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TRS Standard pair #487069334
details
property
value
status
complete
benchmark
polo2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.021786 seconds
cpu usage
0.022303
user time
0.007837
system time
0.014466
max virtual memory
113188.0
max residence set size
5420.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S ALPHA:S BETA:S X:S) (RULES dx(a) -> zero dx(div(ALPHA:S,BETA:S)) -> minus(div(dx(ALPHA:S),BETA:S),times(ALPHA:S,div(dx(BETA:S),exp(BETA:S,two)))) dx(exp(ALPHA:S,BETA:S)) -> plus(times(BETA:S,times(exp(ALPHA:S,minus(BETA:S,one)),dx(ALPHA:S))),times(exp(ALPHA:S,BETA:S),times(ln(ALPHA:S),dx(BETA:S)))) dx(ln(ALPHA:S)) -> div(dx(ALPHA:S),ALPHA:S) dx(minus(ALPHA:S,BETA:S)) -> minus(dx(ALPHA:S),dx(BETA:S)) dx(neg(ALPHA:S)) -> neg(dx(ALPHA:S)) dx(plus(ALPHA:S,BETA:S)) -> plus(dx(ALPHA:S),dx(BETA:S)) dx(times(ALPHA:S,BETA:S)) -> plus(times(BETA:S,dx(ALPHA:S)),times(ALPHA:S,dx(BETA:S))) dx(X:S) -> one ) Problem 1: Dependency Pairs Processor: -> Pairs: DX(div(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(div(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(ln(ALPHA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(neg(ALPHA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(times(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(times(ALPHA:S,BETA:S)) -> DX(BETA:S) -> Rules: dx(a) -> zero dx(div(ALPHA:S,BETA:S)) -> minus(div(dx(ALPHA:S),BETA:S),times(ALPHA:S,div(dx(BETA:S),exp(BETA:S,two)))) dx(exp(ALPHA:S,BETA:S)) -> plus(times(BETA:S,times(exp(ALPHA:S,minus(BETA:S,one)),dx(ALPHA:S))),times(exp(ALPHA:S,BETA:S),times(ln(ALPHA:S),dx(BETA:S)))) dx(ln(ALPHA:S)) -> div(dx(ALPHA:S),ALPHA:S) dx(minus(ALPHA:S,BETA:S)) -> minus(dx(ALPHA:S),dx(BETA:S)) dx(neg(ALPHA:S)) -> neg(dx(ALPHA:S)) dx(plus(ALPHA:S,BETA:S)) -> plus(dx(ALPHA:S),dx(BETA:S)) dx(times(ALPHA:S,BETA:S)) -> plus(times(BETA:S,dx(ALPHA:S)),times(ALPHA:S,dx(BETA:S))) dx(X:S) -> one Problem 1: SCC Processor: -> Pairs: DX(div(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(div(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(ln(ALPHA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(neg(ALPHA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(times(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(times(ALPHA:S,BETA:S)) -> DX(BETA:S) -> Rules: dx(a) -> zero dx(div(ALPHA:S,BETA:S)) -> minus(div(dx(ALPHA:S),BETA:S),times(ALPHA:S,div(dx(BETA:S),exp(BETA:S,two)))) dx(exp(ALPHA:S,BETA:S)) -> plus(times(BETA:S,times(exp(ALPHA:S,minus(BETA:S,one)),dx(ALPHA:S))),times(exp(ALPHA:S,BETA:S),times(ln(ALPHA:S),dx(BETA:S)))) dx(ln(ALPHA:S)) -> div(dx(ALPHA:S),ALPHA:S) dx(minus(ALPHA:S,BETA:S)) -> minus(dx(ALPHA:S),dx(BETA:S)) dx(neg(ALPHA:S)) -> neg(dx(ALPHA:S)) dx(plus(ALPHA:S,BETA:S)) -> plus(dx(ALPHA:S),dx(BETA:S)) dx(times(ALPHA:S,BETA:S)) -> plus(times(BETA:S,dx(ALPHA:S)),times(ALPHA:S,dx(BETA:S))) dx(X:S) -> one ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: DX(div(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(div(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(exp(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(ln(ALPHA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(minus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(neg(ALPHA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(plus(ALPHA:S,BETA:S)) -> DX(BETA:S) DX(times(ALPHA:S,BETA:S)) -> DX(ALPHA:S) DX(times(ALPHA:S,BETA:S)) -> DX(BETA:S) ->->-> Rules: dx(a) -> zero dx(div(ALPHA:S,BETA:S)) -> minus(div(dx(ALPHA:S),BETA:S),times(ALPHA:S,div(dx(BETA:S),exp(BETA:S,two)))) dx(exp(ALPHA:S,BETA:S)) -> plus(times(BETA:S,times(exp(ALPHA:S,minus(BETA:S,one)),dx(ALPHA:S))),times(exp(ALPHA:S,BETA:S),times(ln(ALPHA:S),dx(BETA:S)))) dx(ln(ALPHA:S)) -> div(dx(ALPHA:S),ALPHA:S) dx(minus(ALPHA:S,BETA:S)) -> minus(dx(ALPHA:S),dx(BETA:S)) dx(neg(ALPHA:S)) -> neg(dx(ALPHA:S)) dx(plus(ALPHA:S,BETA:S)) -> plus(dx(ALPHA:S),dx(BETA:S)) dx(times(ALPHA:S,BETA:S)) -> plus(times(BETA:S,dx(ALPHA:S)),times(ALPHA:S,dx(BETA:S))) dx(X:S) -> one Problem 1: Subterm Processor: -> Pairs:
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