -> TIMES(x,y) -> EAxioms: 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) -> Rules: plus(x,plus(s(y),z)) -> plus(s(plus(x,y)),z) plus(x,0) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,times(0,z)) -> times(0,z) times(x,times(s(y),z)) -> times(plus(times(x,y),x),z) times(x,0) -> 0 times(x,s(y)) -> plus(times(x,y),x) -> SRules: PLUS(plus(x3,x4),x5) -> PLUS(x3,x4) PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5) TIMES(times(x3,x4),x5) -> TIMES(x3,x4) TIMES(x3,times(x4,x5)) -> TIMES(x4,x5) Problem 1: SCC Processor: -> FAxioms: 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) -> Pairs: PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(plus(s(plus(x,y)),z),x3) PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(s(plus(x,y)),z) PLUS(plus(x,plus(s(y),z)),x3) -> PLUS(x,y) PLUS(plus(x,0),x3) -> PLUS(x,x3) PLUS(plus(x,s(y)),x3) -> PLUS(s(plus(x,y)),x3) PLUS(plus(x,s(y)),x3) -> PLUS(x,y) PLUS(x,plus(s(y),z)) -> PLUS(s(plus(x,y)),z) PLUS(x,plus(s(y),z)) -> PLUS(x,y) PLUS(x,s(y)) -> PLUS(x,y) TIMES(times(x,times(0,z)),x3) -> TIMES(times(0,z),x3) TIMES(times(x,times(s(y),z)),x3) -> PLUS(times(x,y),x) TIMES(times(x,times(s(y),z)),x3) -> TIMES(plus(times(x,y),x),z) TIMES(times(x,times(s(y),z)),x3) -> TIMES(times(plus(times(x,y),x),z),x3) TIMES(times(x,times(s(y),z)),x3) -> TIMES(x,y) TIMES(times(x,0),x3) -> TIMES(0,x3) TIMES(times(x,s(y)),x3) -> PLUS(times(x,y),x) TIMES(times(x,s(y)),x3) -> TIMES(plus(times(x,y),x),x3) TIMES(times(x,s(y)),x3) -> TIMES(x,y) TIMES(x,times(s(y),z)) -> PLUS(times(x,y),x) TIMES(x,times(s(y),z)) -> TIMES(plus(times(x,y),x),z) TIMES(x,times(s(y),z)) -> TIMES(x,y) TIMES(x,s(y)) -> PLUS(times(x,y),x) TIMES(x,s(y)) -> TIMES(x,y)
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