details

property	value
status	complete
benchmark	Ex2_Luc02a_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n115.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0635581016541 seconds
cpu usage	0.021694032
max memory	1880064.0

stage attributes

key	value
output-size	5269
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 v_NonEmpty:S N:S X:S Y:S) (RULES add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S)) -> cons(Y:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S)) -> cons(Y:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S)) SQR(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) -> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S)) -> cons(Y:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S))) Problem 1: SCC Processor: -> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S)) SQR(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) -> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S)) -> cons(Y:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: DBL(s(X:S)) -> DBL(X:S) ->->-> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S)) -> cons(Y:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S))) ->->Cycle: ->->-> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) ->->-> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) popout

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job log

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actions

all output return to TRS Standard