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TRS Standard pair #516962381
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0271759033203 seconds
cpu usage
0.022373101
max memory
2113536.0
stage attributes
key
value
output-size
7270
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X: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: Dependency Pairs Processor: -> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) HALF(s(s(X:S))) -> HALF(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) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X: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) HALF(s(s(X:S))) -> HALF(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) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X: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: HALF(s(s(X:S))) -> HALF(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) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X: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: DBL(s(X:S)) -> DBL(X:S) ->->-> Rules:
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