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TRS Stand 20472 pair #381717085
details
property
value
status
complete
benchmark
Ex26_Luc03b_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
2.06383490562 seconds
cpu usage
2.047389166
max memory
3.5618816E7
stage attributes
key
value
output-size
60477
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o active : [o] --> o add : [o * o] --> o cons : [o * o] --> o dbl : [o] --> o first : [o * o] --> o mark : [o] --> o nil : [] --> o recip : [o] --> o s : [o] --> o sqr : [o] --> o terms : [o] --> o active(terms(X)) => mark(cons(recip(sqr(X)), terms(s(X)))) active(sqr(0)) => mark(0) active(sqr(s(X))) => mark(s(add(sqr(X), dbl(X)))) active(dbl(0)) => mark(0) active(dbl(s(X))) => mark(s(s(dbl(X)))) active(add(0, X)) => mark(X) active(add(s(X), Y)) => mark(s(add(X, Y))) active(first(0, X)) => mark(nil) active(first(s(X), cons(Y, Z))) => mark(cons(Y, first(X, Z))) mark(terms(X)) => active(terms(mark(X))) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(recip(X)) => active(recip(mark(X))) mark(sqr(X)) => active(sqr(mark(X))) mark(s(X)) => active(s(X)) mark(0) => active(0) mark(add(X, Y)) => active(add(mark(X), mark(Y))) mark(dbl(X)) => active(dbl(mark(X))) mark(first(X, Y)) => active(first(mark(X), mark(Y))) mark(nil) => active(nil) terms(mark(X)) => terms(X) terms(active(X)) => terms(X) cons(mark(X), Y) => cons(X, Y) cons(X, mark(Y)) => cons(X, Y) cons(active(X), Y) => cons(X, Y) cons(X, active(Y)) => cons(X, Y) recip(mark(X)) => recip(X) recip(active(X)) => recip(X) sqr(mark(X)) => sqr(X) sqr(active(X)) => sqr(X) s(mark(X)) => s(X) s(active(X)) => s(X) add(mark(X), Y) => add(X, Y) add(X, mark(Y)) => add(X, Y) add(active(X), Y) => add(X, Y) add(X, active(Y)) => add(X, Y) dbl(mark(X)) => dbl(X) dbl(active(X)) => dbl(X) first(mark(X), Y) => first(X, Y) first(X, mark(Y)) => first(X, Y) first(active(X), Y) => first(X, Y) first(X, active(Y)) => first(X, Y) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] active#(terms(X)) =#> mark#(cons(recip(sqr(X)), terms(s(X)))) 1] active#(terms(X)) =#> cons#(recip(sqr(X)), terms(s(X))) 2] active#(terms(X)) =#> recip#(sqr(X)) 3] active#(terms(X)) =#> sqr#(X) 4] active#(terms(X)) =#> terms#(s(X)) 5] active#(terms(X)) =#> s#(X) 6] active#(sqr(0)) =#> mark#(0) 7] active#(sqr(s(X))) =#> mark#(s(add(sqr(X), dbl(X)))) 8] active#(sqr(s(X))) =#> s#(add(sqr(X), dbl(X))) 9] active#(sqr(s(X))) =#> add#(sqr(X), dbl(X)) 10] active#(sqr(s(X))) =#> sqr#(X) 11] active#(sqr(s(X))) =#> dbl#(X) 12] active#(dbl(0)) =#> mark#(0) 13] active#(dbl(s(X))) =#> mark#(s(s(dbl(X)))) 14] active#(dbl(s(X))) =#> s#(s(dbl(X))) 15] active#(dbl(s(X))) =#> s#(dbl(X)) 16] active#(dbl(s(X))) =#> dbl#(X) 17] active#(add(0, X)) =#> mark#(X) 18] active#(add(s(X), Y)) =#> mark#(s(add(X, Y))) 19] active#(add(s(X), Y)) =#> s#(add(X, Y)) 20] active#(add(s(X), Y)) =#> add#(X, Y) 21] active#(first(0, X)) =#> mark#(nil) 22] active#(first(s(X), cons(Y, Z))) =#> mark#(cons(Y, first(X, Z))) 23] active#(first(s(X), cons(Y, Z))) =#> cons#(Y, first(X, Z)) 24] active#(first(s(X), cons(Y, Z))) =#> first#(X, Z) 25] mark#(terms(X)) =#> active#(terms(mark(X))) 26] mark#(terms(X)) =#> terms#(mark(X)) 27] mark#(terms(X)) =#> mark#(X)
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