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TRS Equational pair #487523200
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
n143.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
13.2727410793 seconds
cpu usage
4.61822181
max memory
1.3910016E7
stage attributes
key
value
output-size
69272
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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)
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